<PAGE>   1
 
   
    AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON AUGUST   , 1998
    
 
                                                      REGISTRATION NO. 333-53873
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                            ------------------------
   
                                AMENDMENT NO. 2
    
                                       TO
                                    FORM S-1
 
            REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933
                            ------------------------
   
                          BRIGHAM EXPLORATION COMPANY
    
   
           (Exact name of Co-Registrant as specified in its charter)
    
 
   
<TABLE>
<S>                                                  <C>
                      DELAWARE                                            75-2692967
          (State or other jurisdiction of                              (I.R.S. Employer
           incorporation or organization)                            Identification No.)
</TABLE>
    
 
   
<TABLE>
<S>                                 <C>                                 <C>
           File No. 333-                       File No. 333-                       File No. 333-
           BRIGHAM, INC.                  BRIGHAM HOLDINGS I, LLC            BRIGHAM HOLDINGS II, LLC
   (Exact name of Co-Registrant        (Exact name of Co-Registrant        (Exact name of Co-Registrant
   as specified in its charter)        as specified in its charter)        as specified in its charter)
              NEVADA                              NEVADA                              NEVADA
  (State or other jurisdiction of     (State or other jurisdiction of     (State or other jurisdiction of
  incorporation or organization)      incorporation or organization)      incorporation or organization)
            75-2354099                          75-2692967                          75-2354099
  (I.R.S. Employer Identification     (I.R.S. Employer Identification     (I.R.S. Employer Identification
               No.)                                No.)                                No.)
</TABLE>
    
 
   
                                 File No. 333-
    
   
                            BRIGHAM OIL & GAS, L.P.
    
   
                          (Exact name of Co-Registrant
    
   
                          as specified in its charter)
    
   
                                    DELAWARE
    
   
                        (State or other jurisdiction of
    
   
                         incorporation or organization)
    
   
                                   75-2429186
    
   
                      (I.R.S. Employer Identification No.)
    
 
   
                                      1311
    
   
            (Primary Standard Industrial Classification Code Number)
    
 
   
<TABLE>
<S>                                                  <C>
             6300 BRIDGE POINT PARKWAY                                  BEN M. BRIGHAM
               BUILDING 2, SUITE 500                              PRESIDENT, CHIEF EXECUTIVE
                AUSTIN, TEXAS 78730                                OFFICER AND CHAIRMAN OF
                   (512) 427-3300                                         THE BOARD
         (Address, including zip code, and                        6300 BRIDGE POINT PARKWAY
            telephone number, including                             BUILDING 2, SUITE 500
           area code, of Co-Registrants'                             AUSTIN, TEXAS 78730
            principal executive offices)                                (512) 427-3300
                                                                (Name, address, including zip
                                                                 code, and telephone number,
                                                                 including area code, of Co-
                                                               Registrants' agent for service)
</TABLE>
    
 
                          Copies of Communication to:
 
   
                                JOE DANNENMAIER
    
   
                            THOMPSON & KNIGHT, P.C.
    
   
                        1700 PACIFIC AVENUE, SUITE 3300
    
   
                              DALLAS, TEXAS 75201
    
                            ------------------------
          APPROXIMATE DATE OF COMMENCEMENT OF PROPOSED SALE TO THE PUBLIC:
As soon as practicable after the effective date of this Registration Statement.
 
     If any of the securities being registered on this Form are to be offered on
a delayed or continuous basis pursuant to Rule 415 under the Securities Act of
1933, check the following box.  [ ]
 
     If this Form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, please check the following box
and list the Securities Act registration statement number of the earlier
effective registration statement for the same offering.  [ ]
 
     If this Form is a post-effective amendment filed pursuant to Rule 462(c)
under the Securities Act, check the following box and list the Securities Act
registration statement number of the earlier effective registration statement
for the same offering.  [ ]
 
     If this Form is a post-effective amendment filed pursuant to Rule 462(d)
under the Securities Act, check the following box and list the Securities Act
registration number of the earlier effective registration statement for the same
offering.  [ ]
 
   
     If delivery of the Prospectus is expected to be made pursuant to Rule 434,
please check the following box.  [ ]
    
<PAGE>   2
 
   
                        CALCULATION OF REGISTRATION FEE
    
 
   
<TABLE>
<CAPTION>
--------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------
                                                                 PROPOSED MAXIMUM
                   TITLE OF EACH CLASS OF                       AGGREGATE OFFERING           AMOUNT OF
               SECURITIES TO BE REGISTERED(1)                      PRICE(2)(3)          REGISTRATION FEE(4)
--------------------------------------------------------------------------------------------------------------
<S>                                                          <C>                      <C>
Senior Subordinated Secured Notes due 2003..................      $50,000,000(5)              $14,750
--------------------------------------------------------------------------------------------------------------
Guaranty Agreements relating to Senior Subordinated Notes
  due 2003..................................................           (6)                      (6)
--------------------------------------------------------------------------------------------------------------
Warrants to Purchase Common Stock...........................           (7)                      (7)
--------------------------------------------------------------------------------------------------------------
Common Stock, par value $.01 per share......................       $10,000,000                 $2,950
--------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------
</TABLE>
    
 
---------------
 
   
(1) The issuer of the Notes, Warrants and Common Stock registered hereby is
    Brigham Exploration Company. The Guaranty Agreements registered hereby are
    made by Brigham, Inc., Brigham Holdings I, LLC., Brigham Holdings II, LLC.
    and Brigham Oil & Gas, L.P.
    
 
   
(2) In accordance with Rule 457(o) under the Securities Act of 1933, the number
    of securities being registered and the proposed maximum offering price per
    security are not included in this table.
    
 
   
(3) Estimated for purposes of calculating registration fee.
    
 
   
(4) $13,940 of this fee was paid with the initial filing of this Registration
    Statement.
    
 
   
(5) $10 million of this amount is for PIK interest.
    
 
   
(6) No additional consideration will be received for the Guaranty Agreements
    registered hereby.
    
 
   
(7) No additional consideration will be received for the Warrants.
    
 
   
     THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT SHALL
FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS REGISTRATION
STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH SECTION 8(a) OF
THE SECURITIES ACT OF 1933 OR UNTIL THE REGISTRATION STATEMENT SHALL BECOME
EFFECTIVE ON SUCH DATE AS THE SECURITIES AND EXCHANGE COMMISSION, ACTING
PURSUANT TO SAID SECTION 8(a), MAY DETERMINE.
    
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
<PAGE>   3
 
INFORMATION CONTAINED HEREIN IS SUBJECT TO COMPLETION OR AMENDMENT. A
REGISTRATION STATEMENT RELATING TO THESE SECURITIES HAS BEEN FILED WITH THE
SECURITIES AND EXCHANGE COMMISSION. THESE SECURITIES MAY NOT BE SOLD NOR MAY
OFFERS TO BUY BE ACCEPTED PRIOR TO THE TIME THE REGISTRATION STATEMENT BECOMES
EFFECTIVE. THIS PROSPECTUS SHALL NOT CONSTITUTE AN OFFER TO SELL OR THE
SOLICITATION OF AN OFFER TO BUY
NOR SHALL THERE BE ANY SALE OF THESE SECURITIES IN ANY STATE IN WHICH SUCH
OFFER, SOLICITATION OR SALE WOULD BE UNLAWFUL PRIOR TO REGISTRATION OR
QUALIFICATION UNDER THE SECURITIES LAWS OF ANY SUCH STATE.
 
   
                  SUBJECT TO COMPLETION, DATED AUGUST   , 1998
    
PROSPECTUS
   
                          BRIGHAM EXPLORATION COMPANY
    
   
             $40,000,000 SENIOR SUBORDINATED SECURED NOTES DUE 2003
    
   
             WARRANTS TO PURCHASE 1,000,000 SHARES OF COMMON STOCK
    
   
                                      SHARES OF COMMON STOCK
    
                         ------------------------------
 
   
    The Senior Subordinated Secured Notes due 2003 (the "Notes"), the warrants
(the "Warrants") to purchase 1,000,000 shares of Common Stock, par value $.01
per share (the "Common Stock") at an exercise price of $    per share and the
              shares (the "Shares") of Common Stock (the "Common Stock") offered
hereby (the "Offering") are being sold by Brigham Exploration Company, a
Delaware corporation ("Brigham" or the "Company"), to no more than three
institutional accredited investors.
    
 
   
    Interest on the Notes will be payable quarterly, beginning on November 15,
1998. Interest rates payable on the Notes shall vary depending upon whether
accrued interest is paid in cash or in kind ("PIK Interest"). Interest shall be
paid in cash at interest rates of     %,     % and     % per annum during years
one through three, year four and year five, respectively, of the term of the
Notes; provided, however, that if the payment of interest accrued on the Notes
in cash would cause a "Borrowing Base Deficiency" under the Company's revolving
credit facility or would cause the Company to be in violation of any covenant or
other restriction set forth in any Senior Loan Document (as defined) or any
agreement entered into by the Company or any subsidiary of the Company in
connection with the Notes, the Company may pay PIK Interest at interest rates of
    %,     % and     % per annum during years one through three, year four and
year five, respectively, of the term of the Notes.
    
 
   
    The Notes mature on                    , 2003, and all principal and accrued
but unpaid interest on the Notes is payable at maturity. The Company may
exercise its option to pay PIK Interest by delivering written notice thereof to
holders of the Notes on or before the quarterly interest payment date. The
Company may not pay PIK Interest for more than six quarters over the term of the
Notes. The Notes may be prepaid at any time in whole or in part, without premium
or penalty, provided that all partial prepayments must be pro rata to the
various holders of the Notes.
    
 
   
    The Notes will rank subordinate in right of payment to the Senior
Indebtedness (as defined) and senior to all other financings (other than any
allowed capital leases and purchase money financings). The guaranty agreements
of the Company's subsidiaries will be similarly subordinated.
    
 
   
    The Notes will be fully and unconditionally guaranteed on a joint and
several basis (the "Subsidiary Guaranty Agreements") by each of the Company's
current and future material subsidiaries and by any other current or future
subsidiaries which guarantee the Senior Indebtedness of the Company or its
subsidiaries, excluding Quest Resources L.L.C. and Venture Acquisitions L.P.
(which are not material) (collectively, the "Subsidiary Guarantors"). All of the
Subsidiary Guarantors are wholly-owned by the Company.
    
 
   
    The Notes shall be secured by a lien on all assets of the Company and the
Subsidiary Guarantors which are now or hereafter pledged or mortgaged to secure
the Senior Indebtedness (or to secure any guaranty of the Senior Indebtedness),
including (and whether or not securing the Senior Indebtedness), a pledge of the
stock or membership interests of Brigham, Inc., Brigham Holdings I, LLC, and
Brigham Holdings II, LLC. Such lien shall be subordinate to that of the Senior
Indebtedness. As of June 30, 1998, after giving pro forma effect to the
application of the net proceeds from the Offering, the Company would have had
Senior Indebtedness outstanding (excluding unused commitments and letters of
credit) of $20.5 million under its revolving credit facility and no senior
subordinated debt outstanding other than the Notes. See "Use of Proceeds."
    
 
   
    The Warrants will expire                    , 2005 and will entitle the
holders thereof to purchase an aggregate of 1,000,000 shares of Common Stock at
an exercise price equal of $    per share. The Common Stock is traded on the
Nasdaq Stock Market(SM) under the trading symbol "BEXP." On August 13, 1998, the
last reported sales price of the Common Stock on The Nasdaq Stock Market(SM) was
$8.50 per share. See "Price Range of Common Stock and Dividend Policy." The
holders of the Warrants and the Shares will have demand and "piggyback"
registration rights. See "Registration Rights Relating to the Warrants and
Shares."
    
                         ------------------------------
   
      ANY INVESTMENT IN THE SECURITIES OFFERED HEREIN INVOLVES A HIGH DEGREE OF
RISK. SEE "RISK FACTORS" BEGINNING ON PAGE 14.
    
                         ------------------------------
  THESE SECURITIES HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE SECURITIES AND
 EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION NOR HAS THE SECURITIES
   AND EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION PASSED UPON THE
ACCURACY OR ADEQUACY OF THIS PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A
                               CRIMINAL OFFENSE.
   
    
 
   
<TABLE>
<CAPTION>
-----------------------------------------------------------------------------------------------------------------------
-----------------------------------------------------------------------------------------------------------------------
                                                                       UNDERWRITING DISCOUNTS        PROCEEDS TO
                                                 PRICE TO PUBLIC          AND COMMISSIONS             COMPANY(1)
-----------------------------------------------------------------------------------------------------------------------
<S>                                          <C>                      <C>                      <C>
Per Note....................................            %                        --                       %
-----------------------------------------------------------------------------------------------------------------------
Per Warrant.................................            --                       --                       --
-----------------------------------------------------------------------------------------------------------------------
Per Share of Common Stock...................            $                        --                       $
-----------------------------------------------------------------------------------------------------------------------
Total.......................................            $                        --                       $
-----------------------------------------------------------------------------------------------------------------------
-----------------------------------------------------------------------------------------------------------------------
</TABLE>
    
 
---------------
 
   
(1) Before deducting expenses of the Offering payable by the Company estimated
    to be $        .
    
 
   
                 The date of this Prospectus is August   , 1998
    
<PAGE>   4
 
                               PROSPECTUS SUMMARY
 
   
     The following summary should be read in conjunction with, and is qualified
in its entirety by, the detailed information and the Financial Statements and
notes thereto included elsewhere in this Prospectus. All references in this
Prospectus to "Brigham" or the "Company" include Brigham Exploration Company,
its subsidiaries and its predecessors and their subsidiaries. Certain terms
relating to the oil and gas industry are defined in "Glossary of Certain Oil and
Gas Terms."
    
 
                                  THE COMPANY
 
   
     Brigham is an independent exploration and production company that applies
3-D seismic imaging and other advanced technologies to systematically explore
and develop onshore domestic natural gas and oil provinces. The Company focuses
its 3-D seismic activity in provinces where it believes 3-D technology may be
effectively applied and which Brigham believes offer relatively large potential
reserve volumes per well and per field, high potential production rates and
multiple producing objectives. The Company's exploration activities are
concentrated primarily in three core provinces: the Anadarko Basin of western
Oklahoma and the Texas Panhandle; the onshore Gulf Coast of Texas and Louisiana;
and West Texas. Brigham is accelerating its 3-D seismic and drilling activities
in the Anadarko Basin and the Gulf Coast and is selectively focusing its
activities in those geologic trends of West Texas where it has achieved its best
results historically.
    
 
     The Company pioneered the acquisition of large scale onshore 3-D seismic
surveys for exploration, obtaining extensive 3-D seismic data and experience in
capturing undiscovered natural gas and oil reserves. Through December 31, 1997,
Brigham had acquired 4,005 square miles (2.6 million acres) of 3-D seismic and
identified 1,170 potential drilling locations, of which the Company had drilled
370. The Company generates most of its exploratory projects and, therefore, has
the ability to retain a sizeable working interest to the extent that it decides
not to place interests with industry participants.
 
     From inception in 1990 through December 31, 1997, Brigham had drilled 324
exploratory and 46 development wells on its 3-D seismic generated prospects with
an aggregate 63% success rate and an average working interest of 24%. Utilizing
the capital it raised in its May 1997 initial public offering, the Company
increased the average working interest it retained in its wells during the
second half of 1997, retaining a 45% average working interest in the 36 wells
that it drilled. As of December 31, 1997, the Company had added approximately 93
Bcfe of net proved reserves (excluding revisions) to its reserve base,
approximately 72 net Bcfe of which were discovered by Brigham through its
systematic 3-D seismic exploration drilling activities. The Company's estimated
net proved reserves as of December 31, 1997 were 72.3 Bcfe having an aggregate
Present Value of Future Net Revenues of $69.2 million, compared to estimated net
proved reserves as of December 31, 1996 of 21.9 Bcfe having an aggregate Present
Value of Future Net Revenues of $44.5 million. The Company's net proved reserve
volumes at December 31, 1997 were 74% natural gas and 65% categorized as proved
developed reserves.
 
                               BUSINESS STRATEGY
 
     Brigham's business strategy is to achieve superior growth in shareholder
value through the application of its systematic exploration approach, which
emphasizes the integrated use of 3-D seismic imaging and other advanced
technologies to reduce drilling risks and finding costs. Since its inception in
1990, the Company has consistently achieved rapid growth in its acquisition of
3-D seismic data, identification of potential drilling locations, discovery of
proved reserves and production volumes.
 
     Brigham completed its initial public offering of common stock in May 1997,
raising approximately $24 million to fund the Company's accelerated 3-D seismic
acquisition and exploration drilling activities. Key elements of the Company's
growth strategy at its initial public offering and continuing today include: (i)
accelerating the rate at which it acquires 3-D seismic and identifies potential
drilling locations; (ii) increasing the working interests it retains in
exploration projects to capture a greater share of the reserves that the Company
discovers; (iii) identifying higher potential, higher impact prospects; and (iv)
accelerating the rate at which its 3-D seismic defined locations are drilled.
 
                                        3
<PAGE>   5
 
     During the second half of 1997, the Company employed the capital raised in
its initial public offering to attain significant growth in each of its core
strategic objectives:
 
          Accelerated 3-D Seismic Acquisition. During 1997, Brigham acquired
     approximately 1,250 square miles of 3-D seismic, which increased the
     Company's aggregate 3-D seismic inventory 45% to approximately 4,000 square
     miles as of December 31, 1997. The overall level of 3-D seismic acquisition
     in 1997 represents the most active year in the Company's history, and 85%
     of this increased 3-D seismic was acquired in its higher potential Anadarko
     Basin and Gulf Coast provinces.
 
          Increased Working Interest. In an effort to retain a greater portion
     of the value generated by its 3-D seismic exploration efforts, Brigham
     increased the average working interests it retained in its 1997 3-D seismic
     projects to 68% as compared with its average project working interest of
     24% in 1990 through 1996. As a result of the higher working interests and
     the accelerated acquisition of 3-D seismic, the Company acquired 845 net
     square miles of 3-D seismic in 1997 as compared with 780 cumulative net
     square miles acquired from 1990 through 1996.
 
          Higher Potential, Higher Impact Prospects. By focusing an increasing
     portion of its exploration activities in the more prolific Anadarko Basin,
     Brigham increased its average proved reserves discovered per net well
     drilled (including dry holes) to 1.2 Bcfe in 1997 from 0.7 Bcfe in 1996 and
     0.4 Bcfe in 1992 through 1995. In the Anadarko Basin alone, Brigham's
     average proved reserves discovered per net well drilled was 3.4 Bcfe in
     1997 compared with 1.8 Bcfe in 1996 and 2 Bcfe in 1994 through 1995.
     Contributing to these increases, the Company's Anadarko Basin drilling in
     1997 produced the two largest field discoveries in Brigham's history, which
     resulted in the discovery of approximately 52 Bcfe of gross proved reserves
     and provided the Company with several development drilling opportunities.
 
          Accelerated Drilling. Through its strategy of retaining higher working
     interests in its 3-D seismic projects and subsequent drilling, Brigham
     participated in the drilling of 28 net wells in 1997, a 75% increase from
     the approximate 16 net wells drilled by the Company in 1996. The Company
     achieved a 63% success rate on the 73 wells in its 1997 drilling program,
     consistent with Brigham's historical average success rate. A key factor
     contributing to its increased level of drilling activity was the Company's
     addition of personnel in engineering, land and administrative functions
     during 1997. These staff additions provided Brigham with the additional
     infrastructure required to increase its operating capabilities, enabling
     the Company to operate 37% of its gross wells and 64% of its net wells
     drilled in 1997.
 
     As a result of the combined effects of the Company's multi-pronged growth
strategy, Brigham generated net proved reserve additions of approximately 38
Bcfe through drilling in 1997, which represents approximately 175% of the
Company's year-end 1996 net proved reserves of approximately 22 Bcfe. In
addition to its drilling efforts in 1997, the Company acquired 21.5 Bcfe of net
proved reserves at an implied cost of $0.63 per proved Mcfe in its November 1997
purchase of certain properties in and adjacent to its West Bradley project area
in its Anadarko Basin province. Brigham believes this acquisition will enable it
to further build its inventory of potential drilling locations over the
historically prolific Carter Knox anticline in the Anadarko Basin through a 3-D
seismic shoot planned for 1998.
 
   
     Primarily through its exploration efforts, the Company increased its net
production volumes 52% to 3.1 Bcfe in 1997 from 2.1 Bcfe in 1996. As further
evidence of the Company's acceleration efforts subsequent to its May 1997
initial public offering, Brigham increased its average net daily production
volumes from 6.6 MMcfe in the second quarter 1997 to 21.2 MMcfe in the second
quarter 1998 representing a compounded growth rate of 34% per quarter.
    
 
   
     Based on the results that the Company has achieved from its growth strategy
since its initial public offering, Brigham intends with the proceeds from the
Offering to increase its exploration activities in 1998 to take advantage of
opportunities currently available to further accelerate the Company's growth.
The Company's current 1998 capital budget contemplates (i) an increase in
budgeted drilling expenditures in the Anadarko Basin and the Gulf Coast
provinces, (ii) a reduction in planned drilling activity in West Texas in part
due to recent declines in oil prices, (iii) an increase in planned 3-D seismic
acquisition activities in an effort to capture additional exploration prospects
for future drilling activities and (iv) potential sales of a
    
 
                                        4
<PAGE>   6
 
   
portion of the Company's interests in certain seismic projects. The Company
intends to continue to retain higher working interests in its 3-D seismic
projects in the Anadarko Basin and the onshore Gulf Coast. By increasing its
working interests retained in the majority of its current and planned seismic
projects, Brigham expects to further accelerate its growth not only by retaining
a greater portion of the reserves it discovers, but also by increasing its
ability to control the timing of the drilling of its exploration projects and
therefore helping to accelerate its drilling pace. The Company's current 1998
budget consists of 90 gross (45 net) wells, compared with the 73 gross (28 net)
wells drilled by the Company in 1997. This increase in anticipated 1998 drilling
is the result of an increase in planned drilling of higher working interest
wells in the Anadarko Basin and the Gulf Coast offset by a reduction in planned
drilling activity in West Texas.
    
 
                             COMPETITIVE ADVANTAGES
 
     Brigham believes that its knowledge base, personnel and technology provide
it with the following competitive advantages to capture undiscovered natural gas
and oil reserves.
 
          3-D Seismic Knowledge Base. From 1990 through 1997, the Company
     acquired 4,005 square miles of 3-D seismic and drilled 370 wells in over 20
     geologic trends in seven basins and seven states. With the resulting
     knowledge of the application of 3-D seismic to different geologic trends,
     the Company has refined its exploration techniques and identified
     exploration areas where it believes 3-D seismic can reduce risks and
     enhance returns on its investments.
 
   
          Technological Expertise. Brigham's 19 explorationists collectively
     have approximately 300 years of experience, including approximately 85
     years of experience using computer aided exploration ("CAEX") workstations,
     and have expertise in many geologic trends.
    
 
          Project Generation and Control. Brigham is not dependent on third
     parties for its project flow, having generated approximately 90% of its 3-D
     seismic exploration projects. With the resulting project control, the
     Company is able to manage the predrilling exploration phases and can
     determine the level of working interest it retains and the extent to which
     it manages drilling and post-drilling operations.
 
   
          Numerous Potential Drilling Locations. As of December 31, 1997, the
     Company had identified 1,170 3-D defined potential drilling locations in
     historically productive geologic trends, of which 370 had been drilled. The
     Company currently anticipates drilling 90 of these locations (45 net) in
     1998 at an aggregate net cost of approximately $40 million.
    
 
          Pioneering Innovations. In 1990 the Company pioneered the assemblage
     of large scale onshore 3-D seismic projects and the use of pre-seismic
     lease options for the systematic exploration of proven natural gas and oil
     provinces. Subsequent innovations include the Company's 3-D seismic
     acquisition and processing alliances and creative industry trade structures
     to financially leverage its drilling program.
 
                         PRIMARY EXPLORATION PROVINCES
 
   
     Brigham's exploration activities are concentrated primarily in three core
provinces: the Anadarko Basin of western Oklahoma and the Texas Panhandle; the
onshore Gulf Coast of Texas and Louisiana; and West Texas. Brigham is
accelerating 3-D seismic activity in the Anadarko Basin and the Gulf Coast and
will selectively continue such activity in those geologic trends of the West
Texas region where it has achieved its best results historically. Brigham is
focusing its 3-D seismic exploration efforts in provinces where it believes 3-D
seismic technology may be effectively applied and which the Company believes
offer relatively large potential reserve volumes per well and per field, high
potential production rates and multiple producing objectives.
    
 
     Although the Company is acquiring 3-D seismic within the provinces listed
below and has identified approximately 800 potential drilling locations yet to
be drilled in those provinces, there can be no assurance that any of the seismic
will be acquired or will generate additional drilling locations or that any
potential drilling locations will be drilled at all or within the expected time
frame. The final determination with respect to the drilling of any well,
including those currently budgeted, will depend on a number of factors,
including
 
                                        5
<PAGE>   7
 
(i) the results of exploration efforts and the review and analysis of the
seismic, (ii) the availability of sufficient capital resources by the Company
and other participants for drilling prospects, (iii) economic and industry
conditions at the time of drilling, including prevailing and anticipated prices
for natural gas and oil and the availability of drilling rigs and crews, (iv)
the financial resources and results of the Company and (v) the availability of
leases on reasonable terms and permitting for the potential drilling location.
There can be no assurance that the budgeted wells will, if drilled, encounter
reservoirs of commercial quantities of natural gas or oil.
 
   
<TABLE>
<CAPTION>
                                                                                             CURRENT 1998 CAPITAL BUDGET(1)
                                                                                      --------------------------------------------
                             3-D SEISMIC       3-D SEISMIC                UNDRILLED                             CAPITAL
                           DATA ACQUIRED/          DATA         GROSS     POTENTIAL                       EXPENDITURES ($MM)
                          INTERPRETED AS OF    BUDGETED TO      WELLS     DRILLING       WELLS       -----------------------------
                              12/31/97        BE ACQUIRED IN   DRILLED    LOCATIONS     BUDGETED       NET
                             (GROSS SQ.        1998 (GROSS     THROUGH      AS OF     ------------   SEISMIC     NET
PROVINCE                       MILES)           SQ. MILES)     12/31/97   12/31/97    GROSS   NET    & LAND    DRILLING   TOTAL(2)
--------                  -----------------   --------------   --------   ---------   -----   ----   -------   --------   --------
<S>                       <C>                 <C>              <C>        <C>         <C>     <C>    <C>       <C>        <C>
Anadarko Basin..........   1,515/1,195              660           55         364        55    28.8    $12.5     $26.5      $39.0
Gulf Coast..............     566/325                600           11         110        20     9.5     (0.5)     10.5       10.0
West Texas..............   1,649/1,600               40          287         302        14     6.5      1.5       2.8        4.3
Others(3)...............     275/275                 --           17          24         1     0.2       --       0.2        0.2
                             -----------          -----          ---         ---       ---    ----    -----     -----      -----
        Total...........   4,005/3,395            1,300          370         800        90    45.0    $13.5     $40.0      $53.5
                             ===========          =====          ===         ===       ===    ====    =====     =====      =====
</TABLE>
    
 
---------------
 
   
(1) Prepared as of August 10, 1998.
    
 
   
(2) Net 3-D seismic and land acquisition costs and drilling expenditures.
    
 
(3) Colorado, Kansas and Montana.
 
     Anadarko Basin. The Anadarko Basin is a prolific natural gas province that
the Company believes has been relatively under explored, particularly with
regard to deep, high potential objectives. The Anadarko Basin contains numerous
historically elusive stratigraphic targets, such as the Red Fork, Morrow and
Springer channel sands, and structural targets, such as the Hunton and Arbuckle
carbonates, which are well-suited to 3-D seismic imaging. In some cases, these
objectives have produced in excess of 30 Bcf of natural gas from a single well
at rates up to 30 MMcf of natural gas per day.
 
     The Company has assembled an extensive digital data base in this province,
including geologic studies, basin wide geologic tops, production data, well
data, geographic data and over 8,400 miles of 2-D seismic. Working with its team
of in-house geologists and supplemented by consulting geologists, the Company's
explorationists integrate this data with their extensive expertise and knowledge
base to generate 3-D projects in the Anadarko Basin.
 
   
     As of December 31, 1997, the Company had acquired or was acquiring 1,515
square miles (969,600 acres) in 30 projects in the Anadarko Basin. The Company
anticipates acquiring 660 square miles (422,400 acres) of additional 3-D seismic
in this province in 1998. As of December 31, 1997, Brigham had completed 44
wells in 55 attempts (80% success rate) in the Anadarko Basin and had found
cumulative proved reserves of 44 net Bcfe. In 1997, the Company completed 19
wells in 23 attempts in the Anadarko Basin with an average working interest of
39%, adding 31 net Bcfe of proved reserves. In addition, the Company acquired
21.5 net Bcfe of proved reserves in this region in November 1997. As of December
31, 1997, the Company had 364 3-D seismic delineated potential drilling
locations in the Anadarko Basin, of which the Company intends to drill 55 gross
(29 net) wells in 1998.
    
 
     Gulf Coast. The onshore Gulf Coast region of Texas and Louisiana is a high
potential, multi-pay province that lends itself to 3-D seismic exploration due
to its substantial structural and stratigraphic complexity. The Company has
assembled a digital data base including geographical, production, geophysical
and geological information that the Company evaluates on its CAEX workstations.
Working with consulting regional geologists, the Company's explorationists
integrate this data with their extensive expertise and knowledge base to
generate 3-D seismic projects in the Gulf Coast. Brigham's commitment to this
province is evidenced by the Company's staff additions, the opening of its
Houston office and the addition of ten new 3-D seismic projects in 1996 and
1997.
 
                                        6
<PAGE>   8
 
     The Company anticipates that its increased project assemblage and 3-D
seismic acquisition activity in the Gulf Coast will generate accelerated
drilling in this province in 1998 and 1999. The Company is currently assembling
projects in the Expanded Wilcox and Expanded Vicksburg trends in South Texas,
the Miocene trend in South Texas and South Louisiana, and the Lower and Middle
Frio trends of South Texas.
 
   
     As of December 31, 1997, the Company had acquired or was acquiring 566
square miles (362,400 acres) of 3-D seismic in seven projects in the onshore
Gulf Coast province. The Company anticipates acquiring 600 square miles (384,000
acres) of additional 3-D seismic in this province in 1998. As of December 31,
1997, Brigham had completed 8 wells in 11 attempts (73% success rate) in the
Gulf Coast and had found cumulative proved reserves of 3 net Bcfe. In 1997, the
Company completed seven wells in 10 attempts with an average working interest of
9% adding 3 net Bcfe of proved reserves. As of December 31, 1997, the Company
had 110 3-D seismic delineated potential drilling locations in the Gulf Coast
province, of which the Company intends to drill 20 gross (10 net) wells in 1998.
    
 
   
     West Texas. The Company's 3-D seismic drilling activity in the West Texas
region has been focused in the Horseshoe Atoll, the Midland Basin and the
Eastern Shelf of the Permian Basin and the Hardeman Basin. Recently the Company
initiated an exploration program in the Delaware Basin and it is selectively
focusing its West Texas activity in portions of geologic trends that the Company
believes offer greater potential for lower finding costs and higher returns,
including the Fusselman formation of the Midland Basin and the Ellenberger and
Devonian formations of the Delaware Basin.
    
 
   
     As of December 31, 1997, the Company had acquired or was acquiring 1,649
square miles (1,055,360 acres) in 74 projects in the West Texas region. The
Company anticipates acquiring 40 square miles (25,600 acres) of additional 3-D
seismic in this region in 1998. As of December 31, 1997, Brigham had completed
180 wells in 287 attempts (63% success rate) in the West Texas region and had
found cumulative proved reserves of 24 net Bcfe. In 1997, the Company completed
19 wells in 34 attempts with an average working interest of 45%, adding 4 net
Bcfe of proved reserves. As of December 31, 1997, the Company had 302 3-D
seismic delineated potential drilling locations in the West Texas region, of
which the Company intends to drill 14 gross (6 net) wells in 1998.
    
 
   
                                  THE OFFERING
    
 
   
ISSUER.....................  Brigham Exploration Company
    
 
   
USE OF PROCEEDS............  The net proceeds of the Offering will be used to
                             fund the Company's accelerated exploration and
                             development activities, and in the interim for
                             repayment of a portion of outstanding indebtedness.
                             See "Use of Proceeds."
    
 
   
                                   The Notes
    
 
   
Securities Offered.........  $40 million aggregate principal amount of Senior
                             Subordinated Secured Notes due 2003.
    
 
   
Maturity Date..............                 , 2003.
    
 
   
Interest Payment Dates.....  November 15, February 15, May 15 and August 15 of
                             each year, commencing November 15, 1998.
    
 
   
Interest Rate..............  Interest rates payable on the Notes shall vary
                             depending upon whether a accrued interest is paid
                             in cash or in kind ("PIK Interest"). Interest shall
                             be paid in cash at interest rates of      %,      %
                             and      % per annum during years one through
                             three, year four and year five, respectively, of
                             the term of the Notes; provided, however, that if
                             the payment of interest accrued on the Notes in
                             cash would cause a "Borrowing Base Deficiency"
                             under the Company's revolving credit facility or
                             would cause
    
 
                                        7
<PAGE>   9
 
   
                             the Company to be in violation of any covenant or
                             other restriction set forth in any Senior Loan
                             Document or any agreement entered into by the
                             Company or subsidiary of the Company in connection
                             with the Notes, the Company may pay PIK Interest at
                             interest rates of   %,   % and   % per annum during
                             years one through three, year four and year five,
                             respectively, of the term of the Notes.
    
 
   
Ranking....................  The Notes will rank subordinate in right of payment
                             to the Senior Indebtedness and senior to all other
                             financings (other than any allowed capital leases
                             and purchase money financings). The Subsidiary
                             Guaranty Agreements will be similarly subordinated.
                             As of June 30, 1998, on a pro forma basis, after
                             giving effect to the application of the net
                             proceeds from the Offering, the Company would have
                             had $20.5 million Senior Indebtedness outstanding,
                             and there would be no senior subordinated debt
                             outstanding other than the Notes. In addition, the
                             Notes may be structurally subordinated to all
                             existing and future liabilities of the Company's
                             subsidiaries. See "Capitalization," "Description of
                             the Notes -- Ranking and Subordination,"
                             "Description of Other Indebtedness" and
                             "Subordination Agreement."
    
 
   
Subsidiary Guaranty
Agreements.................  The Notes will be fully and unconditionally
                             guaranteed, jointly and severally, by each of the
                             Subsidiary Guarantors. The Subsidiary Guaranty
                             Agreements will be secured by substantially all of
                             the assets of the Subsidiary Guarantors. Financial
                             statements for the Subsidiary Guarantors are not
                             presented because management has determined that
                             they would not be material to investors.
    
 
   
Optional Prepayment........  The Notes may be prepaid at any time, in whole or
                             in part, without premium or penalty, provided that
                             all partial prepayments must be pro rata to the
                             various holders of the Notes.
    
 
   
Change of Control..........  A Change of Control would constitute an Event of
                             Default (as defined). If any Event of Default
                             occurs, the holders of the Notes may direct the
                             Trustee (as defined) to declare the principal of
                             and the accrued and unpaid interest on such Notes
                             to be due and payable immediately. However, such
                             repayment would be subject to certain subordination
                             provisions in the Indenture (as defined).
    
 
   
Certain Covenants..........  The Notes will be issued pursuant to an indenture
                             (the "Indenture") containing certain covenants
                             that, among other things, limit the ability of the
                             Company and its Subsidiaries (as defined) to incur
                             additional indebtedness, pay dividends, make
                             distributions, enter into certain sale and
                             leaseback transactions, enter into certain
                             transactions with affiliates, dispose of certain
                             assets, incur liens, and engage in mergers and
                             consolidations. See "Description of the
                             Notes -- Certain Covenants."
    
 
   
Absence of a Public Market
for the Notes..............  The Notes are new securities and may only be traded
                             in compliance with applicable securities laws.
                             There can be no assurance as to the development or
                             liquidity of any market for the Notes. The Company
                             does not intend to apply for a listing of the Notes
                             on any securities exchange or on any automated
                             dealer quotation system.
    
 
                                        8
<PAGE>   10
 
   
                                  The Warrants
    
 
   
Securities Offered.........  Warrants which, when exercised, will entitle the
                             holders thereof to acquire an aggregate of
                             1,000,000 shares of Common Stock (the "Warrant
                             Shares").
    
 
   
Expiration Date............              , 2005.
    
 
   
Exercise...................  Each Warrant will entitle the holder to acquire at
                             any time prior to                  , 2005, one
                             share of Common Stock at a price equal to $     per
                             share, subject to adjustment from time to time upon
                             the occurrence of certain changes in Common Stock,
                             certain Common Stock distributions, certain
                             issuances of options or convertible securities,
                             certain dividends and distributions and certain
                             other increases in the number of shares of Common
                             Stock.
    
 
   
Rights as Shareholders.....  Holders of Warrants will not, by virtue of being
                             such holders, have any rights as stockholders of
                             the Company.
    
 
   
Registration Rights........  Pursuant to the New Registration Rights Agreement
                             (as defined), holders of the Shares, the Warrants,
                             the Warrant Shares and any other securities issued
                             upon the exercise of the Warrants (collectively,
                             the "Registrable Securities") will have demand
                             registration rights for two registrations, provided
                             that a request, which must be made by holders of
                             Registrable Securities collectively owning at least
                             25% of the Registrable Securities (or holding at
                             least a majority of the Registrable Securities for
                             a shelf registration statement if the Company is
                             eligible to use Form S-3), will be "counted"
                             towards the two registrations only when (i) all the
                             Registrable Securities requested to be included in
                             the registration statement have been included, (ii)
                             the corresponding registration statement has become
                             effective and (iii) the public offering has been
                             consummated and the Registrable Securities have
                             been sold on the terms and conditions provided
                             therein, provided that in the event of a shelf
                             registration statement (if the Company is then
                             eligible to file on Form S-3) the Company shall
                             keep such registration statement effective for two
                             years. The Company will agree in the New
                             Registration Rights Agreement to use its best
                             efforts to cause the registration statement to
                             become and remain effective for the period of the
                             distribution in order for it to be "counted" as
                             described above. Subject to other provisions
                             contained in the New Registration Rights Agreement,
                             the holders of the Registrable Securities will have
                             "piggyback" registration rights. Exercise of the
                             right to convert the Warrants to Warrant Shares
                             shall, at the election of the holder of the
                             Warrants, be contingent upon the registration of
                             the Warrant Shares in accordance with the New
                             Registration Rights Agreement and should such
                             registration not be completed such holder shall
                             have the right to rescind its election to convert
                             the Warrants. See "Registration Rights Relating to
                             the Shares and the Warrants."
    
 
   
Transfer Restrictions......  The Warrant Shares have not been registered under
                             the Securities Act and may not be offered or sold,
                             except pursuant to an exemption from, or in a
                             transaction not subject to, the registration
                             requirements of the Securities Act.
    
 
                                        9
<PAGE>   11
 
   
                                The Common Stock
    
 
   
Common Stock Offered by the
  Company..................                 shares
    
 
   
Common Stock to be
  Outstanding after the
  Offering.................                 shares(1)
    
 
   
The Nasdaq Stock Market(SM)
  Symbol...................  "BEXP"
    
 
   
Registration Rights........  The holders of the Shares shall have registration
                             rights with respect to the Shares set forth above
                             in the summary of Registration Rights relating to
                             the Warrants.
    
---------------
 
   
(1) Does not include (a) 935,987 shares of Common Stock issuable, subject to
    vesting, upon exercise of outstanding stock options with an average exercise
    price of $7.61 per share or (b) 1,000,000 shares of Common Stock issuable
    upon exercise of the Warrants with an exercise price of $     per share. See
    "Management -- Executive Director Compensation," "-- Executive
    Compensation," "Capitalization" and "Description of Warrants."
    
 
                                  RISK FACTORS
 
   
     Any investment in the Notes, Warrants or Shares involves a high degree of
risk. For a discussion of certain risks that a potential investor should
carefully evaluate prior to making an investment in the Notes, Warrants or
Shares, see "Risk Factors."
    
 
                                       10
<PAGE>   12
 
                             SUMMARY FINANCIAL DATA
                    (IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)
 
   
     The following table sets forth selected financial data of the Company. The
data for the three years ended December 31, 1997 has been derived from the
consolidated financial statements appearing elsewhere in this Prospectus. The
data for the two years ended December 31, 1994 has been derived from
consolidated financial statements not appearing in this Prospectus. The
consolidated financial data at June 30, 1998 and for the six months ended June
30, 1998 and June 30, 1997 have been derived from the condensed consolidated
financial statements of the Company which, in the opinion of management, include
all adjustments, consisting only of normal adjustments, necessary for a fair
presentation of the results for the periods. The results for the six months
ended June 30, 1998 are not necessarily indicative of the results to be expected
for the full year. The information should be read in conjunction with
"Management's Discussion and Analysis of Financial Condition and Results of
Operations" and the financial statements and notes thereto included elsewhere in
this Prospectus.
    
 
   
<TABLE>
<CAPTION>
                                                                                                          SIX MONTHS
                                                                                                             ENDED
                                                             YEAR ENDED DECEMBER 31,                       JUNE 30,
                                                --------------------------------------------------    -------------------
                                                 1993       1994      1995       1996       1997       1997        1998
                                                -------    -------   -------   --------   --------    -------    --------
<S>                                             <C>        <C>       <C>       <C>        <C>         <C>        <C>
STATEMENT OF OPERATIONS DATA:
  Revenues:
    Natural gas and oil sales.................  $   937    $ 2,565   $ 3,578   $  6,141   $  9,184    $ 3,854    $  7,130
    Workstation revenue.......................      467        815       635        627        637        324         247
                                                -------    -------   -------   --------   --------    -------    --------
        Total revenues........................    1,404      3,380     4,213      6,768      9,821      4,178       7,377
  Costs and expenses:
    Lease operating...........................      111        491       761        726      1,151        470         978
    Production taxes..........................       47        126       165        362        549        219         450
    General and administrative................    1,433      1,785     1,897      2,199      3,570      1,455       2,293
    Depletion of natural gas and oil
      properties..............................    4,371(1)   1,104     1,626      2,323      2,732      1,395       2,784
    Depreciation and amortization.............      406        561       533        487        582        287         365
                                                -------    -------   -------   --------   --------    -------    --------
        Total costs and expenses..............    6,368      4,067     4,982      6,097      8,584      3,826       6,870
                                                -------    -------   -------   --------   --------    -------    --------
  Operating income (loss).....................   (4,964)      (687)     (769)       671      1,237        352         507
  Other income (expense):
    Interest income...........................        6         56       128         52        145         81          77
    Interest expense..........................     (105)      (668)     (936)    (1,173)    (1,190)      (546)     (2,432)
                                                -------    -------   -------   --------   --------    -------    --------
        Total other income (expense)..........      (99)      (612)     (808)    (1,121)    (1,045)      (465)     (2,355)
                                                -------    -------   -------   --------   --------    -------    --------
  Net income (loss) before income taxes.......   (5,063)    (1,299)   (1,577)      (450)       192       (113)     (1,848)
  Income tax (expense) benefit, net...........       --         --        --         --     (1,228)(2)  (4,813)(2)      621
                                                -------    -------   -------   --------   --------    -------    --------
        Net loss..............................  $(5,063)   $(1,299)  $(1,577)  $   (450)  $ (1,036)   $(4,926)   $ (1,227)
                                                =======    =======   =======   ========   ========    =======    ========
  Net loss per share -- basic/diluted.........  $ (0.57)   $ (0.15)  $ (0.18)  $  (0.05)  $  (0.09)   $ (0.50)   $  (0.10)
  Weighted average shares outstanding --
    basic/diluted.............................    8,929      8,929     8,929      8,929     11,081      9,890      12,254
STATEMENT OF CASH FLOWS DATA:
  Net cash provided by (used in) operating
    activities................................  $  (730)   $   626   $ 1,383   $  3,710   $  9,806    $  (195)   $ (1,692)
  Net cash used in investing activities.......   (6,983)    (5,463)   (8,005)   (11,796)   (57,300)   (12,105)    (30,884)
  Net cash provided by financing activities...    7,839      4,634     7,724      7,731     47,748     15,842      33,981
OTHER FINANCIAL DATA:
  Capital expenditures........................  $ 6,632    $ 5,445   $ 7,935   $ 13,612   $ 57,170    $11,796    $ 30,044
  EBITDA(3)...................................     (187)       978     1,390      3,481      4,551      2,034       3,656
  Operating cash flow(4)......................     (286)       366       582      2,360      3,506      1,569       1,567
  Ratio of earnings to fixed charges(6).......       --         --        --         --        1.1x        --          --
PRO FORMA FINANCIAL DATA(7):
  Ratio of earnings to fixed charges(6).......                                                  --                     --
  Interest expense(7).........................                                               2,325                  3,252
</TABLE>
    
 
   
<TABLE>
<CAPTION>
                                                                 AS OF JUNE 30, 1998
                                                              -------------------------
                                                               ACTUAL    AS ADJUSTED(5)
                                                              --------   --------------
<S>                                                           <C>        <C>
BALANCE SHEET DATA:
  Cash and cash equivalents.................................  $  3,106      $  3,106
  Natural gas and oil properties, at cost, net..............   114,454       114,454
  Total assets..............................................   129,699       131,579
  Notes payable.............................................    68,000        20,450
  Stockholders' equity......................................    42,334        56,264
</TABLE>
    
 
---------------
 
(1) Includes a capitalized ceiling impairment charge of $3.3 million in 1993.
 
                                       11
<PAGE>   13
 
(2) In conjunction with the Exchange, the Company recorded a deferred income tax
    liability of $5 million to recognize the temporary differences between the
    financial statement and tax bases of the assets and liabilities of the
    Partnership at February 27, 1997, the date of the Exchange. During the
    fourth quarter of 1997, the Company elected to record a step-up in basis of
    its assets for tax purposes as a result of the Exchange. Related to this
    election, the Company recorded a $3.8 million deferred income tax benefit,
    resulting in a net $1.2 million ($.10 per share) non-cash deferred income
    tax charge for the year ended December 31, 1997. See Note 2 of Notes to the
    December 31, 1997 Consolidated Financial Statements. See "The Company."
 
(3) EBITDA represents net income (loss) plus income taxes, net interest expense
    and depreciation, depletion and amortization expense. EBITDA should not be
    considered in isolation or as a substitute for net income, cash flows from
    operating activities or any other measure of financial performance prepared
    in accordance with generally accepted accounting principles or as a measure
    of a company's profitability or liquidity.
 
(4) Operating cash flow represents net income (loss) plus depreciation,
    depletion and amortization ("DD&A") expenses, deferred income taxes and
    other non-cash items. Operating cash flow should not be considered in
    isolation or as a substitute for net income, cash flows from operating
    activities or any other measure of financial performance prepared in
    accordance with generally accepted accounting principles or as a measure of
    a company's profitability or liquidity.
 
   
(5) As adjusted to give effect to the Offering and the application of the
    estimated $47.6 million net proceeds therefrom to the Company, assuming
    issuance of 1,052,632 Shares at a price of $9.50 per share. See "Use of
    Proceeds" and "Capitalization."
    
 
   
(6) For purposes of calculating the ratio of earnings to fixed charges, earnings
    are defined as income (loss) of the Company from continuing operations
    before income taxes and fixed charges. Fixed charges consist of interest
    expense, including amortization of loan fees, and the portion of rental
    expense pursuant to operating leases deemed to be representative of the
    interest component. Earnings were insufficient to cover fixed charges by
    $5.1 million, $1.3 million, $1.6 million and $450,000 for the years ended
    December 31, 1993, 1994, 1995 and 1996, respectively, and $113,000 and $1.9
    million for the six months ended June 30, 1997 and 1998, respectively. Pro
    forma earnings were insufficient to cover pro forma fixed charges by
    $943,000 for the year ended December 31, 1997 and $2.7 million for the six
    months ended June 30, 1998.
    
 
   
(7) The pro forma financial data have been prepared on the basis of the
    following assumptions: (i) the Offering was consummated at the beginning of
    the respective periods, (ii) the average debt outstanding during the year
    ended December 31, 1997 of $12 million was refinanced with proceeds from the
    Notes, (iii) debt outstanding during the first six months of 1998 was
    partially repaid with proceeds from the issuance of $10 million of Shares
    and was partially refinanced with proceeds from the $40 million of Notes and
    (iv) the Notes bear an assumed effective interest rate of 15.7%.
    
 
                                       12
<PAGE>   14
 
                       SUMMARY RESERVE AND OPERATING DATA
                  (Dollars in thousands, except per Mcfe data)
 
   
<TABLE>
<CAPTION>
                                                                                         SIX MONTHS
                                             YEAR ENDED DECEMBER 31,                   ENDED JUNE 30,
                                --------------------------------------------------    ----------------
                                 1993      1994       1995      1996(1)     1997       1997      1998
                                ------    -------    -------    -------    -------    ------    ------
<S>                             <C>       <C>        <C>        <C>        <C>        <C>       <C>
3-D SEISMIC ACQUIRED:
  Gross square miles..........     908        423        311        655      1,243       645       610
  Net square miles............     272        114         90        241        845       353       459
  Average project working
    interest..................      30%        27%        29%        37%        68%       55%       75%
WELLS DRILLED:
  Gross wells drilled.........      52         73         78         67         73        37        33
  Net wells drilled...........     9.2       16.8       18.5       15.9       28.0      11.8      15.9
  Average drilling working
    interest..................      18%        23%        24%        24%        38%       32%       48%
ESTIMATED PROVED RESERVES (AT
  YEAR END)(2):
  Natural gas (MMcf)..........     227      3,579      4,257     10,257     53,230
  Oil (MBbls).................     336      1,022      1,672      1,940      3,181
  Natural gas equivalent
    (MMcfe)...................   2,243      9,711     14,289     21,897     72,316
  Present Value of Future Net
    Revenues..................  $3,158    $10,240    $18,222    $44,506    $69,249
  Percent natural gas(3)......      10%        37%        30%        47%        74%
  Percent proved
    developed(3)..............     100%        76%        80%        67%        65%
NET PROVED RESERVE
  ADDITIONS(4):
  All sources (MMcfe).........   1,987      8,524      8,884     13,996     59,311
  Excluding acquisitions
    (MMcfe)...................   1,987      8,524      8,884     13,718     38,129
RESERVE REPLACEMENT RATIO(5):
  All sources.................     553%       851%       667%       679%     1,897%
  Excluding acquisitions......     553%       851%       667%       666%     1,220%
NET PRODUCTION VOLUMES:
  Natural gas (MMcf)..........      59        165        272        698      1,382       457     1,947
  Oil (MBbls).................      50        140        177        227        291       127       232
  Natural gas equivalent
    (MMcfe)...................     359      1,002      1,332      2,060      3,126     1,222     3,338
  Percent natural gas.........      16%        16%        20%        34%        44%       37%       58%
PER MCFE DATA:
  Natural gas and oil sales...  $ 2.61    $  2.56    $  2.69    $  2.98    $  2.94    $ 3.16    $ 2.14
  Workstation revenue.........    1.30        .81        .48        .30        .20       .27       .07
  Lease operating expenses....    (.31)      (.49)      (.57)      (.35)      (.37)     (.38)     (.29)
  Production taxes............    (.13)      (.13)      (.12)      (.18)      (.18)     (.18)     (.13)
  General and administrative
    expenses..................   (3.99)     (1.78)     (1.42)     (1.07)     (1.14)    (1.19)     (.69)
                                ------    -------    -------    -------    -------    ------    ------
    Operating margin..........  $ (.52)   $   .97    $  1.06    $  1.68    $  1.45    $ 1.68    $ 1.10
                                ======    =======    =======    =======    =======    ======    ======
</TABLE>
    
 
---------------
 
(1) Net of a sale by the Company in January 1996 of its interest in certain
    properties that accounted for 299 MMcf of natural gas and 272 MBbls of oil
    (1,931 MMcfe of proved reserves) as of December 31, 1995.
 
(2) The estimates of reserve and present value data have been prepared in
    accordance with the SEC's guidelines by Cawley, Gillespie & Associates,
    Inc., the Company's independent petroleum consultants ("Cawley Gillespie").
    Cawley Gillespie's letter summarizing its December 31, 1997 reserve report
    is attached hereto as Appendix A to this Prospectus.
 
(3) Based on volumes.
 
(4) Excludes revisions of previous estimates.
 
(5) Net proved reserve additions divided by the Company's net production volumes
    for the period.
 
                                       13
<PAGE>   15
 
                DISCLOSURE REGARDING FORWARD-LOOKING STATEMENTS
 
     This Prospectus includes statements that are "forward-looking statements"
within the meaning of Section 27A of the Securities Act of 1933 (the "Securities
Act") and Section 21E of the Securities Exchange Act of 1934, including
statements regarding estimated future net revenues from natural gas and oil
reserves and the present value thereof, planned capital expenditures (including
the amount and nature thereof), increases in natural gas and oil production, the
number of wells the Company anticipates drilling through 1998 and the Company's
financial position, business strategy and other plans and objectives for future
operations. Although the Company believes that the expectations reflected in
these forward-looking statements are reasonable, there can be no assurance that
the actual results or developments anticipated by the Company will be realized
or, even if substantially realized, that they will have the expected effects on
its business or operations. Among the factors that could cause actual results to
differ materially from the Company's expectations are general economic
conditions, inherent uncertainties in interpreting engineering data, operating
hazards, delays or cancellations of drilling operations for a variety of
reasons, competition, fluctuations in natural gas and oil prices, the ability of
the Company to successfully integrate the business and operations of acquired
companies, government regulations and other factors disclosed under "Risk
Factors" and elsewhere in this Prospectus. All subsequent oral and written
forward looking statements attributable to the Company or persons acting on its
behalf are expressly qualified in their entirety by these factors. The Company
assumes no obligation to update any of these statements.
 
                                  RISK FACTORS
 
   
     Any investment in the Notes, Warrants or Shares involves a high degree of
risk. Prospective purchasers of the Notes, Warrants or Shares should carefully
consider the risk factors set forth below, as well as the other information
contained in this Prospectus.
    
 
   
EFFECTS OF LEVERAGE
    
 
   
     As of June 30, 1998, after giving pro forma effect to the application of
the estimated net proceeds from the Offering, the Company would have long-term
debt outstanding of $20.5 million. The Indenture will limit the amounts of
additional debt borrowings, including borrowings under the Credit Facility or
other Senior Indebtedness. However, the Indenture will permit the Company to
borrow under the Credit Facility up to the lesser of $75 million or the
borrowing base under the Credit Facility ($65 million upon completion of the
Offering), which, on a pro forma basis for the Offering as of June 30, 1998,
would provide the Company with the ability to borrow up to $44.5 million of
additional indebtedness under its Credit Facility. In addition, the Indenture
will allow the Company to borrow up to $25 million of future subordinated
indebtedness that is pari passu in right of payment with the Notes if the
holders of the Notes have been given a first look and right to make a proposal
for such subordinated indebtedness. See "Use of Proceeds" and "Capitalization."
    
 
   
     The Company's level of indebtedness will have several important effects on
its operations, including (i) a substantial portion of the Company's cash flow
from operations will be dedicated to the payment of interest on its indebtedness
and will not be available for other purposes; (ii) the covenants contained in
the Indenture limit its ability to borrow additional funds or to dispose of
assets and may affect the Company's flexibility in planning for, and reacting
to, changes in business conditions and (iii) the Company's ability to obtain
additional financing in the future for working capital, capital expenditures,
acquisitions, general corporate purposes or other purposes may be impaired.
Moreover, future exploration, development or acquisition activities may require
the Company to alter its capitalization significantly. These changes in
capitalization may significantly alter the leverage of the Company. The
Company's ability to meet its debt service obligations and to reduce its total
indebtedness will be dependent upon the Company's future performance, which will
be subject to general economic conditions and to financial, business and other
factors affecting the operations of the Company, many of which are beyond its
control. There can be no assurance that the Company's future performance will
not be adversely affected by such economic conditions and financial, business
and other factors. See "Management's Discussion and Analysis of Financial
Condition and Results of Operations -- Liquidity and Capital Resources."
    
 
                                       14
<PAGE>   16
 
   
SUBORDINATION OF NOTES; STRUCTURAL SUBORDINATION; HOLDING COMPANY STRUCTURE
    
 
   
     The Indenture governing the Notes will limit, but will not prohibit, the
incurrence by the Company of additional indebtedness that is senior in right of
payment to the Notes. In the event of bankruptcy, liquidation, reorganization or
other winding up of the Company, the assets of the Company will be available to
pay the Company's obligations on the Notes only after all Senior Indebtedness
has been paid in full, and there may not be sufficient assets remaining to pay
amounts due on the Notes. In addition, under certain circumstances, no payments
may be made with respect to principal of, premium, if any, or interest on the
Notes if a default exists with respect to any Senior Indebtedness. See
"Description of the Notes -- Ranking and Subordination."
    
 
   
     The Company conducts all of its operations through subsidiaries.
Accordingly, the Company relies on dividends and cash advances from its
subsidiaries to provide funds necessary to meet its obligations, including the
payment of principal and interest on the Notes. The ability of any such
subsidiary to pay dividends or make cash advances is subject to applicable laws
and contractual restrictions, including restrictions under credit agreements
between such subsidiary and third party lenders, as well as the financial
condition and operating requirements of such subsidiary. As of June 30, 1998,
after giving pro forma effect to the application of the estimated net proceeds
from the Offering, the Company's subsidiaries would have had total liabilities
of approximately $39.8 million. In addition, the Notes will be effectively
subordinated to any indebtedness and liabilities (including trade payables) of
the Company's present and future subsidiaries.
    
 
   
     The Indenture imposes limits on the ability of the Company and its
Subsidiaries (as defined) to incur additional indebtedness and liens and to
enter into agreements that would restrict the ability of such future Restricted
Subsidiaries to make distributions, loans or other payments to the Company.
These limitations are subject to various qualifications. For additional details
of these provisions and the applicable qualifications, see "Description of the
Notes -- Ranking and Subordination" and "-- Certain Covenants."
    
 
   
FRAUDULENT CONVEYANCE CONSIDERATIONS RELATING TO SUBSIDIARY GUARANTY AGREEMENTS
    
 
   
     Various fraudulent conveyance laws have been enacted for the protection of
creditors and may be utilized by a court of competent jurisdiction to
subordinate or avoid any Subsidiary Guaranty Agreement issued by a Subsidiary
Guarantor. It is also possible that under certain circumstances a court could
hold that the direct obligations of a Subsidiary Guarantor could be superior to
the obligations under the Subsidiary Guaranty Agreement.
    
 
   
     To the extent that a court were to find that at the time a Subsidiary
Guarantor entered into a Subsidiary Guaranty Agreement either (x) the Subsidiary
Guaranty Agreement was incurred by a Subsidiary Guarantor with the intent to
hinder, delay or defraud any present or future creditor or that a Subsidiary
Guarantor contemplated insolvency with a design to favor one or more creditors
to the exclusion in whole or in part of others or (y) the Subsidiary Guarantor
did not receive fair consideration or reasonably equivalent value for issuing
the Subsidiary Guaranty Agreement and, at the time it issued the Subsidiary
Guaranty Agreement, the Subsidiary Guarantor (i) was insolvent or rendered
insolvent by reason of the issuance of the Subsidiary Guaranty Agreement; (ii)
was engaged or about to engage in a business or transaction for which the
remaining assets of the Subsidiary Guarantor constituted unreasonably small
capital; or (iii) intended to incur, or believed that it would incur, debts
beyond its ability to pay such debts as they matured, the court could avoid or
subordinate the Subsidiary Guaranty Agreement in favor of the Subsidiary
Guarantor's other credits. Among other things, a legal challenge of a Subsidiary
Guaranty Agreement issued by a Subsidiary Guarantor on fraudulent conveyance
grounds may focus on the benefits, if any, realized by the Subsidiary Guarantor
as a result of the issuance by the Company of the Notes. To the extent a
Subsidiary Guaranty Agreement is avoided as a fraudulent conveyance or held
unenforceable for any other reason, the holders of the Notes would cease to have
any claim in respect of such Subsidiary Guarantor and would be creditors solely
of the Company.
    
 
   
     The measure of insolvency for purposes of determining whether a transfer is
avoidable as a fraudulent transfer varies depending upon the law of the
jurisdiction that is being applied. Generally, however, a debtor would be
considered insolvent if the sum of all its debts, including contingent
liabilities, was greater than the value of all its assets at a fair valuation or
if the present fair saleable value of the debtor's assets was less than
    
 
                                       15
<PAGE>   17
 
   
the amount required to repay its probable liability on its debts, including
contingent liabilities, as they become absolute and mature. To the extent that
proceeds from the Offering are used to refinance the indebtedness of the
Company, a court might find that the Company did not receive fair consideration
or reasonably equivalent value for the incurrence of the indebtedness
represented by the Notes.
    
 
   
     To the extent that a Subsidiary Guaranty Agreement of any Subsidiary
Guarantor is avoided as a fraudulent conveyance or found unenforceable for any
other reason, holders of the Notes would cease to have any claim in respect of
such Subsidiary Guarantor. In such event, the claims of the holders of the Notes
against such Subsidiary Guarantor would be subject to the prior payment of all
liabilities and preferred stock claims of such Subsidiary Guarantor. There can
be no assurance that, after providing for all prior claims and preferred stock
interests, if any, there would be sufficient assets to satisfy the claims of the
holders of the Notes relating to any voided portion of the Subsidiary Guaranty
Agreement of such Subsidiary Guarantor.
    
 
   
ABSENCE OF PUBLIC MARKET FOR THE NOTES AND WARRANTS; RESTRICTIONS ON RESALE FOR
THE WARRANT SHARES
    
 
   
     There is no existing market for the Notes or Warrants and there can be no
assurance as to the liquidity of any markets that may develop for the Notes or
Warrants, the ability of holders of the Notes or Warrants to sell their Notes or
Warrants, or the price at which holders would be able to sell their Notes or
Warrants. The Notes and Warrants may only be traded pursuant to an exemption
from, or in a transaction not subject to, the registration requirements of the
Securities Act and applicable state securities laws. The Company does not intend
to apply for a listing of the Notes or Warrants on any securities exchange or on
any automated dealer quotation system. Any trading prices of the Notes and
Warrants will depend on many factors, including, among other things, prevailing
interest rates, the Company's operating results and the market for similar
securities.
    
 
   
     Historically, the market for noninvestment grade debt has been subject to
disruptions that have caused substantial volatility in the prices of securities
similar to the Notes. There can be no assurance that the market, if any, for the
Notes will not be subject to similar disruptions. Any such disruptions may have
an adverse effect on the holders of the Notes.
    
 
   
     The Warrant Shares have not been registered under the Securities Act or any
state securities laws and, unless so registered, may not be offered or sold
except pursuant to an exemption from, or in a transaction not subject to, the
registration requirements of the Securities Act and applicable state securities
laws. Pursuant to the New Registration Rights Agreement, holders of the Warrants
and Warrant Shares have certain registration rights. Prior to the effectiveness
of a registration statement registering resales of the Warrant Shares, the
ability of the holders to liquidate an investment in the Warrants and Warrant
Shares will be limited.
    
 
   
     The issuance of Warrant Shares by the Company upon exercise of Warrants by
holders who purchase Warrants directly from the Company will not be covered by a
shelf registration statement registering resales of the Warrant Shares.
Accordingly, the exercise of Warrants by such holders much be made pursuant to a
transaction exempt from registration under the Securities Act.
    
 
   
DEPENDENCE ON EXPLORATORY DRILLING ACTIVITIES
    
 
   
     The Company's revenues, operating results and future rate of growth are
highly dependent upon the success of its exploratory drilling program, which
will be funded in part with the proceeds of the Offering. Exploratory drilling
involves numerous risks, including the risk that no commercially productive
natural gas or oil reservoirs will be encountered. The cost of drilling,
completing and operating wells is often uncertain, and drilling operations may
be curtailed, delayed or canceled as a result of a variety of factors, including
unexpected drilling conditions, pressure or irregularities in formations,
equipment failures or accidents, adverse weather conditions, compliance with
governmental requirements and shortages or delays in the availability of
drilling rigs and the delivery of equipment. Despite the use of 3-D seismic and
other advanced technologies, exploratory drilling remains a speculative
activity. Even when fully utilized and properly interpreted, 3-D seismic and
other advanced technologies only assist geoscientists in identifying subsurface
structures and do not enable the interpreter to know whether hydrocarbons are in
fact present in those
    
 
                                       16
<PAGE>   18
 
   
structures. In addition, the use of 3-D seismic and other advanced technologies
requires greater predrilling expenditures than traditional drilling strategies,
and the Company could incur losses as a result of such expenditures. The
Company's future drilling activities may not be successful. There can be no
assurance that the Company's overall drilling success rate or its drilling
success rate for activity within a particular province will not decline.
Unsuccessful drilling activities could have a material adverse effect on the
Company's results of operations and financial condition. The Company often
gathers 3-D seismic over large areas. The Company's interpretation of data
delineates those portions of an area desirable for drilling. Therefore, the
Company may choose not to acquire option and lease rights prior to acquiring
seismic and, in many cases, the Company may identify a drilling location before
seeking option or lease rights in the location. Although the Company has
identified numerous potential drilling locations, there can be no assurance that
they will ever be leased or drilled or that natural gas or oil will be produced
from these or any other potential drilling locations.
    
 
   
VOLATILITY OF NATURAL GAS AND OIL PRICES
    
 
   
     The Company's revenues, operating results and future rate of growth are
highly dependent upon the prices received for the Company's natural gas and oil.
Historically, the markets for natural gas and oil have been volatile and are
likely to continue to be volatile in the future. Various factors beyond the
control of the Company will affect sales prices of its natural gas and oil,
including worldwide and domestic supplies of natural gas and oil, the ability of
the members of the Organization of Petroleum Exporting Countries to agree to and
maintain oil price and production controls, political instability or armed
conflict in oil-producing regions, the price and level of foreign imports, the
level of consumer demand, the price and availability of alternative fuels, the
availability of pipeline capacity, the availability and cost of drilling rigs,
weather conditions, domestic and foreign governmental regulations and taxes, and
the overall economic environment. During 1997, the high and low prices for
natural gas on the NYMEX were $3.79 per MMBtu and $1.78 per MMBtu and the high
and low prices for oil on the NYMEX were $26.26 per Bbl and $17.60 per Bbl. From
January 1, 1998 through August 7, 1998, the high and low prices for natural gas
on the NYMEX were $2.69 per MMBtu and $1.83 per MMBtu and the high and low
prices for oil on the NYMEX were $17.82 per Bbl and $11.56 per Bbl. It is
impossible to predict future natural gas and oil price movements with certainty.
Declines in natural gas and oil prices may materially adversely affect the
Company's business, financial condition and results of operations. Lower natural
gas and oil prices also may reduce the amount of natural gas and oil that the
Company can produce economically. Any significant decline in the price of oil or
natural gas would adversely affect the Company's revenues and operating income
and may require a reduction in the carrying value of the Company's natural gas
and oil properties. See "Risk Factors -- Uncertainty of Reserve Information and
Future Net Revenue Estimates," "Management's Discussion and Analysis of
Financial Condition and Results of Operations -- Other Matters" and "Business
and Properties -- Competition."
    
 
   
     During the six months ended June 30, 1998, the NYMEX crude oil price ranged
from $17.82 to $11.56 per barrel. This decline in prices is generally thought to
be caused primarily by an oversupply of crude oil inventory created, in part, by
an unusually warm winter in the United States and Europe, an announced increase
in crude oil production quotas for OPEC countries and a possible decline in
demand in certain Asian markets. If such a decline in the NYMEX crude oil price
worsens or persists for a protracted period, it would adversely affect the
Company's revenues, net income and cash flows from operations. Also, if these
prices maintain their present level for an extended time period or decline
further, the Company may delay or postpone certain of its capital projects.
    
 
RISKS ASSOCIATED WITH MANAGEMENT OF GROWTH AND IMPLEMENTATION OF GROWTH STRATEGY
 
   
     The Company's rapid growth has placed, and is expected to continue to
place, a significant strain on the Company's financial, technical, operational
and administrative resources. As the Company increases the number of projects it
is evaluating or in which it is participating, there will be additional demands
on the Company's financial, technical, operational and administrative resources.
In addition, the Company has only limited experience operating and managing
field operations, including drilling, and there can be no assurances that the
Company will be successful in doing so. Any increase in the Company's activities
as an operator will increase its exposure to operating hazards. The failure to
continue to upgrade the Company's technical,
    
 
                                       17
<PAGE>   19
 
   
administrative, operating and financial control systems or the occurrence of
unexpected expansion difficulties, including difficulties in recruiting and
retaining geophysicists, geologists, engineers and sufficient numbers of
qualified personnel to enable the Company to expand its role in the drilling and
production phase, or the reduced availability and/or increased costs of seismic
gathering, drilling or other services in the face of growing demand, could have
a material adverse effect on the Company's business, financial condition and
results of operations. See "Risk Factors -- Operating Hazards and Uninsured
Risks."
    
 
SUBSTANTIAL CAPITAL REQUIREMENTS
 
   
     The Company makes and will continue to make substantial capital
expenditures in its exploration and development projects. The Company intends to
finance these capital expenditures with the net proceeds from the Offering, cash
flow from operations and its existing financing arrangements. Additional
financing may be required in the future to fund the Company's exploratory and
developmental drilling and 3-D seismic acquisition activities. No assurance can
be given as to the availability or terms of any such additional financing that
may be required or that financing will continue to be available under the
existing or new financing arrangements. If additional capital resources are not
available to the Company, its drilling and other activities may be curtailed and
its business, financial condition and results of operations could be materially
adversely affected. See "Use of Proceeds" and "Management's Discussion and
Analysis of Financial Condition and Results of Operations -- Liquidity and
Capital Resources."
    
 
HISTORICAL OPERATING LOSSES AND VARIABILITY OF OPERATING RESULTS
 
   
     The Company had net losses of approximately $5.1 million in 1993, $1.3
million in 1994, $1.6 million in 1995, $450,000 in 1996, $1.0 million (including
a net $1.2 million non-cash deferred income tax charge incurred in connection
with the Company's conversion from a partnership to a corporation) in 1997 and
$1.2 million in the first six months of 1998. The Company has incurred net
losses in each year of operation, and there can be no assurance that the Company
will be profitable in the future. At June 30, 1998, the Company's accumulated
deficit was $1.2 million and its total stockholders' equity was $42.3 million.
In addition, the Company's future operating results may fluctuate significantly
depending upon a number of factors, including industry conditions, prices of
natural gas and oil, rates of drilling success, rates of production from
completed wells and the timing of capital expenditures. This variability could
have a material adverse effect on the Company's business, financial condition
and results of operations. In addition, any failure or delay in the realization
of expected cash flows from operating activities could limit the Company's
ability to invest and participate in economically attractive projects. See
"Selected Financial Data" and "Management's Discussion and Analysis of Financial
Condition and Results of Operations."
    
 
RESERVE REPLACEMENT RISK
 
   
     In general, production from natural gas and oil properties declines as
reserves are depleted, with the rate of decline depending on reservoir
characteristics. Except to the extent the Company conducts successful
exploration and development activities or acquires properties containing proved
reserves, or both, the proved reserves of the Company will decline as reserves
are produced. The Company's future natural gas and oil production is highly
dependent upon its ability to economically find, develop or acquire reserves in
commercial quantities. The business of exploring for or developing reserves is
capital intensive. To the extent cash flow from operations is reduced and
external sources of capital become limited or unavailable, the Company's ability
to make the necessary capital investment to maintain or expand its asset base of
natural gas and oil reserves would be impaired. The Company has historically
participated in a substantial percentage of its wells as a non-operator. The
failure of an operator of the Company's wells to adequately perform operations,
or an operator's breach of the applicable agreements, could adversely impact the
Company. In addition, there can be no assurance that the Company's future
exploration and development activities will result in additional proved reserves
or that the Company will be able to drill productive wells at acceptable costs.
Furthermore, although the Company's revenues could increase if prevailing prices
for natural gas and oil increase significantly, the Company's finding and
development costs could also increase. See "Management's Discussion and Analysis
of Financial Condition and Results of Operations."
    
 
                                       18
<PAGE>   20
 
OPERATING HAZARDS AND UNINSURED RISKS
 
     The Company's operations are subject to hazards and risks inherent in
drilling for and producing and transporting natural gas and oil, such as fires,
natural disasters, explosions, encountering formations with abnormal pressures,
blowouts, cratering, pipeline ruptures and spills, any of which can result in
the loss of hydrocarbons, environmental pollution, personal injury claims and
other damage to properties of the Company and others. As protection against
operating hazards, the Company maintains insurance coverage against some, but
not all, potential losses. The Company may elect to self-insure if management
believes that the cost of insurance, although available, is excessive relative
to the risks presented. The Company generally maintains insurance for the
hazards and risks inherent in drilling for and producing and transporting
natural gas and oil and believes this insurance is adequate. Nevertheless, the
occurrence of an event that is not covered, or not fully covered, by insurance
could have a material adverse effect on the Company's business, financial
condition and results of operations. In addition, pollution and environmental
risks generally are not fully insurable. See "Business and
Properties -- Operating Hazards and Uninsured Risks."
 
UNCERTAINTY OF RESERVE INFORMATION AND FUTURE NET REVENUE ESTIMATES
 
     Numerous uncertainties are inherent in estimating quantities of proved
reserves and their values, including many factors beyond the Company's control.
The reserve information in this Prospectus is an estimate only. Although the
Company believes these estimates are reasonable, reserve estimates are imprecise
and are expected to change as additional information becomes available.
Estimates of natural gas and oil reserves by necessity are projections based on
engineering data, and uncertainties are inherent in the interpretation of this
data, the projection of future rates of production and the timing of development
expenditures. Reserve engineering is a subjective process of estimating
underground accumulations of natural gas and oil that are difficult to measure.
The accuracy of any reserve estimate is a function of the quality of available
data, engineering and geologic interpretation, and judgment. Estimates of
economically recoverable natural gas and oil reserves and of future net cash
flows depend upon a number of variable factors and assumptions, such as
historical production from the area compared with production from other
producing areas, the assumed effects of regulations by governmental agencies,
and assumptions concerning future natural gas and oil prices, future operating
costs, severance and excise taxes, development costs and workover and remedial
costs, all of which may in fact vary considerably from actual results. For these
reasons, estimates of the economically recoverable quantities of natural gas and
oil attributable to any particular group of properties, classifications of
reserves based on risk of recovery, and estimates of the future net cash flows
may vary substantially. Moreover, there can be no assurance that the Company's
reserves will ultimately be produced or that the Company's proved undeveloped
reserves will be developed within the periods anticipated. Any significant
variance in the assumptions could materially affect the estimated quantity and
value of the Company's reserves. Actual production, revenues and expenditures
with respect to the Company's reserves will likely vary from estimates, and such
variances may be material. See "Business and Properties -- Natural Gas and Oil
Reserves."
 
   
     The Present Value of Future Net Revenues referred to in this Prospectus
should not be construed as the current market value of the estimated natural gas
and oil reserves attributable to the Company's properties. In accordance with
applicable requirements of the SEC, the estimated discounted future net cash
flows from proved reserves are generally based on prices and costs as of the
date of the estimate, whereas actual future prices and costs may be materially
higher or lower. At December 31, 1997, the date of the estimate of the Company's
reserves and present value data, the prices of natural gas and oil on the NYMEX
were $2.26 per MMBtu and $17.64 per Bbl, respectively. At August 7, 1998, the
prices were $1.83 per MMBtu and $13.80 per Bbl, respectively. Actual future net
cash flows also will be affected by factors such as the amount and timing of
actual production, supply and demand for natural gas and oil, curtailments or
increases in consumption by gas purchasers, and changes in governmental
regulations or taxation. The timing of actual future net cash flows from proved
reserves, and thus their actual present value, will be affected by the timing of
both the production and the incurrence of expenses in connection with
development and production of natural gas and oil properties. In addition, the
10% discount factor, which must be used to calculate discounted future net cash
flows for SEC reporting purposes, is not necessarily the most appropriate
discount factor based on
    
 
                                       19
<PAGE>   21
 
interest rates in effect from time to time and risks associated with the Company
or the oil and gas industry in general.
 
COMPETITION
 
     The Company operates in the highly competitive areas of natural gas and oil
exploration, exploitation, acquisition and production with other companies. In
seeking to acquire desirable producing properties or new leases for future
exploration and in marketing its natural gas and oil production, as well as in
seeking to acquire the equipment and expertise necessary to operate and develop
those properties, the Company faces intense competition from a large number of
independent, technology-driven companies as well as both major and other
independent natural gas and oil companies. Many of these competitors have
financial and other resources substantially in excess of those available to the
Company. The effects of this highly competitive environment could have a
material adverse effect on the Company's business, financial condition and
results of operations. See "Business and Properties -- Competition."
 
COMPLIANCE WITH GOVERNMENTAL REGULATIONS
 
     The Company's business is subject to federal, state and local laws and
regulations relating to the exploration for, and the development, production and
transportation of, natural gas and oil, as well as safety matters. Although the
Company believes it is in substantial compliance with all applicable laws and
regulations, legal requirements are frequently changed and subject to
interpretation, and the Company is unable to predict the ultimate cost of
compliance with these requirements or their effect on its operations.
Significant expenditures may be required to comply with governmental laws and
regulations. See "Business and Properties -- Governmental Regulation."
 
COMPLIANCE WITH ENVIRONMENTAL REGULATIONS
 
     The Company's operations are subject to complex environmental laws and
regulations adopted by federal, state and local governmental authorities.
Environmental laws and regulations are frequently changed. The implementation of
new, or the modification of existing, laws or regulations could have a material
adverse effect on the Company. The discharge of natural gas, oil, or other
pollutants into the air, soil or water may give rise to significant liabilities
on the part of the Company to the government and third parties and may require
the Company to incur substantial costs of remediation. No assurance can be given
that existing environmental laws or regulations, as currently interpreted or
reinterpreted in the future, or future laws or regulations will not materially
adversely affect the Company's results of operations and financial condition.
See "Business and Properties -- Environmental Matters."
 
RISK OF HEDGING ACTIVITIES
 
     In an attempt to reduce its sensitivity to energy price volatility, the
Company has in the past and may continue in the future to enter into hedging
transactions that generally result in a fixed price over a fixed period. If the
Company's reserves are not produced at rates equivalent to the hedged position,
the Company would be required to satisfy its obligations under hedging contracts
on potentially unfavorable terms without the ability to hedge that risk through
sales of comparable quantities of its own production. Further, the terms under
which the Company enters into hedging contracts are based on assumptions and
estimates of numerous factors such as cost of production and pipeline and other
transportation costs to delivery points. Substantial variations between the
assumptions and estimates used by the Company and actual results experienced
could materially adversely affect the Company's anticipated profit margins and
its ability to manage the risk associated with fluctuations in natural gas and
oil prices. Additionally, hedging contracts limit the benefits the Company will
realize if actual prices rise above the contract prices. In addition, hedging
contracts are subject to the risk that the other party may prove unable or
unwilling to perform its obligations under such contracts. Any significant
nonperformance could have a material adverse financial effect on the Company.
For the year ended December 31, 1997, the Company realized a reduction in
revenues attributable to oil hedges of $6,191. In 1997 the Company did not hedge
any of its natural gas production. In February 1998, the Company entered into a
hedging contract whereby 10,000 MMBtu per day of natural gas is purchased and
sold subject to a fixed
 
                                       20
<PAGE>   22
 
   
price swap agreement for monthly periods from April 1998 through October 1999.
Pursuant to these arrangements the Company exchanges a floating market price for
a fixed contract price. As a result of this natural gas hedging contract, the
Company realized an increase in revenues of $38,700 in the three months ended
June 30, 1998. See "Management's Discussion and Analysis of Financial Condition
and Results of Operations -- Other Matters."
    
 
MARKETABILITY OF PRODUCTION
 
     The marketability of the Company's production depends in part upon the
availability, proximity and capacity of natural gas gathering systems, pipelines
and processing facilities. The Company delivers natural gas through gas
transportation systems that it generally does not own. Federal and state
regulation of natural gas and oil production and transportation, tax and energy
policies, changes in supply and demand and general economic conditions all could
adversely affect the Company's ability to produce and market its natural gas and
oil. Any dramatic change in market factors could have a material adverse effect
on the Company's business, financial condition and results of operations.
 
DEPENDENCE ON KEY PERSONNEL
 
     The Company has assembled a team of geologists, geophysicists and engineers
having considerable experience applying 3-D imaging technology. The Company is
dependent upon the knowledge, skills and experience of these experts to provide
3-D imaging and assist the Company in reducing the risks associated with its
participation in natural gas and oil exploration projects. In addition, the
success of the Company's business also depends to a significant extent upon the
abilities and continued efforts of its management, particularly Ben M. Brigham,
the Company's President, Chief Executive Officer and Chairman of the Board. The
Company has an employment agreement with Ben M. Brigham, but does not have an
employment agreement with any of its other employees. The Company has key man
life insurance on Mr. Brigham in the amount of $2.0 million. The loss of
services of key management personnel or the Company's technical experts, or the
inability to attract additional qualified personnel, could have a material
adverse effect on the Company's business, financial condition and results of
operations. There can be no assurance that the Company will be successful in
attracting and retaining such executives, geophysicists, geologists and
engineers. See "Management -- Directors and Executive Officers" and "Business
and Properties -- Exploration Staff."
 
CONTROL BY EXISTING STOCKHOLDERS
 
   
     Upon completion of the Offering, directors, executive officers and
principal stockholders of the Company, and certain of their affiliates, will
beneficially own approximately   % of the Company's outstanding Common Stock.
Accordingly, these stockholders, as a group, will be able to control the outcome
of stockholder votes, including votes concerning the election of directors, the
adoption or amendment of provisions in the Company's Certificate of
Incorporation or Bylaws and the approval of mergers and other significant
corporate transactions. The existence of these levels of ownership concentrated
in a few persons makes it unlikely that any other holder of Common Stock will be
able to affect the management or direction of the Company. These factors may
also have the effect of delaying or preventing a change in the management or
voting control of the Company. See "Principal Stockholders."
    
 
YEAR 2000 COMPLIANCE
 
   
     Many currently installed computer systems and software products are coded
to accept only two digit entries in the date code field. These date code fields
will need to accept four digit entries to distinguish the 21st century dates
from 20th century dates. As a result, computer systems and software used by many
companies may need to be upgraded to comply with such "Year 2000" requirements.
The Company believes that its software products are Year 2000 compliant and does
not anticipate incurring material costs related to Year 2000 compliance.
However, there can be no assurance that the Company's software products contain
all necessary software routines and programs necessary for the accurate
calculation, display, storage and manipulation of data involving dates.
Moreover, the Company cannot determine what effect, if any, the Year 2000
requirements will have on its vendors, customers, other businesses with which
its conducts business and
    
 
                                       21
<PAGE>   23
 
the numerous local, state, federal, and other U.S. and foreign governmental
entities by which it is regulated, governed or taxed. No assurance can be given
that the computer systems and software of such entities will be Year 2000
compliant or that compliance costs or the impact of the Company's failure to
achieve substantial Year 2000 compliance will not have a material adverse effect
on the Company's business, financial position and results of operations.
 
CERTAIN ANTITAKEOVER CONSIDERATIONS
 
     The Company's Certificate of Incorporation authorizes the Board of
Directors of the Company to issue up to 10 million shares of preferred stock
without stockholder approval and to set the rights, preferences and other
designations, including voting rights, of those shares as the Board of Directors
may determine. These provisions, alone or in combination with the matters
described in "Risk Factors -- Control by Existing Stockholders," may discourage
transactions involving actual or potential changes of control of the Company,
including transactions that otherwise could involve payment of a premium over
prevailing market prices to holders of Common Stock. The Company also is subject
to provisions of the Delaware General Corporation Law that may make some
business combinations more difficult. See "Description of Capital Stock --
Delaware Law Provisions."
 
SHARES ELIGIBLE FOR FUTURE SALE; REGISTRATION RIGHTS
 
   
     Sales of a substantial number of shares of Common Stock in the public
market following the Offering could adversely affect the market price for the
Common Stock. Upon completion of the Offering the Company will have      shares
of Common Stock outstanding. 8,928,574 shares of Common Stock that were issued
in reliance on exemptions from the registration requirements of the Securities
Act are now eligible for sale under Rule 144, subject to compliance with the
volume and other limitations of Rule 144, and      shares of Common Stock that
will be issued in the Offering or were sold in the Company's initial public
offering are freely tradeable, except to the extent that they are held by
affiliates of the Company. Investors holding 8,421,431 shares have the right to
require the Company to register the public resale of their shares and holders of
8,928,574 shares are entitled to "piggyback" registration rights. The holders of
the Shares and Warrants will have demand and "piggyback" registration rights
with respect to the Shares and the Warrant Shares, respectively. Options
covering 935,987 shares of Common Stock are outstanding, with an average
exercise price of $7.61 per share, subject to vesting. As a result of the
Offering, Warrants to purchase 1,000,000 shares of Common Stock will be
outstanding with an exercise price of $     per share. See "Shares Eligible for
Future Sale," "Description of Capital Stock -- Registration Rights" and
"Registration Rights Relating to the Warrants and Shares."
    
 
POSSIBLE STOCK PRICE VOLATILITY
 
     The trading price of the Common Stock and the price at which the Company
may sell securities in the future could be subject to large fluctuations in
response to limited trading volume in the Company's stock and changes in
government regulations, quarterly variations in operating results, litigation,
general market conditions, the prices of natural gas and oil, announcements by
the Company and its competitors, the liquidity of the Company, the Company's
ability to raise additional funds and other events.
 
                                       22
<PAGE>   24
 
                                  THE COMPANY
 
     Brigham Exploration Company was formed in February 1997 as a Delaware
corporation and is the holding company for Brigham Oil & Gas, L.P. (the
"Partnership"). The Partnership was formed in May 1992 by contribution of assets
of Brigham, Inc., and its general partners were General Atlantic Partners III,
L.P., a Delaware limited partnership ("GAP III"), and Brigham, Inc. Under the
Exchange Agreement (the "Exchange Agreement"), effective February 27, 1997, the
following transactions occurred: (i) GAP III and the limited partners of the
Partnership transferred all their partnership interests to the Company in
exchange for an aggregate of 3,314,286 shares of Common Stock, (ii) the
stockholders of Brigham, Inc. transferred all the issued and outstanding stock
of Brigham, Inc. to the Company in exchange for an aggregate of 3,859,821 shares
of Common Stock and (iii) Resource Investors Management Company Limited
Partnership ("RIMCO") exchanged all of the Partnership's subordinated
convertible notes for 1,754,464 shares of Common Stock. These transactions are
referred to in this Prospectus as the "Exchange." The stockholders of Brigham,
Inc. were Ben M. Brigham, President, Chief Executive Officer and Chairman of the
Board of the Company, and Anne L. Brigham, Executive Vice President and a
Director of the Company. The limited partners of the Partnership included the
following officers and/or directors of the Company, who received shares of
Common Stock in the Exchange as indicated: Jon L. Glass, Vice
President -- Exploration and a Director (66,964 shares); Craig M. Fleming, Chief
Financial Officer (44,643 shares); David T. Brigham, Vice President -- Land and
Administration and Corporate Secretary (44,643 shares); and Harold D. Carter, a
Director (350,893 shares). As a result of the Exchange, Brigham Exploration
Company owns, directly or indirectly, all the partnership interests in the
Partnership and no instruments, agreements or rights exist which may be
converted, exchanged into, or otherwise become interests in the Partnership. The
Company conducts its active business operations through the Partnership.
References to the "Company" or to "Brigham" are to Brigham Exploration Company
and its predecessors and subsidiaries, including the Partnership and Brigham,
Inc.
 
     Brigham's principal executive offices are located at 6300 Bridge Point
Parkway, Building 2, Suite 500, Austin, Texas 78730 and its telephone number is
(512) 427-3300.
 
                                       23
<PAGE>   25
 
                                USE OF PROCEEDS
 
   
     The net proceeds to the Company from the sale of the Notes, Warrants and
Shares offered by the Company are estimated to be approximately $47.6 million,
assuming a price of $9.50 per share for the Shares and after deducting the
estimated fees and expenses of the Offering.
    
 
   
     The Company intends to use the net proceeds of the Offering to fund the
Company's accelerated exploration and development activities and in the interim
for repayment of outstanding indebtedness under the Credit Facility (as defined)
($72 million was outstanding at August 7, 1998). The interest rate for
borrowings under the Credit Facility is either the lender's base rate or LIBOR
plus 2.25%, at the Company's option. Borrowings under the facility, which
matures on January 26, 2001, currently bear interest at an annual rate of
approximately 8.6%. See "Management's Discussion and Analysis of Financial
Condition and Results of Operations -- Liquidity and Capital
Resources -- Revolving Credit Facilities" for a description of the Credit
Facility.
    
 
                PRICE RANGE OF COMMON STOCK AND DIVIDEND POLICY
 
     The Company's Common Stock is traded on The Nasdaq Stock Market(SM) under
the symbol "BEXP." The following table sets forth, for the periods indicated,
the reported high and low closing prices of the Company's Common Stock, as
reported on The Nasdaq Stock Market(SM):
 
   
<TABLE>
<CAPTION>
                                                               HIGH          LOW
                                                              ------        ------
<S>                                                           <C>           <C>
FISCAL 1997:
Second Quarter (from May 9, 1997)...........................  $ 8.75        $ 7.08
Third Quarter...............................................   14.31          8.25
Fourth Quarter..............................................   17.13         12.00
FISCAL 1998:
First Quarter...............................................  $14.00        $10.50
Second Quarter..............................................   15.50          8.75
Third Quarter (through August 13, 1998).....................   10.25          7.00
</TABLE>
    
 
   
     On August 13, 1998, the last reported sale price of the Common Stock as
reported on The Nasdaq Stock Market(SM) was $8.50 per share. As of August 13,
1998 there were 67 holders of record of the Common Stock.
    
 
   
     The Company has never declared or paid cash dividends on its Common Stock
and anticipates that all future earnings will be retained for use in its
business. In addition, the Credit Facility and the Indenture prohibit the
payment of cash dividends on Common Stock. The Board of Directors of the Company
may review the Company's dividend policy from time to time in light of, among
other things, the Company's earnings and financial position. See "Management's
Discussion and Analysis of Financial Condition and Results of
Operations -- Liquidity and Capital Resources."
    
 
                                       24
<PAGE>   26
 
                                 CAPITALIZATION
 
   
     The following table sets forth the capitalization of the Company (i) as of
June 30, 1998 and (ii) as adjusted for the Offering and the application of the
estimated net proceeds therefrom, assuming issuance of 1,052,632 Shares at a
price of $9.50 per share. The table should be read with "Management's Discussion
and Analysis of Financial Condition and Results of Operations" and the Financial
Statements and notes thereto in this Prospectus.
    
 
   
<TABLE>
<CAPTION>
                                                               AS OF JUNE 30, 1998
                                                              ----------------------
                                                               ACTUAL    AS ADJUSTED
                                                              --------   -----------
                                                                  (IN THOUSANDS)
<S>                                                           <C>        <C>
Total debt:
  Credit Facility...........................................  $ 68,000    $ 20,450
  Senior Subordinated Secured Notes due 2003................        --      35,500
                                                              --------    --------
          Total debt........................................    68,000      55,950
                                                              --------    --------
Stockholders' equity:
  Preferred Stock, $.01 par value, 10 million shares
     authorized; no shares outstanding actual, and as
     adjusted...............................................        --          --
  Common Stock, $.01 par value, 30 million shares
     authorized; 12,253,574 shares issued and outstanding
     actual and 13,306,206 as adjusted(1)...................       123         133
  Additional paid-in capital................................    44,292      58,212
  Unearned stock compensation...............................      (880)       (880)
  Accumulated deficit.......................................    (1,201)     (1,201)
                                                              --------    --------
          Total stockholders' equity........................    42,334      56,264
                                                              --------    --------
Total capitalization........................................  $110,334    $112,214
                                                              ========    ========
</TABLE>
    
 
---------------
 
   
(1) Excludes (i) 1,588,169 shares of Common Stock the Company has reserved for
    future issuance under the Company's 1997 Incentive Plan and 25,000 shares of
    Common Stock reserved for issuance under the Company's 1997 Director Stock
    Option Plan, of which options to purchase 935,987 shares, subject to
    vesting, with an average exercise price of $7.61 per share are outstanding,
    and (ii) on an as adjusted basis, Warrants to purchase 1,000,000 shares of
    Common Stock with an exercise price of $     per share. See "Management" and
    Note 11 of Notes to the December 31, 1997 Consolidated Financial Statements.
    
 
                                       25
<PAGE>   27
 
                            SELECTED FINANCIAL DATA
                    (IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)
 
   
     The following table sets forth selected financial data of the Company. The
data for the three years ended December 31, 1997 has been derived from the
consolidated financial statements appearing in this Prospectus. The data for the
two years ended December 31, 1994 has been derived from consolidated financial
statements not appearing in this Prospectus. The consolidated financial data at
June 30, 1998 and for the six months ended June 30, 1998 and June 30, 1997 have
been derived from the condensed consolidated financial statements of the Company
which, in the opinion of management, include all adjustments, consisting only of
normal adjustments, necessary for a fair presentation of the results for the
periods. The results for the six months ended June 30, 1998 are not necessarily
indicative of the results to be expected for the full year. The information
should be read in conjunction with "Management's Discussion and Analysis of
Financial Condition and Results of Operations" and the financial statements and
notes thereto included elsewhere in this Prospectus.
    
 
   
<TABLE>
<CAPTION>
                                                                                                          SIX MONTHS
                                                                                                            ENDED
                                                           YEAR ENDED DECEMBER 31,                         JUNE 30,
                                              --------------------------------------------------     --------------------
                                               1993       1994      1995       1996       1997        1997         1998
                                              -------    -------   -------   --------   --------     -------     --------
<S>                                           <C>        <C>       <C>       <C>        <C>          <C>         <C>
STATEMENT OF OPERATIONS DATA:
  Revenues:
    Natural gas and oil sales...............  $   937    $ 2,565   $ 3,578   $  6,141   $  9,184     $ 3,854     $  7,130
    Workstation revenue.....................      467        815       635        627        637         324          247
                                              -------    -------   -------   --------   --------     -------     --------
        Total revenues......................    1,404      3,380     4,213      6,768      9,821       4,178        7,377
  Costs and expenses:
    Lease operating.........................      111        491       761        726      1,151         470          978
    Production taxes........................       47        126       165        362        549         219          450
    General and administrative..............    1,433      1,785     1,897      2,199      3,570       1,455        2,293
    Depletion of natural gas and oil
      properties............................    4,371(1)   1,104     1,626      2,323      2,732       1,395        2,784
    Depreciation and amortization...........      406        561       533        487        582         287          365
                                              -------    -------   -------   --------   --------     -------     --------
        Total costs and expenses............    6,368      4,067     4,982      6,097      8,584       3,826        6,870
                                              -------    -------   -------   --------   --------     -------     --------
  Operating income (loss)...................   (4,964)      (687)     (769)       671      1,237         352          507
  Other income (expense):
    Interest income.........................        6         56       128         52        145          81           77
    Interest expense........................     (105)      (668)     (936)    (1,173)    (1,190)       (546)      (2,432)
                                              -------    -------   -------   --------   --------     -------     --------
        Total other income (expense)........      (99)      (612)     (808)    (1,121)    (1,045)       (465)      (2,355)
                                              -------    -------   -------   --------   --------     -------     --------
  Net income (loss) before income taxes.....   (5,063)    (1,299)   (1,577)      (450)       192        (113)      (1,848)
  Income tax (expense) benefit, net.........       --         --        --         --     (1,228)(2)  (4,813)(2)      621
                                              -------    -------   -------   --------   --------     -------     --------
        Net loss............................  $(5,063)   $(1,299)  $(1,577)  $   (450)  $ (1,036)    $(4,926)    $ (1,227)
                                              =======    =======   =======   ========   ========     =======     ========
  Net loss per share -- basic/diluted.......  $ (0.57)   $ (0.15)  $ (0.18)  $  (0.05)  $  (0.09)    $ (0.50)    $  (0.10)
  Weighted average shares outstanding --
    basic/diluted...........................    8,929      8,929     8,929      8,929     11,081       9,890       12,254
STATEMENT OF CASH FLOWS DATA:
  Net cash provided by (used in) operating
    activities..............................  $  (730)   $   626   $ 1,383   $  3,710   $  9,806     $  (195)    $ (1,692)
  Net cash used in investing activities.....   (6,983)    (5,463)   (8,005)   (11,796)   (57,300)    (12,105)     (30,884)
  Net cash provided by financing
    activities..............................    7,839      4,634     7,724      7,731     47,748      15,842       33,981
OTHER FINANCIAL DATA:
  Capital expenditures......................  $ 6,632    $ 5,445   $ 7,935   $ 13,612   $ 57,170     $11,796     $ 30,044
  EBITDA(3).................................     (187)       978     1,390      3,481      4,551       2,034        3,656
  Operating cash flow(4)....................     (286)       366       582      2,360      3,506       1,569        1,567
  Ratio of earnings to fixed charges(5).....       --         --        --         --        1.1x         --           --
PRO FORMA FINANCIAL DATA(6):
  Ratio of earnings to fixed charges(5).....                                                  --                       --
  Interest expense(6).......................                                               2,325                    3,252
</TABLE>
    
 
   
<TABLE>
<CAPTION>
                                                              AS OF DECEMBER 31,                        AS OF JUNE 30,
                                              --------------------------------------------------     --------------------
                                               1993       1994      1995       1996       1997        1997         1998
                                              -------    -------   -------   --------   --------     -------     --------
<S>                                           <C>        <C>       <C>       <C>        <C>          <C>         <C>
BALANCE SHEET DATA:
  Cash and cash equivalents.................  $   903    $   700   $ 1,802   $  1,447   $  1,701     $ 4,989     $  3,106
  Natural gas and oil properties, at cost,
    net.....................................    7,803     11,970    18,538     28,005     84,176      40,199      114,454
  Total assets..............................   14,003     15,781    22,916     33,614     92,401      51,046      129,699
  Notes payable.............................    3,000      7,950    16,000     24,000     32,000          --       68,000
  Stockholders' equity......................    6,570      5,271     3,694      3,244     43,153      38,919       42,334
</TABLE>
    
 
---------------
 
(1) Includes a capitalized ceiling impairment charge of $3.3 million in 1993.
 
                                       26
<PAGE>   28
 
(2) In conjunction with the Exchange, the Company recorded a deferred income tax
    liability of $5 million to recognize the temporary differences between the
    financial statement and tax bases of the assets and liabilities of the
    Partnership at February 27, 1997, the date of the Exchange. During the
    fourth quarter of 1997, the Company elected to record a step-up in basis of
    its assets for tax purposes as a result of the Exchange. Related to this
    election, the Company recorded a $3.8 million deferred income tax benefit,
    resulting in a net $1.2 million ($.10 per share) non-cash deferred income
    tax charge for the year ended December 31, 1997. See Note 2 of Notes to the
    December 31, 1997 Consolidated Financial Statements.
 
(3) EBITDA represents net income (loss) plus income taxes, net interest expense
    and depreciation, depletion and amortization expense. EBITDA should not be
    considered in isolation or as a substitute for net income, cash flows from
    operating activities or any other measure of financial performance prepared
    in accordance with generally accepted accounting principles or as a measure
    of a company's profitability or liquidity.
 
(4) Operating cash flow represents net income (loss) plus DD&A expenses,
    deferred income taxes and other non-cash items. Operating cash flow should
    not be considered in isolation or as a substitute for net income, cash flows
    from operating activities or any other measure of financial performance
    prepared in accordance with generally accepted accounting principles or as a
    measure of a company's profitability or liquidity.
 
   
(5) For purposes of calculating the ratio of earnings to fixed charges, earnings
    are defined as income (loss) of the Company from continuing operations
    before income taxes and fixed charges. Fixed charges consist of interest
    expense, including amortization of loan fees, and the portion of rental
    expense pursuant to operating leases deemed to be representative of the
    interest component. Earnings were insufficient to cover fixed charges by
    $5.1 million, $1.3 million, $1.6 million and $450,000 for the years ended
    December 31, 1993, 1994, 1995 and 1996, respectively, and $113,000 and $1.9
    million for the six months ended June 30, 1997 and 1998, respectively. Pro
    forma earnings were insufficient to cover pro forma fixed charges by
    $943,000 for the year ended December 31, 1997 and $2.7 million for the six
    months ended June 30, 1998.
    
 
   
(6) The pro forma financial data have been prepared on the basis of the
    following assumptions: (i) the Offering was consummated at the beginning of
    the respective periods, (ii) the average debt outstanding during the year
    ended December 31, 1997 of $12 million was refinanced with proceeds from the
    Notes, (iii) debt outstanding during the first six months of 1998 was
    partially repaid with proceeds from the issuance of $10 million of Shares
    and was partially refinanced with proceeds from the $40 million of Notes and
    (iv) the Notes bear an assumed effective interest rate of 15.7%.
    
   
    
 
                                       27
<PAGE>   29
 
                    MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITION AND RESULTS OF OPERATIONS
 
OVERVIEW
 
     The Company is an independent exploration and production company that
applies 3-D seismic imaging and other advanced technologies to systematically
explore and develop onshore domestic natural gas and oil provinces. From
inception in 1990 through December 31, 1997, Brigham had acquired 4,005 square
miles of 3-D seismic, identified 1,170 potential drilling locations and drilled
370 wells delineated by 3-D seismic analysis. The Company believes this
performance demonstrates a systematic methodology for finding natural gas and
oil in onshore domestic natural gas and oil provinces.
 
     Combining its geologic and geophysical expertise with a sophisticated land
effort, the Company manages the majority of its projects from conception through
3-D acquisition, processing and interpretation and leasing. Because it generates
most of its projects, the Company can control the size of the working interest
that it retains as well as the selection of the operator and the non-operating
participants. Additionally, the Company manages the negotiation and drafting of
most of its geophysical exploration agreements, resulting in reduced contract
risk and more consistent deal terms. In 1995, the Company began to manage
operations, on a limited basis, through the drilling and production phases. The
Company had discovered an aggregate of approximately 72 Bcfe of net proved
reserves as of December 31, 1997. Brigham continues to increase the working
interest it retains in its projects, based on capital availability and perceived
risk. The Company's average working interest in its wells drilled during 1995,
1996 and 1997 was 24%, 24% and 38%, respectively.
 
   
     Expenditures made in natural gas and oil exploration vary from project to
project depending primarily on the costs related to land, seismic acquisition,
drilling costs and the working interest retained by the Company. Historically,
the Company's participants have borne a disproportionate share of the costs of
optioning available acreage and acquiring, processing and interpreting the 3-D
seismic, and the Company and its participants each bear leasing, drilling and
completion costs in proportion to their ownership interests. Brigham currently
intends to retain increased working interests in its current 3-D seismic
projects, thereby reducing the financial leverage it has historically received
on the costs of optioning available acreage and acquiring, processing and
interpreting the 3-D seismic and increasing its working interests during the
drilling phase.
    
 
     From inception through 1996, the Company acquired 2,762 square miles of 3-D
seismic in 104 projects. Initially, the Company focused its efforts in West
Texas. In 1995, the Company began to devote substantial attention to the
Anadarko Basin, and since 1996 the Company has devoted the majority of its
resources to the Anadarko Basin and Gulf Coast. With this shift in regional
focus, the majority of the Company's production volumes has shifted from oil to
natural gas. To finance these project generation and drilling activities, the
Company has supplemented cash flow from operations with private placements of
debt and equity, commercial bank credit facilities and placements of working
interests in projects with industry participants. As the Company's cash flows
from operations and other sources of capital have increased, it has retained
larger average working interests in its projects.
 
     In 1997, the Company acquired 1,243 square miles of 3-D seismic and
continued to focus the majority of its 3-D exploration efforts in the Anadarko
Basin and the Gulf Coast. The Company acquired 648 square miles (52%) of 3-D
seismic in nine projects in the Anadarko Basin, making this basin the most
active 3-D seismic acquisition province for the Company again in 1997. Brigham
also significantly increased its Gulf Coast activity, acquiring 412 square miles
(33%) of 3-D seismic in four projects. During 1997, the Company drilled
seventy-three 3-D seismic delineated wells, increasing its revenues from natural
gas and oil production to $9.1 million. The Company's production volumes
consisted of 44% natural gas on an equivalent basis. The Company's average
working interest in wells drilled in 1997 was 38%. The Company's fourth quarter
1997 revenue from natural gas and oil production increased to $3.2 million from
$1.9 million in the fourth quarter of 1996, while its production volumes
consisted of 53% natural gas during the fourth quarter 1997 as compared with 36%
during the prior year period. The Company supplemented cash flow from operations
with borrowings under the credit facility it had in place at the time, $24
million raised in its initial public offering of common
 
                                       28
<PAGE>   30
 
stock in May 1997 and the placement of working interests in projects to industry
participants to finance its project generation, property acquisition and
drilling activities.
 
     The Company uses the full-cost method of accounting for its natural gas and
oil properties. Under this method, all acquisition, exploration and development
costs, including certain internal costs that are directly attributable to the
Company's acquisition, exploration and development activities, are capitalized
in the amortizable base of the "full-cost pool" as incurred. Upon the
interpretation by the Company of the 3-D seismic associated with unproved
properties, the geological and geophysical costs of acreage that is not
specifically identified as prospective are transferred to the amortizable base.
Geological and geophysical costs associated with prospective acreage, as well as
leasehold costs, are transferred to the amortizable base when the prospects are
drilled. The Company records depletion of its full-cost pool using the unit of
production method. To the extent that the costs capitalized in the full-cost
pool (net of depreciation, depletion and amortization and related deferred
taxes) exceed the present value (using a 10% discount rate) of estimated future
net after-tax cash flows from proved natural gas and oil reserves plus the
capitalized cost of unproved properties, such costs are charged to operations.
Once incurred, a write-down of natural gas and oil properties is not reversed at
a later date. See Note 2 of Notes to the December 31, 1997 Consolidated
Financial Statements.
 
     In connection with the Exchange in 1997, the Company issued options to
purchase 644,097 shares of Common Stock to certain of its officers and
employees. The Company recorded an unearned stock compensation balance of $1.9
million in the first quarter 1997, of which approximately one-half will be added
to the amortizable base of the full-cost pool over the vesting period of the
options and the balance will be recorded as a noncash compensation expense over
the vesting period of the options. As a result, the Company expects to incur
unearned stock compensation amortization expenses of approximately $290,000 in
1998, $140,000 in 1999 and an aggregate of $170,000 in the four years
thereafter.
 
     The Company's predecessor was classified as a partnership for federal
income tax purposes. Therefore, no income taxes were paid or provided for by the
Company prior to the Exchange. The Company is a taxable entity. In connection
with the Exchange on February 27, 1997, the Company incurred a $5 million charge
to record a deferred income tax liability to recognize the differences between
the financial statement basis and tax basis of the Company's predecessor
partnership's natural gas and oil properties at the Exchange date, given the
provisions of enacted tax laws. During the fourth quarter 1997, the Company
elected to record a step-up in the basis of its assets for tax purposes as a
result of the Exchange. Due to this election, the Company recorded a $3.8
million non-cash deferred income tax benefit during the fourth quarter 1997,
which resulted in a net $1.2 million non-cash deferred income tax charge for the
year ended December 31, 1997.
 
RESULTS OF OPERATIONS
 
     The following table sets forth certain operating data for the periods
presented.
 
   
<TABLE>
<CAPTION>
                                                                              SIX MONTHS ENDED
                                                 YEAR ENDED DECEMBER 31,          JUNE 30,
                                                --------------------------    -----------------
                                                 1995      1996      1997      1997       1998
                                                ------    ------    ------    ------     ------
<S>                                             <C>       <C>       <C>       <C>        <C>
Production:
  Natural gas (MMcf)..........................     272       698     1,382       457      1,947
  Oil (MBbls).................................     177       227       291       127        232
  Natural gas equivalent (MMcfe)..............   1,332     2,060     3,126     1,222      3,338
Average sales prices per unit (1):
  Natural gas (per Mcf).......................  $ 1.62    $ 2.30    $ 2.56    $ 2.62     $ 2.10
  Oil (per Bbl)...............................   17.76     19.98     19.40     20.87      13.15
  Natural gas equivalent (per Mcfe)...........    2.69      2.98      2.94      3.16       2.14
Costs and expenses per Mcfe:
  Lease operating.............................  $ 0.57    $ 0.35    $ 0.37    $ 0.38     $ 0.29
  Production taxes............................    0.12      0.18      0.18      0.18       0.13
  General and administrative..................    1.42      1.07      1.14      1.19       0.69
  Depletion of natural gas and oil
     properties...............................    1.22      1.13      0.87      1.14       0.83
</TABLE>
    
 
                                       29
<PAGE>   31
 
---------------
 
(1) Reflects the effects of the Company's hedging activities. See "Management's
    Discussion and Analysis of Financial Condition and Results of
    Operations -- Other Matters."
 
   
  Six Months Ended June 30, 1998 Compared to Six Months Ended June 30, 1997
    
 
   
     Natural gas and oil sales. Natural gas and oil sales increased 85% from
$3.9 million in the first six months of 1997 to $7.1 million in the first six
months of 1998. Of this increase, $6.6 million was attributable to an increase
in production, offset by $3.4 million was attributable to a decrease in the
average sales price for natural gas and oil. Production volumes for natural gas
increased 326% from 457 MMcf in the first six months of 1997 to 1,947 MMcf in
the first six months of 1998. The average price received for natural gas
decreased 20% from $2.62 per Mcf in the first six months of 1997 to $2.10 per
Mcf in the first six months of 1998. Production volumes for oil increased 82%
from 127 MBbls in the first six months of 1997 to 232 MBbls in the first six
months of 1998. The average price received for oil decreased 37% from $20.87 per
Bbl in the first six months of 1997 to $13.15 per Bbl in the first six months of
1998. Natural gas and oil sales were increased by production from wells
completed since the first six months of 1997 partially offset by the natural
decline of existing production, and from certain wells acquired from Ward
Petroleum in Grady County, Oklahoma which were included in the Company's results
of operations effective September 1, 1997. As a result of hedging activities,
natural gas revenues increased $38,700 for the first six months of 1998,
compared to a decrease in oil revenues of $6,191 for the first six months of
1997.
    
 
   
     Lease operating expenses. Lease operating expense increased 108% from
$470,000 in the first six months of 1997 to $978,000 in the first six months of
1998, while on a per unit of production basis, lease operating expenses for the
same periods decreased 26% from $.39 per Mcfe to $.29 per Mcfe. The increase in
lease operating expenses was primarily due to an increase in the number of
producing wells for the first six months of 1998 as compared with the same
period in 1997. The decrease in the per unit rate was primarily due to an
increase in natural gas production as a percentage of total equivalent
production (38% and 58% for the first six months of 1997 and 1998, respectively)
since a typical natural gas well produces with lower average lease operating
costs per unit of production than a typical oil well.
    
 
   
     Production taxes. Production taxes increased 106% from $219,000 ($.18 per
Mcfe) for the first six months of 1997 to $450,000 ($.13 per Mcfe) for the first
six months of 1998 as a direct result of increased production volumes. The
effective average production tax rate remained unchanged at 6% of natural gas
and oil sales revenues for the first six months of both 1997 and 1998.
    
 
   
     General and administrative expenses. General and administrative expenses
increased 58% from $1.5 million in the first six months of 1997 to $2.3 million
n the first six months of 1998. This increase was primarily attributable to the
hiring of additional employees to support the Company's increased level of
operational activities. Additionally, office rent, other office expenses and
costs related to the administration of a public corporation increased for the
first six months of 1998 as compared to the same period for 1997. On a per unit
of production basis, general and administrative expenses decreased 42% from
$1.19 per Mcfe for the first six months of 1997 to $.69 per Mcfe for the first
six months of 1998.
    
 
   
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 100% from $1.4 million ($1.14 per Mcfe) in the first
six months of 1997 to $2.8 ($.83 per Mcfe) in the first six months of 1998. Of
this net increase, $2.4 million was due to the increase in production volumes
which was offset by $1 million due to a 27% decrease in the depletion rate. The
depletion rate per unit of production decreased due to an increase in natural
gas and oil reserves at lower average capital costs.
    
 
   
     Interest expense. Net interest expense increased from $465,000 in the first
six months of 1997 to $2.4 million in the first six months of 1998. This
increase was primarily due to a higher average outstanding balance offset
partially by a lower effective interest rate. The weighted average outstanding
debt balance increased from $13.2 million in the first six months of 1997 to
$51.3 million in the first six months of 1998. The effective interest rate
increased 16% from 8.1% in the first six months of 1997 to 9.4% in the first six
months of 1998. In May 1997, the Company received $23.9 million for the sale of
shares of its common stock in a public offering. A portion of these proceeds
were used to repay the $13.3 million in debt outstanding at
    
 
                                       30
<PAGE>   32
 
   
that date. The increase in the average outstanding debt during the first six
months of 1998 compared to the same period for 1997 was due to increased capital
expenditures related to the Company's exploration activities during the first
six months of 1998 and the repayment of debt which occurred in the first six
months of 1997. The increase in the average outstanding debt balance was
primarily a result of increased capital expenditures related to the Company's
exploration activities. Interest expense increased an additional $266,000 for
the first six months of 1998 compared to the same period for 1997 due to the
amortization of deferred loan fees totaling approximately $1.9 million incurred
in connection with the establishment of the Credit Facility in January 1998. The
amortization of these deferred loan fees will continue to be recognized in the
amount of approximately $159,000 per quarter over the term of the Credit
Facility which matures in January 2001.
    
 
   
  Year Ended December 31, 1997 Compared to Year Ended December 31, 1996
    
 
     Natural gas and oil sales. Natural gas and oil sales increased 50% from
$6.1 million in 1996 to $9.2 million in 1997. Production volume increases
accounted for $3.2 million (104%) of this increase and were offset by $134,000
(4%) from a decrease in the average sales price received for natural gas and oil
sales. Production volumes for natural gas increased 98% from 698,036 Mcf in 1996
to 1,381,996 Mcf in 1997. The average price received for natural gas increased
11% from $2.30 per Mcf in 1996 to $2.56 per Mcf in 1997. Production volumes for
oil increased 28% from 226,925 Bbls in 1996 to 290,624 Bbls in 1997. The average
price received for oil decreased 3% from $19.98 per Bbl in 1996 to $19.40 per
Bbl in 1997. Natural gas and oil sales were increased by production from 46
wells completed in 1997, which was partially offset by the natural decline of
existing production. Hedging activities in 1997 reduced the amount by which oil
revenues increased by $6,191, compared to a decrease in oil revenues of $301,280
as a result of hedging activities in 1996.
 
   
     Workstation revenue. Workstation revenue increased 2% from $627,255 in 1996
to $636,702 in 1997. Workstation revenue is recognized by the Company as
industry participants in the Company's seismic programs are charged an hourly
rate for the work performed by the Company on its 3-D seismic interpretation
workstations. The Company expects workstation revenue to decline in 1998 due to
the Company increasing its working interest in the square miles of 3-D seismic
acquired beginning in 1997, reducing the net hours billed to its participants.
    
 
     Lease operating expenses. Lease operating expenses increased 59% from
$725,785 ($.35 per Mcfe) in 1996 to $1,151,238 ($.37 per Mcfe) in 1997. The
increase was primarily due to an increase in producing wells during the year.
 
     Production taxes. Production taxes increased 52% from $362,000 ($.18 per
Mcfe) in 1996 to $549,000 ($.18 per Mcfe) in 1997 as a direct result of
increased production volumes. The effective average production tax rate remained
unchanged at 6% of natural gas and oil sales revenues for each period.
 
     General and administrative expenses. General and administrative expenses
increased 62% from $2.2 million ($1.07 per Mcfe) in 1996 to $3.6 million ($1.14
per Mcfe) in 1997. Approximately $300,000 of the increase in 1997 resulted from
nonrecurring expenses related to the Company's relocation of its corporate
headquarters from Dallas, Texas to Austin, Texas, and the balance was primarily
attributable to the hiring of additional personnel and related expenses
necessary to manage the Company's growing operations. The increase in the per
unit rate was a result of a greater increase in aggregate general and
administrative expenses than natural gas and oil production volumes from 1996 to
1997 due to the aforementioned factors.
 
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 18% from $2.3 million ($1.13 per Mcfe) in 1996 to $2.7
million ($0.87 per Mcfe) in 1997 as a result of higher production volumes. The
per unit amount decreased due to the addition of proved reserves during 1997.
 
   
     Interest expense. Interest expense was essentially unchanged from 1996 to
1997 as the Company's lower average outstanding debt balance in 1997 was offset
by a higher effective average interest rate. The weighted average outstanding
debt balance decreased 39% from $19.7 million in 1996 to $12 million in 1997.
The effective interest rate increased 83% from 5.7% in 1996 to 10.5% in 1997.
The decrease in the weighted average outstanding debt balance and increase in
the effective average interest rate resulted primarily from the conversion to
equity of privately placed 5% notes (the "5% Notes") in February 1997, the
retirement of
    
 
                                       31
<PAGE>   33
 
$13.3 million of borrowings under its previous credit facility in connection
with the Company's May 1997 initial public offering, and $32 million of
borrowings incurred under its previous credit facility subsequent to the
Company's initial public offering to fund the Company's increased exploration
activity and its $13.5 million acquisition of properties from Mobil adjacent to
its West Bradley 3-D Project area. The Company's previous credit facility had an
effective interest rate of 8.8% at December 31, 1997.
 
  Year Ended December 31, 1996 Compared to Year Ended December 31, 1995
 
     Natural gas and oil sales. Natural gas and oil sales increased 72% from
$3.6 million in 1995 to $6.1 million in 1996. Of this increase, $2.0 million or
76% was attributable to an increase in production, and $607,894 or 24% was
attributable to an increase in the average sales price received for natural gas
and oil. Production volumes for natural gas increased 157% from 271,707 Mcf in
1995 to 698,036 Mcf in 1996. The average price received for natural gas
increased 42% from $1.62 per Mcf in 1995 to $2.30 per Mcf in 1996. Production
volumes for oil increased 28% from 176,693 Bbls in 1995 to 226,925 Bbls in 1996.
The average price received for oil increased 13% from $17.76 per Bbl in 1995 to
$19.98 per Bbl in 1996. Natural gas and oil sales were increased by production
from 42 wells completed in 1996, which was partially offset by the sale of
certain producing properties in January 1996 and the natural decline of existing
production. Hedging activities in 1996 reduced the amount by which oil revenues
increased by $301,280, compared to an increase in oil revenues of $40,849 as a
result of hedging activities in 1995.
 
     Workstation revenue. Workstation revenue decreased 1% from $635,401 in 1995
to $627,255 in 1996, primarily as a result of a decrease in the rate at which
3-D seismic was acquired in 1995 and interpreted in 1996.
 
     Lease operating expenses. Lease operating expenses decreased 5% from
$760,784 ($.57 per Mcfe) in 1995 to $725,785 ($.35 per Mcfe) in 1996. The
decrease was primarily due to the sale of certain producing properties in
January 1996 partially offset by an increase in producing wells. The decrease in
the per unit rate was a result of the sale of higher cost oil wells in January
1996 and an increase in the percentage of production from natural gas wells.
 
     Production taxes. Production taxes increased 119% from $165,000 ($.12 per
Mcfe) in 1995 to $362,000 ($.18 per Mcfe) in 1996 primarily as a result of
increased production volumes. The effective average production tax rate
increased from 4.6% in 1995 to 6% in 1996, reflecting the increased percentage
of total production attributable to natural gas, which is taxed at a higher
effective rate than oil.
 
     General and administrative expenses. General and administrative expenses
increased 16% from $1.9 million ($1.42 per Mcfe) in 1995 to $2.2 million ($1.07
per Mcfe) in 1996. Approximately $110,000 of the increase in 1996 resulted from
salary increases for employees, and the remainder was primarily attributable to
an increase in third-party consulting fees. The decrease in the per unit rate
was a result of the increase in natural gas and oil production from 1995 to
1996.
 
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 43% from $1.6 million ($1.22 per Mcfe) in 1995 to $2.3
million ($1.13 per Mcfe) in 1996 as a result of higher production volumes.
 
     Interest expense. Interest expense increased 25% from $936,266 in 1995 to
$1.2 million in 1996. This increase was due to a higher average outstanding debt
balance in 1996, which was partially offset by a lower effective interest rate.
The weighted average outstanding debt balance increased 71% from approximately
$11.5 million in 1995 to $19.7 million in 1996. The effective interest rate
decreased 25% from 7.6% in 1995 to 5.7% in 1996. The increase in the weighted
average outstanding debt balance and decrease in the effective interest rate
resulted primarily from the retirement of privately placed 10% notes (the "10%
Notes") and the issuance of $16 million in principal amount of 5% Notes in
August 1995.
 
LIQUIDITY AND CAPITAL RESOURCES
 
     The Company's primary sources of capital have been its revolving credit
facility and other debt borrowings, public and private equity financing, the
sale of interests in projects and funds generated by
 
                                       32
<PAGE>   34
 
operations. The Company's primary capital requirements are 3-D seismic and land
acquisition costs and drilling expenditures.
 
     Revolving Credit Facilities. In April 1996, the Company entered into a
revolving credit facility. This facility had a three-year term and was subject
to certain borrowing base limitations. The Company had borrowings outstanding
under this credit facility of $32 million as of December 31, 1997. The Company
retired this credit facility in January 1998 with borrowings under its Credit
Facility (as defined).
 
   
     In January 1998, Brigham entered into a new reserve-based credit agreement
(the "Credit Facility"). The Credit Facility's current borrowing base of $75
million will be reduced to $65 million upon issuance of the Notes. On January
31, 1999, the borrowing base will be redetermined by the bank based on the
Company's then proved reserve value. The Company, at its option, can have the
availability under the facility redetermined based on its current proved reserve
value at any time prior to January 31, 1999. Principal outstanding under the
Credit Facility is due at maturity on January 26, 2001 with interest due
monthly. The interest rate for borrowings under the Credit Facility is either
the lender's base rate or LIBOR plus 2.25%, at the Company's option. Borrowings
under the facility currently bear interest at an annual rate of approximately
8.6%. The Company's obligations under the Credit Facility are secured by
substantially all of the natural gas and oil properties of the Company. See Note
5 of Notes to the December 31, 1997 Consolidated Financial Statements. The
Company used a portion of the funds available under the Credit Facility to repay
the $32 million in borrowings outstanding at December 31, 1997 under its
previous credit facility.
    
 
   
     The proceeds of the Offering will be used to fund partially the Company's
planned capital expenditures and in the interim for repayment of outstanding
indebtedness under the Credit Facility.
    
 
   
     The terms of the Notes will permit the Company to borrow under the Credit
Facility, up to the lesser of $75 million or the Credit Facility borrowing base.
    
 
   
     The Company believes that through the foreseeable future it will be able to
comply with the financial covenants contained in the Credit Facility. These
covenants include a minimum interest coverage ratio that the Company's lender in
May 1998 amended following a determination that the Company did not meet for the
first quarter of 1998 and would not meet for the second quarter of 1998 the
covenant as originally formulated. In connection with the issuance of the Notes,
the Company's lender will further amend the Credit Facility covenants to
accommodate the Notes. In the event that the Company in the future cannot meet a
covenant, no assurance can be given that its lender will amend the covenant or
waive compliance.
    
 
  Cash Flow Analysis
 
   
     Cash Flows from Operating Activities. Cash flows provided by operating
activities were $9.8 million in 1997, $3.7 million in 1996, and $1.4 million in
1995. The increase in cash flows for 1997 compared to 1996 was due primarily to
an increase in natural gas and oil revenues, net of lease operating expenses,
production taxes and general and administrative expenses, and changes in balance
sheet items. The increase in cash flows for 1996 compared to 1995 was due
primarily to an increase in natural gas and oil revenues, net of lease operating
expenses, production taxes and general and administrative expenses. In the first
six months of 1998, cash flow used by operations was $1.7 million primarily as a
result of the net effects of increased natural gas and oil revenues, net of
production taxes, lease operating expenses, general and administrative expenses
and interest expenses, and an increase in working capital components.
    
 
     Cash Flows from Investing Activities. Cash flows used in investing
activities increased to $57.3 million in 1997 compared to $11.8 million in 1996
and $8.0 million in 1995. These increases are directly related to an increase in
capital expenditures. Capital expenditures were $57.2 million in 1997, $13.6
million in 1996 and $7.9 million in 1995. The Company acquired 1,243 gross (845
net) square miles of 3-D seismic in 1997, 655 gross (241 net) square miles in
1996, and 311 gross (90 net) square miles in 1995. The Company's drilling
efforts resulted in the successful completion of 46 wells (17.6 net) in 1997, 42
wells (8.7 net) in 1996 and 46 wells (9.9 net) in 1995, which resulted in
aggregate net increases in proved reserve volumes of 38.1 Bcfe in 1997, 13.7
Bcfe in 1996 and 8.9 Bcfe in 1995. In addition, the Company sold certain
producing properties in 1996 for $2.1 million and acquired certain producing
properties and related interests in 1997 for
 
                                       33
<PAGE>   35
 
   
$13.5 million. Cash flow used in investing activities was $30.9 million in the
first six months of 1998 primarily as a result of capital expenditures related
to exploration activities.
    
 
   
     Cash Flows from Financing Activities. Cash flows from financing activities
for 1997 were $47.7 million, primarily as a result of borrowings under the
Company's previous credit facility and proceeds from the common stock sold in
the Company's initial public offering. Cash flows from financing activities for
1996 were $7.7 million, primarily as a result of borrowings under the Company's
previous credit facility. Cash flows from financing activities for 1995 were
$7.7 million, primarily as a result of the issuance of the 5% Notes offset by
the net repayment of the $7.9 million outstanding balance on the 10% Notes. Cash
flows from financing activities for the first six months of 1998 were $34
million, net of deferred loan fees of $1.9 million, primarily as a result of an
increase in borrowings under the Credit Facility to fund the difference between
cash flow from operations and cash flow from investing activities.
    
 
  Capital Expenditures
 
   
     The Company currently estimates that its net capital expenditures in 1998
will be approximately $59 million. The Company expects to incur these capital
expenditures primarily to drill 90 gross (45 net) planned wells, to acquire
approximately 1,300 gross (925 net) square miles of 3-D seismic and to continue
to add to and upgrade its 3-D seismic interpretation hardware and software. The
actual number of wells drilled, square miles acquired and costs incurred may
differ significantly from these estimates. See "Business and
Properties -- Primary Exploration Provinces."
    
 
   
     Due to the Company's active 3-D seismic acquisition and drilling programs,
the Company has experienced and expects to continue to experience substantial
working capital requirements. While the Company believes that the net proceeds
of the Offering, cash flow from operations, borrowings under the Credit Facility
and proceeds expected to be received from potential sales of interests in
certain of its seismic projects to industry participants should allow the
Company to finance its operations at least through 1998 based on current
conditions, additional financing may be required in the future to fund the
Company's 3-D seismic acquisition and drilling programs. In the event additional
financing is not available, the Company may be required to curtail these
activities.
    
 
OTHER MATTERS
 
  Hedging Activities
 
     The Company believes that hedging, although not free of risk, allows the
Company to reduce its exposure to natural gas and oil sales price fluctuations
and thereby to achieve more predictable cash flows. However, hedging
arrangements, when utilized, limit the benefit to the Company of increases in
the prices of the hedged commodity. Moreover, the Company's hedging arrangements
apply only to a portion of its production and provide only partial price
protection against declines in commodity prices. The Company expects that the
amount of its hedges will vary from time to time. See "Risk Factors -- Risk of
Hedging Activities."
 
     In 1995 the Company, in an attempt to reduce its sensitivity to volatile
commodity prices, began using crude oil swap arrangements resulting in a fixed
price over a period of six months. Total oil purchased and sold subject to swap
arrangements entered into by the Company was 118,150 Bbls in 1996 and 54,900
Bbls in 1995. The Company accounts for all these transactions as hedging
activities and, accordingly, adjusts the price received for natural gas and oil
production during the period the hedged transactions occur. Adjustments to the
price received for oil under these swap arrangements resulted in an increase in
oil revenues of $40,849 in 1995 and decreases in oil revenues of $301,280 in
1996 and $6,191 in 1997. As of December 31, 1997, the Company had no hedging
contracts outstanding.
 
     In February 1998, the Company entered into a hedging contract whereby
10,000 MMBtu per day of natural gas is purchased and sold subject to a fixed
price swap agreement for monthly periods from April 1998 through October 1999.
Pursuant to these arrangements the Company exchanges a floating market price for
a fixed contract price. Payments are made by the Company when the floating price
exceeds the fixed price for a contract month and payments are received when the
fixed price exceeds the floating price. Settlements on
 
                                       34
<PAGE>   36
 
   
these swaps are based on the difference between the ANR Pipeline Co.-Oklahoma
index price (as published in Inside FERC's Gas Market Report) for a contract
month and the fixed contract price for the same month. Total natural gas subject
to this hedging contract is 2,750,000 MMBtu in 1998 and 3,040,000 MMBtu in 1999.
As a result of this natural gas hedging contract, the Company realized an
increase in revenues of $38,700 in the three months ended June 30, 1998.
    
 
  Effects of Inflation and Changes in Prices
 
     The Company's results of operations and cash flows are affected by changing
natural gas and oil prices. If the price of natural gas and oil increases
(decreases), there could be a corresponding increase (decrease) in revenues as
well as the operating costs that the Company is required to bear for operations.
Inflation has had a minimal effect on the Company.
 
  Environmental and Other Regulatory Matters
 
     The Company's business is subject to certain federal, state and local laws
and regulations relating to the exploration for and the development, production
and marketing of natural gas and oil, as well as environmental and safety
matters. Many of these laws and regulations have become more stringent in recent
years, often imposing greater liability on a larger number of potentially
responsible parties. Although the Company believes it is in substantial
compliance with all applicable laws and regulations, the requirements imposed by
laws and regulations are frequently changed and subject to interpretation, and
the Company is unable to predict the ultimate cost of compliance with these
requirements or their effect on its operations. Any suspensions, terminations or
inability to meet applicable bonding requirements could materially adversely
affect the Company's financial condition and operations. Although significant
expenditures may be required to comply with governmental laws and regulations
applicable to the Company, compliance has not had a material adverse effect on
the earnings or competitive position of the Company. Future regulations may add
to the cost of, or significantly limit, drilling activity. See "Risk
Factors -- Compliance with Environmental Regulations," "Business and
Properties -- Governmental Regulation" and "Business and
Properties -- Environmental Matters."
 
  Year 2000 Issues
 
   
     The Company has reviewed the effect of the Year 2000 issues relating to its
information systems. The Company has determined that the Year 2000 issues
directly related to its information systems will not have a material impact on
its business, operations nor its financial position. However, the Company cannot
determine what effect, if any, the Year 2000 issues affecting its vendors,
customers, other businesses and the numerous local, state, federal and other
U.S. governmental entities with which it conducts business or by which it is
regulated or governed or taxed will have on its business or financial position.
See "Risk Factors -- Year 2000 Compliance."
    
 
  Recent Accounting Pronouncements
 
   
     In June 1997, the Financial Accounting Standards Board (the "FASB") issued
SFAS No. 130, "Reporting Comprehensive Income," and SFAS No. 131, "Disclosure
about Segments of an Enterprise and Related Information." Neither of these
standards is expected to have a material impact on the Company.
    
 
   
     In June 1998, the FASB issued SFAS No. 133, "Accounting for Derivative
Instruments and Hedging Activities," which is effective for fiscal years
beginning after June 15, 1999. The Company is currently assessing the impact
adoption of this standard will have on its balance sheet and statement of
operations.
    
 
                                       35
<PAGE>   37
 
                            BUSINESS AND PROPERTIES
 
   
     Brigham is an independent exploration and production company that applies
3-D seismic imaging and other advanced technologies to systematically explore
and develop onshore domestic natural gas and oil provinces. The Company focuses
its 3-D seismic activity in provinces where it believes 3-D technology may be
effectively applied and which Brigham believes offer relatively large potential
reserve volumes per well and per field, high potential production rates and
multiple producing objectives. The Company's exploration activities are
concentrated primarily in three core provinces: the Anadarko Basin of western
Oklahoma and the Texas Panhandle; the onshore Gulf Coast of Texas and Louisiana;
and West Texas. Brigham is accelerating its 3-D seismic and drilling activities
in the Anadarko Basin and the Gulf Coast and is selectively focusing its
activities in those geologic trends of West Texas where it has achieved its best
historical results.
    
 
     The Company pioneered the acquisition of large scale onshore 3-D seismic
surveys for exploration, obtaining extensive 3-D seismic data and experience in
capturing undiscovered natural gas and oil reserves. Through December 31, 1997,
Brigham had acquired 4,005 square miles (2.6 million acres) of 3-D seismic and
identified 1,170 potential drilling locations, of which the Company had drilled
370. The Company generates most of its exploratory projects and, therefore, has
the ability to retain a sizeable working interest to the extent that it decides
not to place interests with industry participants.
 
     From inception in 1990 through 1997, Brigham had drilled 324 exploratory
and 46 development wells on its 3-D seismic generated prospects with an
aggregate 63% success rate and an average working interest of 24%. Utilizing the
capital it raised in its May 1997 initial public offering, the Company increased
the average working interest it retained in its wells during the second half of
1997, retaining a 45% average working interest in the 36 wells that it drilled.
As of December 31, 1997, the Company had added approximately 93 Bcfe of net
proved reserves (excluding revisions) to its reserve base, approximately 72 net
Bcfe of which were discovered by Brigham through its systematic 3-D seismic
exploration drilling activities. The Company's estimated net proved reserves as
of December 31, 1997 were 72.3 Bcfe having an aggregate Present Value of Future
Net Revenues of $69.2 million, compared to estimated net proved reserves as of
December 31, 1996 of 21.9 Bcfe having an aggregate Present Value of Future Net
Revenues of $44.5 million. The Company's net proved reserve volumes at December
31, 1997 were 74% natural gas and 65% categorized as proved developed reserves.
 
BUSINESS STRATEGY
 
     Brigham's business strategy is to achieve superior growth in shareholder
value through the application of its systematic exploration approach, which
emphasizes the integrated use of 3-D seismic imaging and other advanced
technologies to reduce drilling risks and finding costs. Since its inception in
1990, the Company has consistently achieved rapid growth in its acquisition of
3-D seismic data, identification of potential drilling locations, discovery of
proved reserves and production volumes.
 
     Brigham completed its initial public offering of common stock in May 1997,
raising approximately $24 million to fund the Company's accelerated 3-D seismic
acquisition and exploration drilling activities. Key elements of the Company's
growth strategy at its initial public offering and continuing today include: (i)
accelerating the rate at which it acquires 3-D seismic and identifies potential
drilling locations; (ii) increasing the working interests it retains in
exploration projects to capture a greater share of the reserves that the Company
discovers; (iii) identifying higher potential, higher impact prospects; and (iv)
accelerating the rate at which its 3-D seismic defined locations are drilled.
 
     During the second half of 1997, the Company employed the capital raised in
its initial public offering to attain significant growth in each of its core
strategic objectives:
 
          Accelerated 3-D Seismic Acquisition. During 1997, Brigham acquired
     approximately 1,250 square miles of 3-D seismic, which increased the
     Company's aggregate 3-D seismic inventory 45% to approximately 4,000 square
     miles as of December 31, 1997. The overall level of 3-D seismic acquisition
     in 1997 represents the most active year in the Company's history, and 85%
     of this increased 3-D seismic was acquired in its higher potential Anadarko
     Basin and Gulf Coast provinces.
 
                                       36
<PAGE>   38
 
          Increased Working Interest. In an effort to retain a greater portion
     of the value generated by its 3-D seismic exploration efforts, Brigham
     increased the average working interest it retained in its 1997 3-D seismic
     projects to 68% as compared with its average project working interest of
     24% in 1990 through 1996. As a result of the higher working interests and
     the accelerated acquisition of 3-D seismic, the Company acquired 845 net
     square miles of 3-D seismic in 1997 as compared with 780 cumulative net
     square miles acquired from 1990 through 1996.
 
          Higher Potential, Higher Impact Prospects. By focusing an increasing
     portion of its exploration activities in the more prolific Anadarko Basin,
     Brigham increased its average proved reserves discovered per net well
     drilled (including dry holes) to 1.2 Bcfe in 1997 from 0.7 Bcfe in 1996 and
     0.4 Bcfe in 1992 through 1995. In the Anadarko Basin alone, Brigham's
     average proved reserves discovered per net well drilled was 3.4 Bcfe in
     1997 compared with 1.8 Bcfe in 1996 and 2 Bcfe in 1994 through 1995.
     Contributing to these increases, the Company's Anadarko Basin drilling in
     1997 produced the two largest field discoveries in Brigham's history, which
     resulted in the discovery of approximately 52 Bcfe of gross proved reserves
     and provided the Company with several development drilling opportunities.
 
          Accelerated Drilling. Through its strategy of retaining higher working
     interests in its 3-D projects and subsequent drilling, Brigham participated
     in the drilling of 28 net wells in 1997, a 75% increase from the
     approximate 16 net wells drilled by the Company in 1996. The Company
     achieved a 63% success rate on the 73 wells in its 1997 drilling program,
     consistent with Brigham's historical average success rate. A key factor
     contributing to its increased level of drilling activity was the Company's
     addition of personnel in engineering, land and administrative functions
     during 1997. These staff additions provided Brigham with the additional
     infrastructure required to increase its operating capabilities, enabling
     the Company operate 37% of its gross wells and 64% of its net wells drilled
     in 1997.
 
     As a result of the combined effects of the Company's multi-pronged growth
strategy, Brigham generated net proved reserve additions of approximately 38
Bcfe through drilling in 1997, which represents approximately 175% of the
Company's year-end 1996 net proved reserves of approximately 22 Bcfe. In
addition to its drilling efforts in 1997, the Company acquired 21.5 Bcfe of net
proved reserves at an implied cost of $0.63 per proved Mcfe in its November 1997
purchase of certain properties in and adjacent to its West Bradley project area
in its Anadarko Basin province. Brigham believes this acquisition will enable it
to further build its inventory of potential drilling locations over the
historically prolific Carter Knox anticline in the Anadarko Basin through a 3-D
seismic shoot planned for 1998.
 
   
     Primarily through its exploration efforts, the Company increased its net
production volumes 52% to 3.1 Bcfe in 1997 from 2.1 Bcfe in 1996. As further
evidence of the Company's acceleration efforts subsequent to its May 1997
initial public offering, Brigham increased its average net daily production
volumes from 6.6 MMcfe in the second quarter 1997 to 21.2 MMcfe in the second
quarter 1998 representing a compounded growth rate of 34% per quarter.
    
 
   
     Based on the results that the Company has achieved from its growth strategy
since its initial public offering, Brigham intends with the proceeds from the
Offering to increase its exploration activities in 1998 to take advantage of
opportunities currently available to further accelerate the Company's growth.
The Company's current 1998 capital budget contemplates (i) an increase in
budgeted drilling expenditures in the Anadarko Basin and the Gulf Coast
provinces, (ii) a reduction in planned drilling activity in West Texas in part
due to recent declines in oil prices, (iii) an increase in planned 3-D seismic
acquisition activities in an effort to capture additional exploration prospects
for future drilling activities and (iv) potential sales of a portion of the
Company's interests in certain seismic projects. The Company intends to continue
to retain higher working interests in its 3-D seismic projects in the Anadarko
Basin and the onshore Gulf Coast. By increasing its working interests retained
in the majority of its current and planned seismic projects, Brigham expects to
further accelerate its growth not only by retaining a greater portion of the
reserves its discovers, but also by increasing its ability to control the timing
of the drilling of its exploration projects and therefore helping to accelerate
its drilling pace. The Company's current 1998 budget consists of 90 gross (45
net) wells, compared with the 73 gross (28 net) wells drilled by the Company in
1997. This increase in anticipated 1998
    
 
                                       37
<PAGE>   39
 
   
drilling is the result of an increase in planned drilling of higher working
interest wells in the Anadarko Basin and the Gulf Coast offset by a reduction in
planned drilling activity in West Texas.
    
 
COMPETITIVE ADVANTAGES
 
     Brigham believes that its knowledge base, personnel and technology provide
it with the following competitive advantages to capture undiscovered natural gas
and oil reserves.
 
          3-D Seismic Knowledge Base. The Company began acquiring 3-D seismic in
     1990 and drilled its first 3-D delineated well, which was a discovery, in
     February 1991. From inception through 1997, the Company has acquired 4,005
     square miles of 3-D seismic and drilled 370 wells in over 20 geologic
     trends in seven basins and seven states. As a result, the Company has
     gained extensive technological and economic knowledge relating to the
     application of 3-D seismic to different geologic trends. This experience
     and knowledge enable the Company to refine its exploration techniques and
     identify exploration areas where Brigham believes 3-D seismic can be
     applied to reduce risks and enhance returns on its investments.
 
   
          Technological Expertise. Led by its CEO, who is an experienced,
     practicing geophysicist, the Company has built an exploration staff that
     includes nine other geophysicists and ten geologists. Brigham's
     explorationists collectively have approximately 300 years of experience,
     including approximately 85 years of experience using CAEX workstations, and
     have expertise in many geologic trends. The Company makes extensive use of
     advanced technologies, including 3-D seismic imaging and CAEX and in-house
     analytical and processing capabilities, to define drilling prospects. To
     support the efforts of its explorationists, Brigham has invested in
     advanced hardware and software, including 20 UNIX-based CAEX workstations.
    
 
          Project Generation and Control. Brigham is not dependent on third
     parties for its project flow, having generated approximately 90% of its 3-D
     seismic exploration projects through the acquisition of proprietary
     seismic. Therefore, the Company is able to manage the predrilling
     exploration phases, from project conception and assemblage through 3-D
     seismic acquisition, processing and interpretation and subsequent leasing.
     Brigham believes that its management of the exploration process enhances
     project quality and compresses the cycle time, contributing to lower
     finding and development costs and an enhanced project rate of return.
     Furthermore, the Company can determine the level of working interest it
     retains and the extent to which it manages drilling and post-drilling
     operations and continues to expand its efforts in these areas.
 
   
          Numerous Potential Drilling Locations. As of December 31, 1997, the
     Company had identified 1,170 3-D defined potential drilling locations in
     historically productive geologic trends, of which 370 had been drilled. The
     Company currently anticipates drilling 90 of these locations (45 net) in
     1998 at an aggregate drilling cost of approximately $40 million. The
     Company also anticipates net expenditures for seismic and land in 1998 of
     approximately $13.5 million, including the acquisition of approximately
     1,300 gross (925 net) square miles of 3-D seismic. The Company continually
     evaluates and prioritizes potential drilling locations to determine whether
     to drill them, farm them out or replace them with higher quality locations.
    
 
          Pioneering Innovations.  In 1990 the Company pioneered the assemblage
     of large scale onshore 3-D seismic projects and the use of preseismic lease
     options for the systematic exploration of proven natural gas and oil
     provinces. The Company believes it was one of the first to form alliances
     and joint participation arrangements with companies and individuals
     possessing extensive local geologic or operating expertise to complement
     its 3-D seismic exploration expertise. Subsequent innovations include the
     Company's 3-D seismic acquisition and processing alliances and its creative
     industry trade structures to financially leverage its drilling program.
 
                                       38
<PAGE>   40
 
EXPLORATION AND OPERATING APPROACH
 
     From inception through December 31, 1997, the Company had acquired 3-D
seismic in 119 projects covering 4,005 square miles (2.6 million acres) in 20
geologic trends in seven basins and seven states. Through this activity, the
Company has developed expertise in the selection of geologic trends that are
suitable for 3-D seismic exploration. Brigham uses experience that it gains
within a trend to enhance the quality of subsequent projects in the same trend
and other analogous trends, contributing to lower finding and development costs,
compressing project cycle times and increasing project rates of return.
 
     The Company typically acquires 3-D seismic in and around existing
production where the Company can benefit from the imaging of producing analogs.
These 3-D seismic defined analogs, combined with the Company's experience in
drilling 370 wells, provide the Company with a knowledge base to evaluate other
potential geologic trends, 3-D seismic projects within trends and 3-D seismic
delineated potential drilling locations. The Company's knowledge base assists in
identifying geologic trends where Brigham believes it can find and develop
economic volumes of natural gas and oil.
 
     The Company has experience exploring with 3-D seismic in a wide range of
reservoir types and geologic trapping styles, both stratigraphic and structural
(including reefs, salt domes, channel sands, complex faulted and fractured
reservoirs and pinchout plays). The Company seeks to supplement its knowledge
base with local geologic expertise for a particular geologic trend by hiring new
explorationists, engaging consultants and entering into joint ventures with
industry participants. In addition, if the targeted geologic trend is extensive,
the Company typically acquires a digital data base for integration on the
Company's CAEX workstations, including digital land grids, well information, log
curves, production information, geologic studies, geologic top data bases and
existing 2-D seismic.
 
     The Company uses its knowledge base, local geological expertise and
acquired digital data bases, integrated with 3-D seismic, to create maps of
producing reservoirs. The Company believes its 3-D generated maps are more
accurate than previous reservoir maps used by the industry (which generally were
based on subsurface geological information and 2-D seismic surveys), enabling
the Company to better evaluate recoverable reserves and the economic feasibility
of projects and drilling locations.
 
     Brigham acquires most of its raw 3-D seismic on a proprietary basis using
seismic acquisition vendors. Additionally, the Company acquires data through
alliances affording it the exclusive right to interpret and use data for
extended periods of time. Occasionally the Company participates in
non-proprietary group shoots of 3-D seismic. In its proprietary acquisitions and
alliances, Brigham selects the sites of projects, primarily guided by its
knowledge and experience in the core provinces it explores; establishes and
monitors the seismic parameters of each project for which data is shot; and
typically selects the equipment that will be used. Data is generally priced on
the basis of square miles shot. See "Business and Properties -- Industry
Alliances."
 
PRIMARY EXPLORATION PROVINCES
 
   
     Brigham's exploration activities are concentrated primarily in three core
provinces: the Anadarko Basin of western Oklahoma and the Texas Panhandle; the
onshore Gulf Coast of Texas and Louisiana; and West Texas. Brigham is
accelerating 3-D seismic activity in the Anadarko Basin and the Gulf Coast and
will selectively continue such activity in those geologic trends of the West
Texas region where it has achieved its best results historically. Brigham is
focusing its 3-D seismic exploration efforts in provinces where it believes 3-D
technology may be effectively applied and which the Company believes offer
relatively large potential reserve volumes per well and per field, high
potential production rates and multiple producing objectives.
    
 
     Although the Company is acquiring 3-D seismic within the provinces listed
below and has identified approximately 800 potential drilling locations yet to
be drilled in those provinces, there can be no assurance that any of the seismic
will be acquired or will generate additional drilling locations or that any
potential drilling locations will be drilled at all or within the expected time
frame. The final determination with respect to the drilling of any well,
including those currently budgeted, will depend on a number of factors,
including (i) the results of exploration efforts and the review and analysis of
the seismic, (ii) the availability of sufficient capital resources by the
Company and other participants for drilling prospects, (iii) economic and
industry
 
                                       39
<PAGE>   41
 
conditions at the time of drilling, including prevailing and anticipated prices
for natural gas and oil and the availability of drilling rigs and crews, (iv)
the financial resources and results of the Company and (v) the availability of
leases on reasonable terms and permitting for the potential drilling location.
There can be no assurance that the budgeted wells will, if drilled, encounter
reservoirs of commercial quantities of natural gas or oil.
 
   
<TABLE>
<CAPTION>
                             3-D SEISMIC                                                    CURRENT 1998 CAPITAL BUDGET(1)
                                 DATA                                                --------------------------------------------
                              ACQUIRED/       3-D SEISMIC                UNDRILLED                             CAPITAL
                             INTERPRETED          DATA         GROSS     POTENTIAL                        EXPENDITURES($MM)
                                AS OF         BUDGETED TO      WELLS     DRILLING       WELLS       -----------------------------
                               12/31/97      BE ACQUIRED IN   DRILLED    LOCATIONS     BUDGETED       NET
                              (GROSS SQ.      1998 (GROSS     THROUGH      AS OF     ------------   SEISMIC     NET
PROVINCE                        MILES)         SQ. MILES)     12/31/97   12/31/97    GROSS   NET    & LAND    DRILLING   TOTAL(2)
--------                    --------------   --------------   --------   ---------   -----   ----   -------   --------   --------
<S>                         <C>     <C>      <C>              <C>        <C>         <C>     <C>    <C>       <C>        <C>
Anadarko Basin............   1,515/ 1,195          660           55         364        55    28.8    $12.5     $26.5      $39.0
Gulf Coast................     566/ 325            600           11         110        20     9.5     (0.5)     10.5       10.0
West Texas................   1,649/ 1,600           40          287         302        14     6.5      1.5       2.8        4.3
Others(3).................     275/ 275             --           17          24         1     0.2       --       0.2        0.2
                            ------- ------       -----          ---         ---       ---    ----    -----     -----      -----
        Total.............   4,005/ 3,395        1,300          370         800        90    45.0    $13.5     $40.0      $53.5
                            ======= ======       =====          ===         ===       ===    ====    =====     =====      =====
</TABLE>
    
 
---------------
 
   
(1) Prepared as of August 10, 1998.
    
 
   
(2) Net 3-D seismic and land acquisition costs and drilling expenditures.
    
 
(3) Colorado, Kansas and Montana.
 
     Anadarko Basin. The Anadarko Basin is a prolific natural gas province that
the Company believes has been relatively under explored, particularly with
regard to deep, high potential objectives. The Anadarko Basin contains numerous
historically elusive stratigraphic targets, such as the Red Fork, Morrow and
Springer channel sands, and structural targets, such as the Hunton and Arbuckle
carbonates, which are well-suited to 3-D seismic imaging. In some cases, these
objectives have produced in excess of 30 Bcf of natural gas from a single well
at rates up to 30 MMcf of natural gas per day.
 
     The Company has assembled an extensive digital data base in this province,
including geologic studies, basin wide geologic tops, production data, well
data, geographic data and over 8,400 miles of 2-D seismic. Working with its team
of in-house geologists and supplemented by consulting geologists, the Company's
explorationists integrate this data with their extensive expertise and knowledge
base to generate 3-D seismic projects in the Anadarko Basin.
 
   
     Over the last several years the Company has accelerated its 3-D seismic
acquisition activity in the Anadarko Basin, acquiring 195 square miles in 1995,
457 square miles in 1996 and 648 square miles in 1997. The Company retained a
66% average working interest in the 3-D seismic it acquired in this province in
1997. The Company believes its increased level of activity in the Anadarko Basin
will be a significant factor in the Company's growth. As of December 31, 1997,
the Company had acquired or was acquiring 1,515 square miles (969,600 acres) in
30 projects in the Anadarko Basin. The Company anticipates acquiring 660 square
miles (422,400 acres) of additional 3-D seismic in this province in 1998.
    
 
   
     As of December 31, 1997, Brigham had completed 44 wells in 55 attempts (80%
success rate) in the Anadarko Basin and had found cumulative proved reserves of
44 net Bcfe. In 1997, the Company completed 19 wells in 23 attempts in its
Anadarko Basin province with an average working interest of 39%, adding 31 net
Bcfe of proved reserves. In addition, the Company acquired 21.5 net Bcfe of
proved reserves in this region in November 1997. As of December 31, 1997, the
Company had 364 3-D delineated potential drilling locations in the Anadarko
Basin, of which the Company intends to drill 55 gross (29 net) wells in 1998.
    
 
     Brigham's Anadarko Basin activity provides a blend of intermediate depth,
moderate risk objectives and deeper, higher potential but somewhat higher risk
objectives. The intermediate depth targets at 9,000 to 13,000 feet have provided
Brigham with good drilling results to date. These include the Upper Morrow
channel sands and the Lower Morrow shallow marine sands of the Texas Panhandle,
the Springer channels of
 
                                       40
<PAGE>   42
 
the Watonga Chikasha trend of western Oklahoma, and structural traps in the
Hunton carbonates of the northeastern portion of the Anadarko Basin.
 
   
     Intermediate depth objectives in the Anadarko Basin can provide significant
reserve additions, as evidenced by Brigham's Lower Morrow discovery in its
Pistol Pete 3-D seismic project. In late 1997, the Brigham-operated Christopher
84 #1 (36% Brigham working interest) was completed in one of four apparently
productive Lower Morrow zones at approximately 12,000 feet, and initially tested
at 2.65 MMcfe per day with a flowing tubing pressure of 1,800 pounds per square
inch. This well was producing approximately 4 MMcfe per day with a flowing
tubing pressure of 2,750 pounds per square inch at the end of July 1998. The
Company has drilled two offset wells to the Christopher 84 #1 discovery during
1998. The first of these offsets, the Brigham-operated Madison 85 #1 (36%
Brigham working interest), was completed and is currently producing 1.1 MMcf of
natural gas per day from the sand common to the producing zone in the
Christopher 84 #1. The second offset well, the Brigham-operated Alexander 70 #1
(91% Brigham working interest), was drilled and found the producing objective to
be tight, resulting in a dry hole. The Company plans to drill at least two
additional tests of this structure during the balance of 1998.
    
 
   
     The deeper Anadarko Basin objectives provided Brigham's first significant
Hunton formation discovery, the Brigham-operated Weise 28 #1 (33% Brigham
working interest), in its Jayhawk 3-D seismic project in Wheeler County, Texas.
Drilled to a total depth of approximately 14,800 feet, the Weise 28 #1 tested an
initial production rate of 6.1 MMcfe per day. This well was producing
approximately 2 MMcf of natural gas and 20 barrels of condensate per day with a
flowing tubing pressure of 900 pounds per square inch at the end of July 1998. A
development well to the Weise 28 #1 discovery, the Brigham-operated Amelia 31 #1
(36% Brigham working interest), has been drilled and is currently completing.
Brigham plans to drill several higher potential tests in the deeper portions of
the Anadarko Basin primarily in the Texas Panhandle and far western Oklahoma in
1998.
    
 
   
     On November 12, 1997, Brigham acquired an interest in producing properties
and undeveloped acreage at the northern end of the Carter Knox anticline in
Grady County, Oklahoma (the "Chitwood Acquisition"). For $13.5 million, Brigham
acquired estimated net proved reserves totaling 21.3 Bcfe and received a 50%
working interest in 3,600 net acres of leasehold and 750 net mineral acres in
the Chitwood Acquisition. The properties were acquired from Mobil Oil
Corporation through Ward Petroleum Corporation ("Ward"), and Ward will act as
drilling operator. Brigham and Ward are currently participating in an
approximately 130 square mile 3-D seismic in this area to delineate
opportunities in the Springer, Big Four, Bromide and Arbuckle formations. The
Chitwood Acquisition overlaps and is adjacent to Brigham's West Bradley 3-D
Seismic Project, where Ward operates the majority of the drilling operations.
    
 
     Gulf Coast. The onshore Gulf Coast region of South Texas and South
Louisiana is a high potential, multi-pay province that lends itself to 3-D
seismic exploration due to its substantial structural and stratigraphic
complexity. The Company has assembled a digital data base including
geographical, production, geophysical and geological information that the
Company evaluates on its CAEX workstations. Working with consulting regional
geologists, the Company's explorationists integrate this data with their
extensive expertise and knowledge base to generate and evaluate 3-D seismic and
projects in the Gulf Coast. Brigham's commitment to this province is evidenced
by the Company's staff additions, the opening of its Houston office and the
addition of ten new 3-D seismic projects in 1996 and 1997.
 
   
     The Company anticipates that its increased project assemblage and 3-D
seismic acquisition activity in the Gulf Coast will generate accelerated
drilling in this province in 1998 and 1999. The Company is currently assembling
projects in the Expanded Wilcox and Expanded Vicksburg trends in South Texas,
the Lower and Middle Frio trends of South Texas and the Miocene Trend of South
Louisiana.
    
 
   
     As of December 31, 1997, the Company had acquired or was acquiring 566
square miles (362,240 acres) of 3-D seismic in seven projects in the onshore
Gulf Coast province. The Company anticipates acquiring 600 square miles (384,000
acres) of additional 3-D seismic in this province in 1998. As of December 31,
1997, Brigham had completed 8 wells in 11 attempts (73% success rate) in the
Gulf Coast and had found cumulative proved reserves of 3 net Bcfe. In 1997, the
Company completed seven wells in 10 attempts with an average working interest of
9% adding 3 net Bcfe of proved reserves. As of December 31, 1997, the Company
    
 
                                       41
<PAGE>   43
 
   
had 110 3-D delineated potential drilling locations in the Gulf Coast province,
of which the Company intends to drill 20 gross (10 net) wells in 1998.
    
 
   
     Brigham initiated its Gulf Coast effort in 1995 with the Esperson Dome
Project in Liberty County, Texas where the Company and its participants
currently control approximately 9,600 gross (7,500 net) acres through leases and
farmouts and have acquired 39 square miles of 3-D seismic. The Esperson Dome
Project targets structurally trapped sands in the Miocene, Vicksburg and
Yegua/Cook Mountain series ranging in depth from 1,200 feet to 10,000 feet on a
complexly faulted salt dome feature. As of year-end 1997, ten wells had been
drilled in the project (one Miocene, three Yegua/Cook Mountain and six
Vicksburg), yielding seven discoveries. Brigham currently maintains a small net
profits interest in the Esperson Dome Project that will convert to a variable
back-in working interest of 12% to 20% in the project after payout.
    
 
   
     Brigham's Welder Ranch and Caliente projects encompass an area covering
more than 400 square miles within a non-proprietary 3-D seismic program
currently being conducted in Duval and Webb counties, Texas. Initially Brigham
acquired 48 square miles of 3-D seismic over the Welder Cabeza Ranch, where the
Company controls a 100% working interest in a seismic option on approximately
17,000 acres. The first well in the project, the Brigham-operated Welder-State
212 #1, (80% Brigham working interest), was completed in February 1998, and
tested naturally at a rate of 2.75 MMcf per day from the Lower Wilcox formation
at 13,350 feet. After adding perforations in two behind pipe zones, the well was
producing approximately 700 Mcf of natural gas per day at the end of July 1998.
In mid-1998, the Company participated in the drilling of the Tesoro-operated
John and Elva Dinn #1 well (48% Brigham working interest), a 14,500 foot Lower
Wilcox test in the Company's Caliente Project. This well encountered 70 feet of
pay in the Lower Wilcox formation and is currently waiting on completion.
Brigham plans to drill four additional wells in this trend in the second half of
1998.
    
 
   
     Another project in South Texas is Brigham's Diablo Project covering
approximately 12,000 acres in Brooks County, Texas. The Company acquired 25
square miles of proprietary 3-D seismic in 1997 and an additional 33 square
miles in 1998. Brigham recently teamed up with Exxon Company, USA, which
controls adjoining acreage to jointly explore the combined acreage for potential
below 10,000 feet in the Vicksburg formation. Brigham has retained a 33% working
interest in this deep joint exploration project. In prospective zones above
10,000 feet, primarily the Frio, Brigham has retained a 100% working interest in
its original 4,000 acre lease block. The Company plans to drill a number of
wells in this project in 1998 to test the shallow Frio and deeper Vicksburg
objectives.
    
 
   
     In its Southwest Danbury Project in Brazoria County, Texas, Brigham is the
operator of a 13,000 foot Frio test that was drilled during the first half of
1998. In early August 1998, this well was producing 2 MMcf of natural gas and 30
barrels of condensate per day with a flowing tubing pressure of 6,100 pounds per
square inch from the Lower Frio formation. Brigham has retained a 46% working
interest in this test, and plans to drill at least one additional wells in this
project during the balance of 1998.
    
 
     In May 1997, Brigham initiated its El Sauz Project with a seismic option
covering approximately 94,000 acres in Willacy and Kennedy counties, Texas. The
El Sauz Project is an underexplored area due north of the Willamar Field, which
has produced a cumulative 350 Bcf from the Miocene and Frio sands. Brigham
expects to define Miocene and Frio sands at 6,000 to 10,000 feet, with
additional potential as deep as 18,000 feet. Reserve targets range from 5 to 20
Bcf per well. The Company initiated a 200 square mile 3-D seismic program over
this acreage in 1998, with initial drilling anticipated for early 1999. Brigham
has retained a 55% working interest in the El Sauz Project after it brought in
two industry participants to leverage preseismic land and 3-D seismic
acquisition costs of this project.
 
   
     Also in the Miocene/Frio trend of South Texas, Brigham acquired a seismic
option covering approximately 28,000 acres in the Hawkins Ranch located in
Matagorda County, Texas. The region has potential in the shallow, nonpressured
Miocene and Frio sands as well as the deeper, pressured Frio sands. The Company
has acquired approximately 94 square miles of new proprietary 3-D seismic to
merge with 65 square miles of non-proprietary 3-D seismic already in inventory.
The Company has negotiated a transaction pursuant to which the above described
94 square miles of proprietary 3-D seismic will become non-proprietary after an
    
 
                                       42
<PAGE>   44
 
   
exclusivity period benefiting the Company, allowing the Company to acquire the
3-D seismic at a substantial cost savings. Brigham currently retains a 75%
working interest in this project.
    
 
     Brigham's first significant venture into South Louisiana, its Tigre Point
Project, is located in six feet of water in the transition zone off Vermilion
Parish. The project consists of 44 square miles of 3-D seismic covering a 7,200
acre lease block in Louisiana State waters, where Brigham currently controls a
75% working interest. The project has targeted the same series of sands that
produce in the prolific Freshwater Bayou field, located five miles to the north.
An 18,000 foot Lower Miocene test is scheduled for late 1998. Currently, Brigham
plans to retain a 30% to 40% working interest in this project following the sale
of a portion of its interest to an industry participant.
 
   
     West Texas. The Company's 3-D seismic drilling activity in the West Texas
region has been focused in the Horseshoe Atoll, the Midland Basin and the
Eastern Shelf of the Permian Basin and the Hardeman Basin. Recently the Company
initiated an exploration program in the Delaware Basin and it is selectively
focusing its West Texas activity in portions of geologic trends that the Company
believes offer greater potential for lower finding costs and higher returns,
including the Fusselman formation of the Midland Basin and the Ellenberger and
Devonian formations of the Delaware Basin.
    
 
   
     As of December 31, 1997, the Company had acquired or was acquiring 1,649
square miles (1,055,360 acres) in 74 projects in the West Texas region. The
Company anticipates acquiring 40 square miles (25,600 acres) of additional 3-D
seismic in this province in 1998. As of December 31, 1997, Brigham had completed
180 wells in 287 attempts (63% success rate) in the West Texas province and had
found cumulative proved reserves of 24 net Bcfe. In 1997, the Company completed
19 wells in 34 attempts with an average working interest of 45% adding 4 net
Bcfe of proved reserves. As of December 31, 1997, the Company had 302 3-D
delineated potential drilling locations in the West Texas region, of which the
Company intends to drill 14 gross (6 net) wells in 1998.
    
 
   
     The Company has recently experienced success in the deeper portions of the
Midland Basin, where it has drilled five Fusselman discoveries to date.
Currently the most significant of these discoveries is the Elizabeth Rose field,
with gross proved reserves estimated by the Company's independent petroleum
consultants at December 31, 1997 of 1.5 MMBbls of oil. The Company has drilled
five wells in this Fusselman field that were producing an aggregate of
approximately 610 Bbls of oil per day in July 1998. Brigham's working interest
in its five Fusselman discoveries ranges from 19% to 91%. In 1998 the Company
has acquired 27 square miles of 3-D seismic in three additional 3-D seismic
projects adjacent to the Elizabeth Rose field and currently retains working
interests of 100% in these projects.
    
 
   
     The Company completed three Canyon Reef discoveries during 1997 in its
Discovery Project located in the Horseshoe Atoll Trend. This project, in which
Brigham currently retains a working interest of 75%, targets oil producing
Canyon-age reef objectives at depths of approximately 9,500 feet. The Company's
three 1997 discoveries in its Discovery Project were producing an aggregate of
approximately 160 Bbls of oil and 510 Mcf of natural gas per day in July 1998.
Brigham's working interests in these three wells range from 48% to 91%.
    
 
   
     Among Brigham's higher potential, higher risk projects in its West Texas
province are its Buffalo and Longhorn projects, located in the Delaware Basin,
in which the Company owns a 25% working interest. From two 3-D seismic programs
covering approximately 137 square miles acquired in 1996 and 1997, the Company
has identified numerous potential 3-D seismic delineated drilling locations and
has leased over 23,000 gross (5,780 net) acres. These projects are surrounded by
prolific production from the Devonian and Ellenberger formations at depths of
15,000 to 21,000 feet, in fields such as Evetts (approximately 600 Bcf of
natural gas to date from 16 wells) and War Wink South (approximately 295 Bcf of
natural gas to date from eight wells). Brigham plans to participate with a 24%
working interest in two wells to test Bone Springs formation objectives in this
area during the second half of 1998.
    
 
                                       43
<PAGE>   45
 
NATURAL GAS AND OIL RESERVES
 
     The Company's estimated total net proved reserves of natural gas and oil as
of December 31, 1995, 1996 and 1997 and the present values attributable to these
reserves as of those dates were as follows:
 
<TABLE>
<CAPTION>
                                                              AS OF DECEMBER 31,
                                                          ---------------------------
                                                           1995     1996(1)    1997
                                                          -------   -------   -------
<S>                                                       <C>       <C>       <C>
Estimated net proved reserves:
  Natural gas (MMcf)....................................    4,257    10,257    53,230
  Oil (MBbls)...........................................    1,672     1,940     3,181
  Natural gas equivalent (MMcfe)........................   14,289    21,897    72,316
Proved developed reserves as a percentage of proved
  reserves..............................................      80%       67%       65%
Present Value of Future Net Revenues(2) (in
  thousands)............................................  $18,222   $44,506   $69,249
Standardized Measure of Discounted Future Net Cash
  Flows(3) (in thousands)...............................  $18,222   $44,506   $64,274
</TABLE>
 
---------------
 
(1) Net of a sale by the Company in January 1996 of its interest in certain
    properties that accounted for 299 MMcf of natural gas and 272 MBbls of oil
    (1,931 MMcfe of proved reserves) as of December 31, 1995.
 
(2) The Present Value of Future Net Revenues attributable to the Company's
    reserves was prepared using prices in effect at the end of the respective
    periods presented, discounted at 10% per annum on a pre-tax basis. These
    amounts reflect the effects of the Company's hedging activities in the
    periods presented.
 
(3) The Standardized Measure of Discounted Future Net Cash Flows prepared by the
    Company represents the present value of future net revenues after income
    taxes discounted at 10%. These amounts reflect the effects of the Company's
    hedging activities in the periods presented.
 
     The average prices for the Company's reserves were $1.85 per Mcf of natural
gas and $18.22 per Bbl of oil as of December 31, 1995, $3.62 per Mcf of natural
gas and $24.66 per Bbl of oil as of December 31, 1996 and $2.11 per Mcf of
natural gas and $16.64 per Bbl of oil as of December 31, 1997.
 
   
     In accordance with applicable requirements of the SEC, estimates of the
Company's proved reserves and future net revenues are made using sales prices
estimated to be in effect as of the date of such reserve estimates and are held
constant throughout the life of the properties (except to the extent a contract
specifically provides for escalation). Estimated quantities of proved reserves
and future net revenues therefrom are affected by natural gas and oil prices,
which have fluctuated widely in recent years. At December 31, 1997, the date the
Company's reserves and present value were estimated, the prices of natural gas
and oil on the NYMEX were $2.26 per MMBtu and $17.64 per Bbl, respectively. From
January 1, 1998 through August 7, 1998, the price of natural gas on the NYMEX
ranged from $2.69 per MMBtu to $1.83 per MMBtu and the price of oil on the NYMEX
ranged from $17.82 per Bbl to $11.56 per Bbl. There are numerous uncertainties
inherent in estimating natural gas and oil reserves and their estimated values,
including many factors beyond the control of the Company. The reserve data set
forth herein represents only estimates. Reservoir engineering is a subjective
process of estimating underground accumulations of natural gas and oil that
cannot be measured in an exact manner. The accuracy of any reserve estimate is a
function of the quality of available data and of engineering and geologic
interpretation and judgment. As a result, estimates of different engineers,
including those used by the Company, may vary. In addition, estimates of
reserves are subject to revision based upon actual production, results of future
development and exploration activities, prevailing natural gas and oil prices,
operating costs and other factors. The revisions may be material. Accordingly,
reserve estimates are often different from the quantities of natural gas and oil
that are ultimately recovered and are highly dependent upon the accuracy of the
assumptions upon which they are based. The Company's estimated proved reserves
have not been filed with or included in reports to any federal agency. See "Risk
Factors -- Uncertainty of Reserve Information and Future Net Revenue Estimates."
    
 
     Estimates with respect to proved reserves that may be developed and
produced in the future are often based upon volumetric calculations and upon
analogy to similar types of reserves rather than actual production
 
                                       44
<PAGE>   46
 
history. Estimates based on these methods are generally less reliable than those
based on actual production history. Subsequent evaluation of the same reserves
based upon production history will result in variations in the estimated
reserves that may be substantial.
 
DRILLING ACTIVITIES
 
     The Company drilled, or participated in the drilling of, the following
number of wells during the periods indicated.
 
   
<TABLE>
<CAPTION>
                                                                                              SIX MONTHS
                                                         YEAR ENDED DECEMBER 31,                ENDED
                                                ------------------------------------------     JUNE 30,
                                                    1995           1996           1997           1998
                                                ------------   ------------   ------------   ------------
                                                GROSS   NET    GROSS   NET    GROSS   NET    GROSS   NET
                                                -----   ----   -----   ----   -----   ----   -----   ----
<S>                                             <C>     <C>    <C>     <C>    <C>     <C>    <C>     <C>
Exploratory Wells:
  Natural gas.................................    5      1.2     5      1.2    15      6.3    13      4.8
  Oil.........................................   37      8.1    22      5.2    21      7.9     4      1.7
  Non-productive..............................   32      8.7    24      7.0    26      9.8     4      2.4
                                                 --     ----    --     ----    --     ----    --     ----
          Total...............................   74     18.0    51     13.4    62     24.0    21      8.9
                                                 ==     ====    ==     ====    ==     ====    ==     ====
Development Wells:
  Natural gas.................................   --       --    10      1.3     4      1.6     7      4.4
  Oil.........................................    4      0.5     5      1.0     6      1.8     2      0.6
  Non-productive..............................   --       --     1      0.2     1      0.6     3      2.1
                                                 --     ----    --     ----    --     ----    --     ----
          Total...............................    4      0.5    16      2.5    11      4.0    12      7.0
                                                 ==     ====    ==     ====    ==     ====    ==     ====
</TABLE>
    
 
   
     The Company does not own any drilling rigs, and the majority of its
drilling activities have been conducted by industry participant operators or
independent contractors under standard drilling contracts. Consistent with its
business strategy, the Company has chosen to retain operations of an increasing
number of the wells it drills and expects to continue to operate more wells in
1998.
    
 
PRODUCTIVE WELLS AND ACREAGE
 
  Productive Wells
 
     The following table sets forth the Company's ownership interest as of
December 31, 1997 in productive natural gas and oil wells in the areas
indicated.
 
<TABLE>
<CAPTION>
                                                    NATURAL GAS        OIL           TOTAL
                                                    ------------   ------------   ------------
PROVINCE                                            GROSS   NET    GROSS   NET    GROSS   NET
--------                                            -----   ----   -----   ----   -----   ----
<S>                                                 <C>     <C>    <C>     <C>    <C>     <C>
Anadarko Basin....................................   43     13.0      5     1.2     48    14.2
Gulf Coast........................................    1      0.0      5     0.1      6     0.1
West Texas........................................    2      0.7     91    24.5     93    25.2
Other.............................................   --       --      1     0.5      1     0.5
                                                     --     ----    ---    ----    ---    ----
          Total...................................   46     13.7    102    26.3    148    40.0
                                                     ==     ====    ===    ====    ===    ====
</TABLE>
 
     Productive wells consist of producing wells and wells capable of
production, including wells waiting on pipeline connection. Wells that are
completed in more than one producing horizon are counted as one well. Of the
gross wells reported above, none had multiple completions.
 
  Acreage
 
     Undeveloped acreage includes leased acres on which wells have not been
drilled or completed to a point that would permit the production of commercial
quantities of natural gas and oil, regardless of whether or not such acreage
contains proved reserves. A gross acre is an acre in which an interest is owned.
A net acre is deemed to exist when the sum of fractional ownership interests in
gross acres equals one. The number of net
 
                                       45
<PAGE>   47
 
acres is the sum of the fractional interests owned in gross acres expressed as
whole numbers and fractions thereof. The following table sets forth the
approximate developed and undeveloped acreage in which the Company held a
leasehold, mineral or other interest at December 31, 1997:
 
<TABLE>
<CAPTION>
                                                DEVELOPED         UNDEVELOPED            TOTAL
                                              --------------   -----------------   -----------------
PROVINCE                                      GROSS     NET     GROSS      NET      GROSS      NET
--------                                      ------   -----   -------   -------   -------   -------
<S>                                           <C>      <C>     <C>       <C>       <C>       <C>
Anadarko Basin..............................  16,600   7,716    75,377    32,181    91,977    39,897
Gulf Coast..................................      --      --    18,588    14,902    18,588    14,902
West Texas..................................   6,035   1,794    19,957    11,517    25,992    13,311
Other.......................................     160      80   145,295    51,546   145,455    51,626
                                              ------   -----   -------   -------   -------   -------
          Total.............................  22,795   9,590   259,217   110,146   282,012   119,736
                                              ======   =====   =======   =======   =======   =======
</TABLE>
 
     All the leases for the undeveloped acreage summarized in the preceding
table will expire at the end of their respective primary terms unless the
existing leases are renewed, production has been obtained from the acreage
subject to the lease prior to that date, or some other "savings clause" is
implicated. The following table sets forth the minimum remaining terms of leases
for the gross and net undeveloped acreage:
 
<TABLE>
<CAPTION>
                                                               ACRES EXPIRING
                                                              -----------------
                                                               GROSS      NET
                                                              -------   -------
<S>                                                           <C>       <C>
Twelve Months Ending:
  December 31, 1998.........................................  120,186    46,491
  December 31, 1999.........................................   65,254    30,857
  December 31, 2000.........................................   51,984    24,263
  Thereafter................................................   21,793     8,535
                                                              -------   -------
          Total.............................................  259,217   110,146
                                                              =======   =======
</TABLE>
 
     In addition, the Company had lease options as of December 31, 1997 to
acquire an additional 254,699 acres, substantially all of which expire within
one year.
 
VOLUMES, PRICES AND PRODUCTION COSTS
 
     The following table sets forth the production volumes, average prices
received and average production costs associated with the Company's sale of
natural gas and oil for the periods indicated.
 
   
<TABLE>
<CAPTION>
                                                           YEAR ENDED          SIX MONTHS ENDED
                                                          DECEMBER 31,             JUNE 30,
                                                    ------------------------   -----------------
                                                     1995     1996     1997     1997      1998
                                                    ------   ------   ------   -------   -------
<S>                                                 <C>      <C>      <C>      <C>       <C>
Production:
  Natural gas (MMcf)..............................     272      698    1,382      457     1,947
  Oil (MBbls).....................................     177      227      291      127       232
  Natural gas equivalent (MMcfe)..................   1,332    2,060    3,126    1,222     3,338
Average sales price(1):
  Natural gas (per Mcf)...........................  $ 1.62   $ 2.30   $ 2.56   $ 2.62    $ 2.10
  Oil (per Bbl)...................................   17.76    19.98    19.40    20.87     13.15
Average production expenses and taxes (per
  Mcfe)...........................................  $  .69   $  .53   $  .55   $  .56    $  .42
</TABLE>
    
 
---------------
 
(1) Reflects the results of hedging activities in the periods presented.
 
                                       46
<PAGE>   48
 
COSTS INCURRED
 
     The costs incurred in natural gas and oil acquisition, exploration and
development activities are as follows (in thousands):
 
<TABLE>
<CAPTION>
                                                            YEAR ENDED DECEMBER 31,
                                                          ---------------------------
                                                           1995      1996      1997
                                                          -------   -------   -------
<S>                                                       <C>       <C>       <C>
Cost incurred for the year:
  Exploration...........................................  $ 6,893   $10,527   $29,421
  Property acquisition..................................    1,885     6,195    26,922
  Development...........................................      713     1,328     2,953
  Proceeds from participants............................   (1,296)   (4,111)     (319)
                                                          -------   -------   -------
                                                          $ 8,195   $13,939   $58,977
                                                          =======   =======   =======
</TABLE>
 
     Costs incurred represent amounts incurred by the Company for exploration,
property acquisition and development activities. Periodically, the Company will
receive reimbursement of certain costs from participants in its projects
subsequent to project initiation in return for an interest in the project. These
payments are described as "Proceeds from participants" in the table above.
 
EXPLORATION STAFF
 
   
     Over the last seven years the Company has assembled an exploration staff
that includes nine geophysicists, ten geologists, four petroleum engineers, five
computer applications specialists, five geophysical/geological/engineering
technicians, five landmen and five lease and division order analysts. Brigham's
nine geophysicists have different but complementary backgrounds, and their
diversity of experience in varied geological and geophysical settings, combined
with various technical specializations (from hardware and systems to software
and seismic data processing), provide the Company with valuable technical
intellectual resources. The Company's team of explorationists has approximately
300 years of exploration experience and approximately 85 years of 3-D CAEX
workstation experience, most of which was acquired at Brigham and various major
and large independent oil companies. Occasionally, the Company complements and
leverages its exploration staff by seeking out alliances or retainer
relationships with geologists having extensive experience in a particular area
of interest.
    
 
3-D SEISMIC TECHNOLOGY
 
     The Company's strategy is to use 3-D seismic and other advanced
technologies, including CAEX, to systematically explore and develop domestic
onshore natural gas and oil provinces. In general, 3-D seismic is the process of
acquiring seismic data along multiple lines and grids. The primary advantage of
3-D seismic over 2-D seismic is that it provides information with respect to
multiple horizontal and vertical points within a geologic formation instead of
information on a single vertical line or multiple vertical lines within the
formation. Acquiring larger amounts of data relating to a geologic formation
allows a user to better correlate the data and, in some cases, obtain a greater
understanding and image of the formation. Although it is impossible to predict
with certainty the specific configuration or composition of any underground
geologic formation, the use of 3-D seismic provides clearer and more accurate
projected images of complex geologic formations, which can assist a user in
evaluating whether to drill for natural gas and oil reserves. If a decision to
drill is made, 3-D seismic can also help in determining the optimal location to
drill.
 
     CAEX is the process of accumulating and analyzing the various seismic,
production and other data obtained relating to a geographic area. In general,
CAEX involves accumulating various 2-D and 3-D seismic with respect to a
potential drilling location, correlating that data with historical well control
and production data from similar properties and analyzing the available data
through computer programs and modeling techniques to project the likely geologic
composition of a potential drilling location and potential locations of
undiscovered natural gas and oil reserves. This process relies on a comparison
of data with respect to the potential drilling location and historical data with
respect to the density and sonic characteristics of different
 
                                       47
<PAGE>   49
 
types of rock formations, hydrocarbons and other subsurface minerals, resulting
in a projected three dimensional image of the subsurface. This modeling is
performed through the use of advanced interactive computer workstations and
various combinations of available computer programs that have been developed
solely for this application.
 
     Brigham has invested extensively in the advanced computer hardware and
software necessary for 3-D seismic exploration. The Company has both Landmark
and Geoquest CAEX workstations. This workstation flexibility provides the
Company the opportunity to interpret a project on the particular CAEX
workstation that it believes is best suited for defining those particular
geologic objectives. Brigham's explorationists can access a diverse software
tool kit including SeisWorks, StratWorks, SeisCube, OpenVision, ZAP, Zmap+,
ARIES, SynTool, Poststack, Continuity Cube, TDQ, AutoPix, MapView, GeoViz,
Voxels, SynView, CSA (Computed Seismic Attributes), Surface Slice,
Hampson -- Russell AVO Analysis and Modeling and ZEH Graphics CGMage Builder
(graphics montage tool).
 
     The Company believes that its use of 3-D seismic technology provides it
with a number of benefits in the exploration, delineation and development
process that are not generally available to those who only use 2-D seismic and
conventional processing methods. In particular, the Company believes that it
obtains clearer and more accurate projected images of underground formations
through computer modeling, and is therefore better able to identify potential
locations of hydrocarbon accumulations based on the characteristics of the
formations and analogies made with nearby fields and formations where
hydrocarbons have been found. This enhanced data has been used to assist the
Company in eliminating potential drilling locations that might otherwise have
been drilled had the Company relied solely on 2-D seismic. This data has also
been used to assist the Company in attempting to identify the most desirable
location for the wellbore to increase the prospects of a successful exploratory
or development well and production from the reservoir.
 
INDUSTRY ALLIANCES
 
   
     Veritas Anadarko Basin Acquisition Alliances. Pursuant to certain alliances
with Veritas DGC Land Ltd.("Veritas"), Brigham had acquired approximately 850
square miles of 3-D seismic in the Anadarko Basin through December 31, 1997 and
had agreed to acquire from 775 to 875 additional square miles of data to be
divided among numerous projects in that province. In exchange for the Company's
commitment to Veritas, the Company and its assignees only pay a portion of the
3-D seismic acquisition costs as the data is acquired. As the Company leases
acreage or drills wells, it pays Veritas the balance of the costs in the form of
leasing and drilling fees. In addition, in the event that the outstanding
balance of deferred seismic acquisition costs exceeds certain threshold amounts,
the Company must pre-pay part of the leasing and drilling fees to cause the
outstanding balance to fall below the current threshold amount. Under these
arrangements, Veritas has agreed to make a designated 3-D seismic crew available
to the Company on a continuous basis and, as long as the Company has a project
area ready for surveying and field seismic acquisition, to send the crew from
one project area to the next without interruption. If the Company does not have
a project area designated upon completion of one project, and Veritas has not
been able to secure an intervening project from a third party, the Company is
obligated to pay Veritas a stand-by fee. The Company has never incurred a
stand-by fee to Veritas. These arrangements afford the Company access to 3-D
seismic acquisition in a compressed cycle time, providing the Company with
operational efficiencies.
    
 
     In addition, Veritas Geoservices, Ltd. provides three employees that
maintain and operate four seismic data processing workstations in Brigham's
offices. Supervised by Brigham's geophysicists, the vendor's employees process
most of the Company's 3-D seismic. The associated improvement in communication
and integration, from field data acquisition to processing, reduces project
cycle times, and therefore costs, while improving the quality of the data for
Brigham's subsequent interpretation.
 
   
     Anadarko Basin Alliance I. The Company has entered into alliances with
Vintage Petroleum, Inc. ("Vintage") and Stephens Production Company ("Stephens")
providing for their participation with Brigham in all projects that the Company
conducts within a 625 square mile 3-D seismic program that was completed in 1997
with Veritas in the Anadarko Basin. Vintage and Stephens bear a disproportionate
share of all pre-seismic and certain seismic costs on all projects in the
program. Net of the interests of Vintage and Stephens,
    
 
                                       48
<PAGE>   50
 
the Company holds a 37.5% interest in the program. The Company believes that
this leveraging of its costs is possible because of the expertise and knowledge
that the Company has developed, enabling the Company to build its revenue and
cash flow base at a time when it has been capital constrained.
 
   
     Anadarko Basin Alliance II. Brigham is currently acquiring 3-D seismic
under a second alliance with Veritas in the Anadarko Basin. From August through
December 1997, the Company acquired approximately 225 square miles of 3-D
seismic under this alliance and expects to acquire an additional 825 square
miles in various Brigham-generated projects by mid-1999. The Company currently
has a 100% working interest in the projects under its second seismic acquisition
alliance with Veritas, and it plans to retain at least a 75% working interest in
these projects following a potential sale of a portion of its interest to an
industry participant.
    
 
   
     Carry-to-Casing Point Programs. In order to participate in wells drilled by
the Company between April 1, 1996 and March 31, 1997, each of Gasco Limited
Partnership ("Gasco") and Middle Bay Oil Company, Inc. ("Middle Bay") agreed to
fund 25% of the Company's drilling costs and 12.5% of its completion costs for
each well drilled. In return, the Company assigned to each an undivided 12.5% of
the Company's interest in the leasehold allocated to the proration unit for each
completed well. As a result, the Company paid for 50% of costs attributable to
its working interest to casing point, and 75% of its completion costs, for 75%
of its original working interest for each well funded during the term of the
agreement.
    
 
     The Company renewed its agreement with Gasco in early 1997. In order to
participate in wells drilled by the Company between April 1, 1997 and March 31,
1998, Gasco agreed to fund 18% of the Company's drilling costs and 9% of its
completion cost for each well. In return, the Company has agreed to assign to
Gasco an undivided 9% of the Company's interest in the leasehold allocated to
the production unit for each completed well. As a result, the Company pays for
82% of costs attributable to its working interest to casing point, and 91% of
its completion costs, for 91% of its original working interest for each well
funded during the term of the agreement.
 
   
     The Company renewed its agreement with Gasco in early 1998. In order to
participate in wells drilled by the Company between April 1, 1998 and March 31,
1999, Gasco agreed to fund 8% of the Company's drilling costs and 4% of its
completion cost for each well. In return, the Company has agreed to assign to
Gasco an undivided 4% of the Company's interest in the leasehold allocated to
the production unit for each completed well. As a result, the Company pays for
92% of costs attributable to its working interest to casing point, and 96% of
its completion costs, for 96% of its original working interest for each well
funded during the term of the agreement.
    
 
     The Company believes that its agreements with Middle Bay and Gasco have
been beneficial because they have allowed the Company to leverage its working
interests in its properties by requiring it to bear a disproportionately smaller
share of drilling costs. Depending on future conditions, the Company may seek to
enter into similar types of arrangements with industry or financial
participants. To the extent that the Company does seek to enter into such future
arrangements, the terms of these arrangements, including the percentages of
costs borne and interests assigned, may vary from those in the Company's past
and present arrangements.
 
NATURAL GAS AND OIL MARKETING AND MAJOR CUSTOMERS
 
     Most of the Company's natural gas and oil production is sold through
various marketing arrangements under price sensitive or spot market contracts.
The revenues generated by the Company's operations are highly dependent upon the
prices of and demand for natural gas and oil. The price received by the Company
for its natural gas and oil production depends on numerous factors beyond the
Company's control, including seasonality, competition, the condition of the
United States economy, foreign imports, political conditions in other
oil-producing and natural gas-producing countries, the actions of the
Organization of Petroleum Exporting Countries, and domestic government
regulation, legislation and policies. Decreases in the prices of natural gas and
oil could have an adverse effect on the carrying value of the Company's proved
reserves and the Company's revenues, profitability and cash flow. Although the
Company is not currently experiencing any significant involuntary curtailment of
its natural gas or oil production, market, economic and regulatory factors may
in the future materially affect the Company's ability to sell its natural gas or
oil production. See
 
                                       49
<PAGE>   51
 
"Management's Discussion and Analysis of Financial Condition and Results of
Operations," "Risk Factors -- Volatility of Natural Gas and Oil Prices" and
"Risk Factors -- Marketability of Production." For the year ended December 31,
1997, sales to Cobra Oil & Gas Corporation and Pride Pipeline Company were
approximately 14% and 12%, respectively, of the Company's natural gas and oil
revenues. Due to the availability of other markets and pipeline connections, the
Company does not believe that the loss of any single natural gas or oil customer
would have a material adverse effect on the Company's results of operations.
 
COMPETITION
 
     The oil and gas industry is highly competitive in all of its phases. The
Company encounters competition from other oil and gas companies in all areas of
its operations, including the acquisition of seismic and leasing options and
natural gas and oil leases on properties. The Company's competitors include
major integrated natural gas and oil companies and numerous independent natural
gas and oil companies, individuals and drilling and income programs. Many of its
competitors are large, well established companies with substantially larger
operating staffs and greater capital resources than the Company's. Such
companies may be able to pay more for seismic and lease options on natural gas
and oil properties and exploratory prospects and to define, evaluate, bid for
and purchase a greater number of properties and prospects than the Company's
financial or human resources permit. The Company's ability to acquire additional
properties and to discover reserves in the future will be dependent upon its
ability to evaluate and select suitable properties and to consummate
transactions in a highly competitive environment. See "Risk
Factors -- Competition" and "Risk Factors -- Substantial Capital Requirements."
 
OPERATING HAZARDS AND UNINSURED RISKS
 
     Drilling activities are subject to many risks, including the risk that no
commercially productive reservoirs will be encountered. There can be no
assurance that new wells drilled by the Company will be productive or that the
Company will recover all or any portion of its investment. Drilling for natural
gas and oil may involve unprofitable efforts, not only from dry wells, but also
from wells that are productive but do not produce sufficient net revenues to
return a profit after drilling, operating and other costs. The cost of drilling,
completing and operating wells is often uncertain. The Company's drilling
operations may be curtailed, delayed or canceled as a result of numerous
factors, many of which are beyond the Company's control, including title
problems, weather conditions, compliance with governmental requirements and
shortages or delays in the delivery of equipment and services. The Company's
future drilling activities may not be successful and, if unsuccessful, such
failure may have a material adverse effect on the Company's business, financial
condition or results of operations. See "Risk Factors -- Dependence on
Exploratory Drilling Activities." In addition, use of 3-D seismic technology
requires greater pre-drilling expenditures than traditional drilling strategies.
Although the Company believes that its use of 3-D seismic technology will
increase the probability of success, some unsuccessful wells are likely, and
there can be no assurance unsuccessful drilling efforts will not have a material
adverse effect on the Company's business, financial condition or results of
operations.
 
     The Company's operations are subject to hazards and risks inherent in
drilling for and producing and transporting natural gas and oil, such as fires,
natural disasters, explosions, encountering formations with abnormal pressures,
blowouts, cratering, pipeline ruptures and spills, any of which can result in
the loss of hydrocarbons, environmental pollution, personal injury claims and
other damage to properties of the Company and others. The Company maintains
insurance against some but not all of the risks described above. In particular,
the insurance maintained by the Company does not cover claims relating to
failure of title to natural gas and oil leases, trespass during 3-D survey
acquisition or surface change attributable to seismic operations, business
interruption or loss of revenues due to well failure. In certain circumstances
in which insurance is available the Company may not purchase it. The occurrence
of an event that is not covered, or not fully covered, by insurance could have a
material adverse effect on the Company's business, financial condition and
results of operations.
 
                                       50
<PAGE>   52
 
EMPLOYEES
 
   
     On August 7, 1998, the Company had 66 full-time employees. None is
represented by any labor union. The Company believes its relations with its
employees are good. The Company also relies on several regional consulting
service companies to provide field landmen to support the Company on a
project-by-project basis. One of these companies, Brigham Land Management, is
owned by Vincent M. Brigham, who is the brother of Ben M. Brigham, the Company's
Chief Executive Officer, President and Chairman of the Board. See "Certain
Transactions."
    
 
FACILITIES
 
     The Company's principal executive offices are located in Austin, Texas,
where it leases approximately 28,000 square feet of office space at 6300 Bridge
Point Parkway, Building 2, Suite 500, Austin, Texas 78730. In the fall of 1998,
the Company expects to lease an additional 5,000 square feet of office space
adjacent to its principal executive offices. The Company also leases a 4,100
square foot office at 450 Gears Road, Suite 240, Houston, Texas 77067.
 
TITLE TO PROPERTIES
 
   
     The Company believes it has satisfactory title, in all material respects,
to substantially all of its producing properties in accordance with standards
generally accepted in the oil and gas industry. The Company's properties are
subject to royalty interests, standard liens incident to operating agreements,
liens for current taxes and other inchoate burdens which the Company believes do
not materially interfere with the use of or affect the value of such properties.
The Company's Credit Facility is secured by a first lien against substantially
all of the Company's natural gas and oil properties and, pursuant to the terms
of the Offering, the Notes will be secured by a second lien against all
collateral pledged by the Company as security under its Credit Facility. See
"Management's Discussion and Analysis of Financial Condition and Results of
Operations."
    
 
GOVERNMENTAL REGULATION
 
     The Company's natural gas and oil exploration, production and marketing
activities are subject to extensive laws, rules and regulations promulgated by
federal and state legislatures and agencies. Failure to comply with such laws,
rules and regulations can result in substantial penalties. The legislative and
regulatory burden on the oil and gas industry increases the Company's cost of
doing business and affects its profitability. Although the Company believes it
is in substantial compliance with all applicable laws and regulations, because
those laws and regulations are frequently amended, interpreted and
reinterpreted, the Company is unable to predict the future cost or impact of
complying with such laws and regulations.
 
     The State of Texas and many other states require permits for drilling
operations, drilling bonds and reports concerning operations and impose other
requirements relating to the exploration and production of natural gas and oil.
These states also have statutes or regulations addressing conservation matters,
including provisions for the unitization or pooling of natural gas and oil
properties, the establishment of maximum rates of production from wells and the
regulation of spacing, plugging and abandonment of such wells.
 
     The Federal Energy Regulatory Commission ("FERC") regulates interstate
natural gas transportation rates and service conditions, which affect the
marketing of gas produced by the Company, as well as the revenues received by
the Company for sales of such production. Since the mid-1980s, FERC has issued a
series of orders, culminating in Order Nos. 636, 636-A 636-B and 636-C ("Order
636"), that have significantly altered the marketing and transportation of gas.
Order 636 mandates a fundamental restructuring of interstate pipeline sales and
transportation service, including the unbundling by interstate pipelines of the
sale, transportation, storage and other components of the city-gate sales
services such pipelines previously performed and the provision of open-access
transportation on a nondiscriminatory basis. One of FERC's purposes in issuing
the order was to increase competition within all phases of the natural gas
industry. Numerous parties have filed petitions for review of Order 636, as well
as orders in individual pipeline restructuring proceedings. In July 1996, Order
636 was generally upheld on appeal, and the portions remanded
 
                                       51
<PAGE>   53
 
for further action do not appear to materially affect the Company. Because Order
636 may be modified as a result of the appeals, it is difficult to predict the
ultimate impact of the orders on the Company and its gas marketing efforts.
Generally, Order 636 has eliminated or substantially reduced the interstate
pipelines' traditional role as wholesalers of natural gas and has substantially
increased competition and volatility in natural gas markets.
 
     The FERC frequently reexamines its transportation-related policies,
including the terms and conditions under which interstate pipeline shippers may
release interstate pipeline capacity for resale in the secondary market, the
appropriateness of the use of negotiated and market-based rates, and the
implementation of additional standardized terms and conditions for interstate
gas transmission. In April 1998, the FERC issued a new rule to further
standardize pipeline transportation tariffs that could adversely affect the
reliability of scheduled interruptible transportation service on some pipelines.
While any resulting FERC action would affect the Company only indirectly, any
new rules and policy statements may have the effect of enhancing competition in
natural gas markets or affecting the cost or availability of pipeline
transportation.
 
     The price the Company receives from the sale of natural gas liquids and oil
is affected by the cost of transporting products to markets. Effective January
1, 1995, FERC implemented regulations establishing an indexing system for
transportation rates for oil pipelines, which, generally, would index such rates
to inflation, subject to certain conditions and limitations. The Company is not
able to predict with certainty the effect, if any, of these regulations on its
operations. However, the regulations may increase transportation costs or reduce
well head prices for natural gas liquids and oil. See "Risk
Factors -- Compliance with Government Regulations."
 
ENVIRONMENTAL MATTERS
 
     The Company's operations and properties are, like the oil and gas industry
in general, subject to extensive and changing federal, state and local laws and
regulations relating to environmental protection, including the generation,
storage, handling, emission, transportation and discharge of materials into the
environment, and relating to safety and health. The recent trend in
environmental legislation and regulation generally is toward stricter standards,
and this trend will likely continue. These laws and regulations may require the
acquisition of a permit or other authorization before construction or drilling
commences and for certain other activities; limit or prohibit seismic
acquisition, construction, drilling and other activities on certain lands lying
within wilderness and other protected areas; and impose substantial liabilities
for pollution resulting from the Company's operations. The permits required for
various of the Company's operations are subject to revocation, modification and
renewal by issuing authorities. Governmental authorities have the power to
enforce compliance with their regulations, and violations are subject to fines
or injunction, or both. In the opinion of management, the Company is in
substantial compliance with current applicable environmental laws and
regulations, and the Company has no material commitments for capital
expenditures to comply with existing environmental requirements. Nevertheless,
changes in existing environmental laws and regulations or in interpretations
thereof could have a significant impact on the Company, as well as the oil and
gas industry in general. The Comprehensive Environmental Response, Compensation
and Liability Act and comparable state statutes impose strict and arguably joint
and several liability on owners and operators of certain sites and on persons
who disposed of or arranged for the disposal of "hazardous substances" found at
such sites. It is not uncommon for the neighboring land owners and other third
parties to file claims for personal injury and property damage allegedly caused
by the hazardous substances released into the environment. The Resource
Conservation and Recovery Act and comparable state statutes govern the disposal
of "solid waste" and "hazardous waste" and authorize imposition of substantial
fines and penalties for noncompliance. Although CERCLA currently excludes
petroleum from its definition of "hazardous substance," state laws affecting the
Company's operations impose clean-up liability relating to petroleum and
petroleum related products. In addition, although RCRA classifies certain oil
field wastes as "non-hazardous," such exploration and production wastes could be
reclassified as hazardous wastes thereby making such wastes subject to more
stringent handling and disposal requirements.
 
     Federal regulations require certain owners or operators of facilities that
store or otherwise handle oil, such as the Company, to prepare and implement
spill prevention, control countermeasure and response plans
 
                                       52
<PAGE>   54
 
relating to the possible discharge of oil into surface waters. The Oil Pollution
Act of 1990 contains numerous requirements relating to the prevention of and
response to oil spills into waters of the United States. For onshore and
offshore facilities that may affect waters of the United States, the OPA
requires an operator to demonstrate financial responsibility. Regulations are
currently being developed under federal and state laws concerning oil pollution
prevention and other matters that may impose additional regulatory burdens on
the Company. In addition, the Clean Water Act and analogous state laws require
permits to be obtained to authorize discharge into surface waters or to
construct facilities in wetland areas. With respect to certain of its
operations, the Company is required to maintain such permits or meet general
permit requirements. The EPA recently adopted regulations concerning discharges
of storm water runoff. This program requires covered facilities to obtain
individual permits, participate in a group or seek coverage under an EPA general
permit. The Company believes that it will be able to obtain, or be included
under, such permits, where necessary, and to make minor modifications to
existing facilities and operations that would not have a material effect on the
Company.
 
     The Company has acquired leasehold interests in numerous properties that
for many years have produced natural gas and oil. Although the previous owners
of these interests have used operating and disposal practices that were standard
in the industry at the time, hydrocarbons or other wastes may have been disposed
of or released on or under the properties. In addition, some of the Company's
properties are operated by third parties over whom the Company has no control.
Notwithstanding the Company's lack of control over properties operated by
others, the failure of the operator to comply with applicable environmental
regulations may, in certain circumstances, adversely impact the Company. See
"Risk Factors -- Compliance with Environmental Regulations" and "Management's
Discussion and Analysis of Financial Condition and Results of
Operations -- Other Matters."
 
LEGAL PROCEEDINGS
 
     The Company is not a party to any material legal proceedings.
 
                                   MANAGEMENT
 
DIRECTORS AND EXECUTIVE OFFICERS
 
     The following table sets forth certain information regarding the executive
officers and directors of the Company:
 
   
<TABLE>
<CAPTION>
                 NAME                    AGE                  POSITION
                 ----                    ---                  --------
<S>                                      <C>   <C>
Ben M. Brigham........................   38    President, Chief Executive Officer and
                                                 Chairman of the Board
Anne L. Brigham.......................   36    Executive Vice President and Director
Jon L. Glass..........................   42    Vice President -- Exploration and
                                               Director
Craig M. Fleming......................   41    Chief Financial Officer
David T. Brigham......................   37    Vice President -- Land and
                                               Administration, Corporate Secretary
A. Lance Langford.....................   36    Vice President -- Operations
Karen E. Lynch........................   37    Vice President -- Legal and General
                                                 Counsel
Harold D. Carter......................   59    Director
Alexis M. Cranberg....................   42    Director
Gary J. Milavec.......................   36    Director
Stephen P. Reynolds...................   46    Director
</TABLE>
    
 
                                       53
<PAGE>   55
 
     Set forth below is a description of the backgrounds of the executive
officers and directors of the Company.
 
     Ben M. "Bud" Brigham has served as Chief Executive Officer, President and
Chairman of the Board of the Company since founding the Company in 1990. From
1984 to 1990, Mr. Brigham served as an exploration geophysicist with Rosewood
Resources, an independent oil and gas exploration and production company. Mr.
Brigham began his career in Houston as a seismic data processing geophysicist
for Western Geophysical, a provider of 3-D seismic services, after earning his
B.S. in Geophysics from the University of Texas.
 
     Anne L. Brigham has served as Executive Vice President and a Director of
the Company since its inception in 1990 and as Corporate Secretary from 1990 to
February 1998. Before joining the Company full-time in 1991, Ms. Brigham
practiced law in the oil and gas and real estate sections of Thompson & Knight,
P.C. Ms. Brigham worked as a geologist for Hunt Petroleum Corporation, an
independent oil and gas exploration and production company, for over two years
before attending law school. Ms. Brigham holds a B.S. in Geology from the
University of Texas and a J.D. from Southern Methodist University.
 
     Jon L. Glass joined the Company in 1992 and has served as Vice
President -- Exploration since 1994 and a Director of the Company since 1995.
From 1984 to 1992, Mr. Glass served in various capacities with Santa Fe
Minerals, an oil and gas exploration company, in a variety of staff and
managerial positions mainly focused on Santa Fe Minerals' exploration activities
in the midcontinent and Gulf of Mexico (onshore and offshore). During this time
Mr. Glass also assisted in the development of exploration and acquisition
opportunities for Santa Fe Minerals in Canada and South America. Mr. Glass'
early geological experience includes three years with Mid-America Pipeline
Company and two years with Texaco USA, serving mainly as a midcontinent
exploration geologist. Mr. Glass holds a B.S. and an M.S. in Geology from
Oklahoma State University and an M.B.A. from the University of Tulsa.
 
     Craig M. Fleming has served as the Chief Financial Officer of the Company
since 1993. From 1990 to 1993, Mr. Fleming served as Controller of Odyssey
Petroleum Co., Ltd., an independent energy company. From 1988 to 1990, Mr.
Fleming served as Controller and Treasurer for Harken Exploration Company, an
independent energy company. Mr. Fleming began his career with Arthur Anderson &
Co. in the Oil and Gas Audit Division and is a Certified Public Accountant. Mr.
Fleming holds a B.B.A. in Accounting from Texas A&M University.
 
     David T. Brigham joined the Company in 1992 and has served as Vice
President -- Land and Administration and Corporate Secretary of the Company
since February 1998. Mr. Brigham served as Vice President -- Legal of the
Company from 1994 until February 1998. From 1987 to 1992, Mr. Brigham was an oil
and gas attorney with Worsham, Forsythe, Sampels & Wooldridge. Before attending
law school, Mr. Brigham was a landman for Wagner & Brown Oil and Gas Producers,
an independent oil and gas exploration and production company. Mr. Brigham holds
a B.B.A. in Petroleum Land Management from the University of Texas and a J.D.
from Texas Tech School of Law.
 
     A. Lance Langford joined the Company as Manager of Operations in 1995 and
has served as Vice President -- Operations since January 1997. From 1987 to
1995, Mr. Langford served in various engineering capacities with Meridian Oil
Inc., handling a variety of reservoir, production and drilling responsibilities.
Mr. Langford holds a B.S. in Petroleum Engineering from Texas Tech University.
 
   
     Karen E. Lynch joined the Company in October 1997 as General Counsel and
has served as Vice President -- Legal and General Counsel of the Company since
February 1998. Prior to joining the Company, Ms. Lynch was a shareholder in the
Dallas-based law firm of Thompson & Knight, P.C., where she practiced in the
energy area since joining the firm in 1987. Ms. Lynch holds a B.B.A. in
Petroleum Land Management from the University of Texas and a J.D. from the
University of Oklahoma.
    
 
     Harold D. Carter has served as a Director of and consultant to the Company
since 1992. Mr. Carter has more than 30 years experience in the oil and gas
industry and has been an independent consultant since 1990. Prior to consulting,
Mr. Carter served as Executive Vice President of Pacific Enterprises Oil Company
(USA). Before that, Mr. Carter was associated for 20 years with Sabine
Corporation, ultimately serving as President and Chief Operating Officer from
1986 to 1989. Mr. Carter consults for Endowment Advisors, Inc.
 
                                       54
<PAGE>   56
 
with respect to its EEP Partnerships and Associated Energy Managers, Inc. with
respect to its Energy Income Fund, L.P. and is a director of Abraxas Petroleum
Corporation. Mr. Carter has a B.B.A. in Petroleum Land Management from the
University of Texas and has completed the Program for Management Development at
the Harvard University Business School.
 
     Alexis M. Cranberg has served as a Director of the Company since 1992. Mr.
Cranberg is President of Aspect Management Corporation, an oil and gas
exploration and investment company. In addition, Mr. Cranberg is a Director of
Esenjay Exploration, Inc. and Westport Oil and Gas, Inc. and a past Director of
General Atlantic Resources, Inc. and United Meridian Corporation. He holds a
B.S. in Petroleum Engineering from the University of Texas and an M.B.A. from
Stanford University.
 
     Gary J. Milavec has served as a Director of the Company since 1995. Mr.
Milavec is a Managing Director of RIMCO, an investment management firm
specializing in the energy industry. Prior to joining RIMCO in 1990, Mr. Milavec
spent two years in the corporate finance department of Rauscher Pierce Refsnes,
Inc. and three years as a geological engineer with Shell Western E&P, Inc. He
also serves as a director of Universal Seismic Associates, Inc. and Texoil, Inc.
Mr. Milavec holds a B.A. in Geology from the University of Rochester, an M.S. in
Geology from the University of Oklahoma and an M.B.A. from the University of
Houston.
 
     Stephen P. Reynolds has served as a Director of the Company since 1996. Mr.
Reynolds is a managing member of General Atlantic Partners, LLC ("GAP LLC") and
has been with GAP LLC or its predecessor entities since April 1980. Mr. Reynolds
is also President of GAP III Investors, Inc., the general partner of General
Atlantic Partners III, L.P., and is a general partner and limited partner of
GAP-Brigham Partners, L.P. Mr. Reynolds is on the board of directors of Solo
Serve Corporation, a publicly traded off-price soft goods retail company, and
Computer Learning Centers, Inc., a publicly traded company providing technology
related training. Mr. Reynolds is a nominee for Director of SS&C Technologies,
Inc. Mr. Reynolds holds a B.A. in Economics from Amherst College and a Masters
degree in Accounting from New York University.
 
     All directors are elected to serve until the next annual meeting of
stockholders and until their successors are elected and qualified. Executive
officers are generally elected annually by the Board of Directors to serve,
subject to the discretion of the Board of Directors, until their successors are
elected or appointed.
 
     There is no family relationship between any of the directors or between any
director and any executive officer of the Company except that Ben M. Brigham and
Anne L. Brigham are married and David T. Brigham is the brother of Ben M.
Brigham. For information regarding certain business relationships between the
Company and certain of its directors, see "Certain Transactions."
 
   
COMMITTEES OF THE BOARD
    
 
     The Company's Board of Directors formed standing audit and compensation
committees on February 26, 1997, which are composed of Harold D. Carter, Alexis
M. Cranberg and Gary J. Milavec. The Audit Committee's primary responsibilities
are to (i) recommend the Company's independent auditors to the Board of
Directors, (ii) review with the Company's auditors the plan and scope of the
auditor's annual audit, the results thereof and the auditors' fees, (iii) review
the Company's financial statements and (iv) take such other action as it deems
appropriate as to the accuracy and completeness of financial records of the
Company and financial information gathering,reporting policies and procedures of
the Company. The Compensation Committee exercises the power of the Board of
Directors in connection with all matters relating to compensation of executive
officers, employee benefit plans and the administration of the Company's stock
option programs.
 
DIRECTOR COMPENSATION
 
     Fees and Expenses; Other Arrangements. Directors who are also employees of
the Company are not separately compensated for serving on the Board of
Directors. Directors who are not employees of the Company receive $5,000 per
year and $500 per meeting for their services as directors. In addition, the
 
                                       55
<PAGE>   57
 
Company reimburses Directors for the expenses incurred in connection with
attending meetings of the Board of Directors and its committees.
 
     Pursuant to a consulting agreement with Harold D. Carter that expired May
1, 1997, the Company paid Mr. Carter $6,000 per month through June 1996 and then
$7,200 per month for the remainder of the term of the agreement to spend
approximately 50% of his working time performing such consulting and advisory
services regarding the operations of the Company as the Company requested,
including service on the management committee of the Company's predecessor
partnership. Pursuant to a subsequent consulting agreement that expires December
31, 1998, Mr. Carter continues to serve as a consultant to the Company and is
currently being compensated $7,200 per month for such services and is reimbursed
by the Company for his out-of-pocket expenses. In addition, pursuant to the
terms of Mr. Carter's consulting agreement, the Company pays Associated Energy
Managers, Inc. $1,000 per month to offset a portion of Mr. Carter's office
overhead expenses and to provide the Company with limited use of part of Mr.
Carter's office space for purposes of conducting business while employees of the
Company are in Dallas, Texas.
 
     Alexis M. Cranberg and Stephen P. Reynolds served on the management
committee of the Company's predecessor partnership pursuant to the terms of an
agreement with General Atlantic, and Gary J. Milavec served on the committee
pursuant to the terms of an agreement with RIMCO. The Company is not obligated
to nominate any of the three to serve as a Director of the Company in the
future.
 
     Director Stock Options. The Company's stockholders have approved the 1997
Director Stock Option Plan, pursuant to which each newly elected nonemployee
director shall be granted an option to purchase 1,000 shares of Common Stock and
each nonemployee director will receive an option to purchase 500 shares of
Common Stock on December 31 of each year. The options under the plan are granted
at fair market value on the grant date and become exercisable, subject to
certain conditions, in five equal annual installments on the first five
anniversaries of the grant date. The options terminate ten years from the grant
date, unless terminated sooner. Twenty-five thousand shares of Common Stock have
been authorized and reserved for issuance pursuant to the plan. Options to
purchase 2,000 shares of Common Stock were granted on December 31, 1997 to the
Company's four nonemployee directors pursuant to the 1997 Director Stock Option
Plan.
 
LIMITATION OF LIABILITY AND INDEMNIFICATION MATTERS
 
     In accordance with Section 102(b)(7) of the Delaware General Corporation
Law ("DGCL"), the Company's Certificate of Incorporation includes a provision
that, to the fullest extent permitted by law, eliminates the personal liability
of members of its Board of Directors to the Company or its stockholders for
monetary damages for breach of fiduciary duty as a director. Such provision does
not eliminate or limit the liability of a director (1) for any breach of a
director's duty of loyalty to the Company or its stockholders, (2) for acts or
omissions not in good faith or which involve intentional misconduct or a knowing
violation of a law, (3) for paying an unlawful dividend or approving an illegal
stock repurchase (as provided in Section 174 of the DGCL) or (4) for any
transaction from which the director derived an improper personal benefit.
 
     The Company has entered into indemnity agreements with each of its
executive officers and directors that provide for indemnification in certain
instances against liability and expenses incurred in connection with proceedings
brought by or in the right of the Company or by third parties by reason of a
person serving as an officer or director of the Company.
 
     The Company believes that these provisions and agreements will assist the
Company in attracting and retaining qualified individuals to serve as directors
and officers.
 
COMPENSATION COMMITTEE INTERLOCKS AND INSIDER PARTICIPATION
 
     The Company's compensation committee during the last ten months of the past
fiscal year consisted of Messrs. Carter, Cranberg and Milavec and all
determinations concerning executive compensation for such period for the
Company's executive officers were made by the compensation committee. The
compensation committee members abstained from participation in compensation
determinations concerning their own
 
                                       56
<PAGE>   58
 
compensation. None of the executive officers of the Company has served on the
board of directors or on the compensation committee of any other entity, any of
whose officers served on the Board of Directors of the Company.
 
EXECUTIVE COMPENSATION
 
     Summary of Cash and Certain Compensation. The following table sets forth
certain summary information concerning the compensation paid or awarded to the
Chief Executive Officer of the Company and the only other executive officers of
the Company who earned in excess of $100,000 in 1997 (the "named executive
officers") for the years indicated.
 
                           SUMMARY COMPENSATION TABLE
 
<TABLE>
<CAPTION>
                                                                                  LONG-TERM
                                                                                COMPENSATION
                                                                          -------------------------
                                              ANNUAL COMPENSATION                          SHARES
               NAME AND                  ------------------------------    RESTRICTED    UNDERLYING       ALL OTHER
          PRINCIPAL POSITION             YEAR   SALARY($)   BONUS($)(1)   STOCK AWARDS    OPTIONS     COMPENSATION($)(2)
          ------------------             ----   ---------   -----------   ------------   ----------   ------------------
<S>                                      <C>    <C>         <C>           <C>            <C>          <C>
Ben M. Brigham.........................  1997    228,125      30,600             --            --           5,690
  Chief Executive Officer, President
    and                                  1996    144,000      15,000             --            --           4,817
  Chairman of the Board
Jon L. Glass...........................  1997    127,301      43,268         66,964       208,334             354
  Vice President -- Exploration          1996    109,782       3,223             --            --              --
Craig M. Fleming.......................  1997    122,272      44,971         44,643        69,445             477
  Chief Financial Officer                1996    102,919       8,063             --            --              --
David T. Brigham.......................  1997    108,895      32,712         44,643        69,445             428
  Vice President -- Land and             1996     94,874      10,505             --            --              --
  Administration, Corporate Secretary
A. Lance Langford......................  1997    107,469      43,111             --        52,085             410
  Vice President -- Operations           1996     94,090       7,261             --            --              --
</TABLE>
 
---------------
 
(1) Includes the following moving allowances granted in 1997 to employees in
    connection with the Company's relocation of its corporate headquarters from
    Dallas, Texas, to Austin, Texas: Ben M. Brigham -- $30,600; Jon L.
    Glass -- $12,076; Craig M. Fleming -- $23,654; David T. Brigham -- $17,529;
    and A. Lance Langford -- $23,524.
 
(2) Amounts for Ben M. Brigham represent premiums paid by the Company under life
    and disability insurance plans of $1,442 and $4,248, respectively, in 1997,
    and $1,404 and $3,413, respectively, in 1996. Amounts for Jon L. Glass,
    Craig M. Fleming, David T. Brigham and A. Lance Langford represent premiums
    paid by the Company under a disability insurance plan in 1997.
 
     Option Grants. The following table contains information about stock option
grants to the named executive officers in 1997:
 
                       OPTION GRANTS IN LAST FISCAL YEAR
 
<TABLE>
<CAPTION>
                                                                                POTENTIAL REALIZED VALUE AT
                                                                                  ASSUMED ANNUAL RATES OF
                                                                                 STOCK PRICE APPRECIATION
                                         INDIVIDUAL GRANTS                          FOR OPTION TERM(1)
                         -------------------------------------------------   ---------------------------------
                         NUMBER OF     % OF TOTAL
                         SECURITIES     OPTIONS      EXERCISE
                         UNDERLYING    GRANTED TO    OR BASE
                          OPTIONS     EMPLOYEES IN    PRICE     EXPIRATION
         NAME            GRANTED(#)   FISCAL YEAR     ($/SH)       DATE        0%($)       5%($)      10%($)
         ----            ----------   ------------   --------   ----------   ---------   ---------   ---------
<S>                      <C>          <C>            <C>        <C>          <C>         <C>         <C>
Ben M. Brigham.........        --           --           --           --            --          --          --
Jon L. Glass...........   208,334         32.3         5.00       7/1/04     2,005,215   3,142,280   4,619,530
Craig M. Fleming.......    69,445         10.8         5.00       7/1/04       668,408   1,047,433   1,539,851
David T. Brigham.......    69,445         10.8         5.00       7/1/04       668,408   1,047,433   1,539,851
A. Lance Langford......    52,085          8.1         5.00       7/1/04       501,318     785,593   1,154,916
</TABLE>
 
                                       57
<PAGE>   59
 
---------------
 
(1) Amounts represent hypothetical gains that could be achieved for the options
    if they are exercised at the end of the option term. Those gains are based
    on assumed rates of stock price appreciation of 0%, 5% and 10% compounded
    annually from February 27, 1997, the date such options had been granted,
    through the expiration date. For the option term ending July 1, 2004, based
    on the closing price on The Nasdaq Stock Market(SM) of the Common Stock of
    $14.63 on December 31, 1997, a share of the Common Stock would have a value
    on July 1, 2004 of approximately $20.08 at an assumed appreciation rate of
    5% and approximately $27.17 at an assumed appreciation rate of 10%.
 
     Option Exercises and Year-End Option Values. The following table provides
information about the number of shares issued upon option exercises by the named
executive officers during 1997, and the corresponding value realized by the
named executive officers. The table also provides information about the number
and value of options that were held by the named executive officers at December
31, 1997.
 
                AGGREGATED OPTION EXERCISES IN LAST FISCAL YEAR
                            AND FY-END OPTION VALUES
 
<TABLE>
<CAPTION>
                                                           NUMBER OF SECURITIES          VALUE OF UNEXERCISED
                                                          UNDERLYING UNEXERCISED             IN-THE-MONEY
                              SHARES                       OPTIONS AT FY-END(#)          OPTIONS AT FY-END($)
                            ACQUIRED ON      VALUE      ---------------------------   ---------------------------
           NAME             EXERCISE(#)   REALIZED($)   EXERCISABLE   UNEXERCISABLE   EXERCISABLE   UNEXERCISABLE
           ----             -----------   -----------   -----------   -------------   -----------   -------------
<S>                         <C>           <C>           <C>           <C>             <C>           <C>
Ben M. Brigham............      --            --            --                --          --                 --
Jon L. Glass..............      --            --            --           208,334          --          2,005,215
Craig M. Fleming..........      --            --            --            69,445          --            668,408
David T. Brigham..........      --            --            --            69,445          --            668,408
A. Lance Langford.........      --            --            --            52,085          --            501,318
</TABLE>
 
  Employment Agreements
 
     The Company employs Ben M. Brigham under an employment agreement (the
"Employment Agreement") as Chief Executive Officer and President of the Company
for a five year term that began in February 1997. The Employment Agreement
contains rollover provisions so that at all times the term of the Employment
Agreement shall be not less than three years. The agreement provides for an
annual salary of $275,000, which the Board of Directors may further increase
from time to time. Mr. Brigham is also entitled to an annual cash bonus, not to
exceed 75% of his then current salary, determined based on criteria established
by the Board of Directors. Under the Employment Agreement, Mr. Brigham is
entitled to participate in any employee benefit programs that the Company
provides to its executive officers. The only employee benefit programs that the
Company offers to its officers and employees are group insurance coverage and
participation in the Company's 401(k) Retirement Plan, the 1997 Incentive Plan
and the Incentive Bonus Plan. If Mr. Brigham terminates his employment for good
reason, which includes a material reduction of Mr. Brigham's position without
cause or his written consent, breach of a material provision of the Employment
Agreement or improper notice of termination, or if the Company terminates Mr.
Brigham without cause, the Company must pay Mr. Brigham a sum equal to the
amount of his annual base salary that he would have received during the
remainder of his employment term plus the average of his annual bonuses received
in the preceding two years times the number of years in the remainder of his
employment term. Mr. Brigham's agreement also contains a three-year non-compete
and confidentiality clause with standard terms.
 
     Each of the other named executive officers of the Company is a party to a
confidentiality and noncompete agreement.
 
EMPLOYEE BENEFIT PLANS
 
     Employees' Restricted Stock. In February 1997, the Company, in connection
with the Exchange, issued 66,964 shares, 44,643 shares and 44,643 shares of
restricted stock to Jon L. Glass, Craig M. Fleming and David T. Brigham,
respectively, in exchange for restricted limited partnership interests issued to
them in 1994.
 
                                       58
<PAGE>   60
 
Each agreement relating to the restricted stock contains confidentiality,
noncompete and vesting provisions. The shares awarded Messrs. Brigham and
Fleming vest over a three-year period -- 30% in each of July 1997 and 1998 and
40% in July 1999. Of the shares awarded to Mr. Glass, 45% have already vested,
28.33% vest in July 1998, and 26.67% vest in July 1999.
 
     1997 Incentive Plan. The Board of Directors and the stockholders of the
Company approved the adoption of the Company's 1997 Incentive Plan (the "1997
Incentive Plan") as of February 27, 1997. The Compensation Committee selects
participants in the 1997 Incentive Plan from among those key employees and
others who hold positions of responsibility with the Company and whose
performance may have a significant effect on the success of the Company. An
aggregate of 1,588,169 shares of Common Stock have been authorized and reserved
for issuance pursuant to the 1997 Incentive Plan. In March 1997, options were
granted to purchase a total of 644,097 shares of Common Stock at an exercise
price per share of $5.00. These options vest over six years. Jon L. Glass, Craig
M. Fleming and David T. Brigham were granted options to purchase 208,334 shares,
69,445 shares and 69,445 shares of Common Stock, respectively. With the
exception of options to purchase 138,889 shares of Common Stock granted to Jon
L. Glass, these options vest as follows: 30% on July 1, 1998; 20% on July 1,
1999; 16.66% on July 1, 2000; 16.67% on July 1, 2001; and the balance on July 1,
2002. The balance of Mr. Glass' options (138,889 shares) vest as follows: 30% on
February 1, 1999; 20% on July 1, 1999; 16.66% on July 1, 2000; 16.67% on July 1,
2001; and 16.67% on July 1, 2002. Of the options issued in 1997 pursuant to the
1997 Incentive Plan, options to purchase 17,360 have been forfeited by certain
employees.
 
     In January 1998, options were granted to purchase 307,250 shares of Common
Stock at an exercise price of $12.875 per share. These options vest over six
years in three equal bi-annual installments starting the second year following
the date of grant.
 
     Subject to the provisions of the 1997 Incentive Plan, the Compensation
Committee is authorized to determine the type or types of awards made to each
participant and the terms, conditions and limitations applicable to each award.
In addition, the Compensation Committee has the exclusive power to interpret the
1997 Incentive Plan and to adopt rules and regulations that it may deem
necessary or appropriate, in keeping with the objectives of the 1997 Incentive
Plan.
 
     Pursuant to the 1997 Incentive Plan, participants will be eligible to
receive awards consisting of stock options, stock appreciation rights, stock,
restricted stock, cash or any combination of the foregoing. Stock options may be
either incentive stock options within the meaning of Section 422 of the Internal
Revenue Code of 1986, as amended, or nonqualified stock options.
 
     Incentive Bonus Plan. In connection with the Exchange, the Company adopted
the Incentive Bonus Plan (the "Incentive Bonus Plan") previously established by
the Company's predecessor partnership. The Incentive Bonus Plan is designed to
pay cash compensation and bonuses to eligible employees of the Company. Under
the Incentive Bonus Plan, the Company maintains an incentive account for each
calendar year (each an "Incentive Account") and a discretionary bonus account
(the "Discretionary Bonus Account"). Prior to the beginning of each calendar
year, the President of the Company designates the employees of the Company who
are eligible to participate in the Incentive Account being established for such
year, and each such employee's percentage of interest (an "Account Percentage")
in such Incentive Account. Subject to certain adjustments provided under the
Incentive Bonus Plan, each Incentive Account is credited with an amount equal to
one-half of the net revenue received by the Company which is equivalent to a one
percent interest in the Company's net revenue interest in the oil and gas
produced from each Company well drilled or reentered after April 30, 1992, and
the Discretionary Bonus Account is credited with an amount equal to the amount
credited to each Incentive Account. The President has discretion to allocate a
greater interest to the accounts. Within 30 days after each March 31 and
September 30, an employee who has been designated to have an Account Percentage
in the Incentive Account established for a particular year receives cash
compensation equal to his or her Account Percentage in such Incentive Account
multiplied by the amount credited to that Incentive Account for the six-month
period then ended. In addition, the President of the Company has the discretion
to award cash bonuses to any Company employee from the amounts credited to the
Discretionary Bonus Account. The participation of an employee under the
Incentive Bonus Plan
 
                                       59
<PAGE>   61
 
terminates when he or she ceases to be an employee of the Company for any
reason. The President of the Company may amend or terminate the Incentive Bonus
Plan at any time.
 
                              CERTAIN TRANSACTIONS
 
     In connection with the land work necessary prior to and during 3-D seismic
acquisitions, the Company engages Brigham Land Management ("BLM"), an
independent company owned and managed by Vincent M. Brigham, a brother of Ben M.
Brigham, who is the Company's Chief Executive Officer, President and Chairman of
the Board, and David T. Brigham, who is a Vice President of the Company. BLM
specializes in conducting the field land work necessary prior to and during 3-D
seismic acquisitions. BLM has regional expertise in the Anadarko Basin and the
Texas Panhandle, and, to a lesser extent, West Texas. BLM performs these
services for the Company using BLM's employees and independent contractors. In
1995, 1996 and 1997, the Company paid BLM approximately $382,000, $596,000 and
$837,000, respectively. Other participants in the Company's 3-D seismic projects
reimbursed the Company for a portion of these amounts. Based on its experience
with other firms in the area, the Company believes that BLM's charges are at or
below those of other firms.
 
     In 1994, the Company, through its subsidiary Quest Resources, L.L.C.,
formed Venture Acquisitions, L.P. ("Venture") with affiliates of RIMCO, a holder
of in excess of 5% of the Common Stock, to provide the Company with the capital
to acquire interests in certain potential drilling locations, producing
properties and 3-D seismic projects. The RIMCO affiliates have contributed $5.2
million to Venture, and the Company has contributed $286,138. Until the first
payout under the Venture limited partnership agreement, the Company's share of
all capital costs is 5%, and the Company's share of revenues and related
production expenses and costs is 10%. Between the first and second payout
levels, the Company's share of capital costs and revenues and related production
expenses and costs is 25% and thereafter increases to 50%. Venture acquired from
the Company an interest in (i) a 3-D project for approximately $75,000 in 1995,
and (ii) two 3-D delineated potential drilling locations and 3-D seismic for
approximately $83,000 in 1996. The Company billed Venture approximately $14,924
in 1995, $16,500 in 1996 and $56,658 in 1997 for its proportionate share of
exploration and overhead costs. Because RIMCO was not an affiliate of the
Company when the Venture partnership was formed, the Company believes that the
terms of the Venture partnership are no less favorable than could be obtained
from an unaffiliated third party. Gary J. Milavec, a director of the Company and
member of the Company's compensation committee, is employed by RIMCO.
 
     In November 1994, the Company, certain RIMCO affiliates and other unrelated
industry participants entered into a geophysical exploration agreement creating
an area of mutual interest in its Esperson Dome Project in Liberty and Harris
counties, Texas. The Company financed its participation in this project by
assigning its interest, and obligation to bear costs, to Vaquero Gas Company,
Inc. ("Vaquero"), a RIMCO affiliate, subject to a 5% net profits overriding
royalty interest and the right to receive up to 50% of Vaquero's interest on the
occurrence of certain payouts. The Company also retained responsibility for
managing the 3-D seismic acquisition and interpretation of the data after it had
been acquired. During 1995, 1996 and 1997, the Company received approximately
$25,000, $123,000 and $50,000, respectively, from the RIMCO affiliates,
including Vaquero, for workstation time and geoscientists' time in interpreting
the 3-D seismic that were acquired. Because RIMCO was not an affiliate of the
Company when the project was initiated and the interest to Vaquero was
transferred, the Company believes that the terms of the arrangement are no less
favorable than could be obtained from an unaffiliated third party.
 
     In January 1997, the Company, RIMCO and Tigre Energy Corporation ("Tigre")
entered into an agreement under which the Company had been initially assigned an
undivided 22% interest (subject to a proportionately reduced 3% overriding
royalty interest) in a project ("Tigre Point") located in Vermillion Parish,
Louisiana in return for paying certain costs of acquiring 3-D seismic and land
within the project area. The Company acquired an additional 12.5% working
interest from RIMCO and an additional 37.5% working interest from Tigre in parts
of the project under the same terms as the initial 25% interest. The Company
believes that the arrangements with RIMCO affiliates relating to Tigre Point are
on terms no less favorable
 
                                       60
<PAGE>   62
 
than could be obtained from an unaffiliated third party, because RIMCO and
Tigre, an unaffiliated third party, are participants in the project on
substantially similar terms.
 
     The Company and an affiliate of Universal Seismic Associates, Inc. ("USA"),
a public company of which RIMCO affiliates beneficially own approximately 22% of
the outstanding common stock, have entered into a geophysical exploration
agreement covering an area of mutual interest on the Gulf Coast. Under the terms
of the agreement, USA conducted a 3-D seismic program established by the Company
and USA and processed the data acquired under the program at cost, and the
Company will interpret the resulting seismic for the benefit of the Company and
USA at no charge to USA. Subject to a party's electing not to participate in an
acquired interest, the Company and USA will each own an undivided 50% interest
in all land interests acquired within the area of mutual interest. Through
December 31, 1997, the Company had incurred $209,314 of costs under those
arrangements. Based on its experience in acquiring 3-D seismic, the Company
believes that it has acquired 3-D seismic under this agreement on terms, and
that the arrangement is on terms, no less favorable than could be obtained from
an unaffiliated third party.
 
     In 1993 and 1994 the Company issued to RIMCO 10% Notes in principal amounts
of $3.0 million and $4.9 million, respectively. In 1995 the Company issued RIMCO
additional 10% Notes in a principal amount of $2.6 million, and in the same
year, issued RIMCO 5% Notes in a principal amount of $16.0 million, $10.5
million of which was used to repay all the outstanding 10% Notes. The 5% Notes
were exchanged for 1,754,464 shares of Common Stock in the Exchange. In 1995,
1996 and 1997, the Company paid RIMCO $631,989, $809,332 and $340,000,
respectively, in interest payments on the 5% Notes and the 10% Notes. In 1995,
1996 and 1997, the Company distributed to RIMCO $102,107, $82,097 and $48,150,
respectively for RIMCO's overriding royalty interest in certain natural gas and
oil properties.
 
     Pursuant to a consulting agreement with Harold D. Carter that expired May
1, 1997, the Company paid Mr. Carter $6,000 per month through June 1996 and
$7,200 per month for the remainder of the term of the agreement to spend
approximately 50% of his working time performing such consulting and advisory
services regarding the operations of the Company as the Company requested,
including service on the management committee of the Company's predecessor
partnership. Pursuant to this agreement, Mr. Carter received $72,000 in 1995,
$79,200 in 1996 and $86,580 in 1997. Additional disbursements totaling
approximately $13,000 were made by the Company to Mr. Carter during 1997 for the
reimbursement of certain expenses. Pursuant to the terms of a subsequent
consulting agreement, the Company will continue to utilize Mr. Carter's
consulting services through December 31, 1998 and pay Mr. Carter $7,200 per
month for those services and reimburse Mr. Carter for certain out-of-pocket
expenses during the term of the agreement. In addition, pursuant to the terms of
Mr. Carter's consulting agreement, the Company pays Associated Energy Managers,
Inc. $1,000 per month to offset a portion of Mr. Carter's office overhead
expenses and to provide the Company with limited use of part of Mr. Carter's
office space for purposes of conducting business while employees of the Company
are in Dallas, Texas.
 
     In 1995, 1996 and 1997, the Company paid $35,000, $110,000 and $18,000 to
Aspect and affiliates of Alexis M. Cranberg, a director of the Company, to
acquire interests in a project in Grady County, Oklahoma and a project in
Hardeman and Wilbarger counties, Texas and Jackson County, Oklahoma. Based on
its experience in the industry, the Company believes that these transactions are
on terms no less favorable than could be obtained from an unaffiliated third
party. The Company billed Aspect and other affiliates of Alexis M. Cranberg
$13,000 in 1995 and $68,000 in 1996 for its proportionate share of the costs
related to the projects.
 
     The Company has entered into a Registration Rights Agreement with General
Atlantic Partners III, L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P.
II, RIMCO Partners, L.P. III and RIMCO Partners, L.P. IV, Ben M. Brigham, Anne
L. Brigham, Harold D. Carter, Craig M. Fleming, David T. Brigham and Jon L.
Glass. Pursuant to the Registration Rights Agreement, Anne and Ben Brigham,
acting together, the RIMCO entities, acting together, and the General Atlantic
entities, acting together, each may separately require the Company to register
securities, on one occasion, if the shares to be registered have an estimated
aggregate offering price to the public of at least $3.0 million. One additional
registration is allowed if any registrable securities requested to be included
in a previous registration statement have not been disposed
 
                                       61
<PAGE>   63
 
of in accordance with that previous registration. The Registration Rights
Agreement also provides "piggyback" registration rights for all registrations of
registrable securities for the Company or another security holder. In an
underwritten offering, however, the Company may exclude all or a portion of the
securities being registered pursuant to "piggyback" registration rights if the
managing underwriter determines that including those securities would raise a
substantial doubt about whether the proposed offering could be consummated. The
Registration Rights Agreement contains customary indemnity by the Company in
favor of persons selling securities in a registration governed by the
Registration Rights Agreement, and by those persons in favor of the Company,
relating to the information included in or omitted from the Registration
Statement.
 
   
                             PRINCIPAL STOCKHOLDERS
    
 
   
     The table below sets forth information concerning (i) the only persons
known by the Company, based upon statements filed by such persons pursuant to
Section 13(d) or 13(g) of the Securities Exchange Act of 1934, as amended (the
"Exchange Act"), to own beneficially in excess of 5% of the Common Stock as of
August 13, 1998, and (ii) the shares of Common Stock beneficially owned, as of
August 13, 1998, by each director of the Company, each executive officer listed
in the Summary Compensation Table included elsewhere in this Prospectus, and all
directors and executive officers of the Company as a group. Except as indicated,
each individual has sole voting power and sole investment power over all shares
listed opposite his name.
    
 
   
<TABLE>
<CAPTION>
                                                                SHARES             SHARES BENEFICIALLY
                                                          BENEFICIALLY OWNED         OWNED AFTER THE
                                                       PRIOR TO THE OFFERING(1)         OFFERING
                                                       -------------------------   -------------------
NAME AND ADDRESS OF BENEFICIAL OWNER                      NUMBER       PERCENT      NUMBER     PERCENT
------------------------------------                   ------------   ----------   ---------   -------
<S>                                                    <C>            <C>          <C>         <C>
Ben M. Brigham(2)....................................   3,720,342        30.01%    3,720,342        %
  6300 Bridge Point Parkway, Bldg. 2, Suite 500
  Austin, Texas 78730
Anne L. Brigham(2)...................................   3,720,342        30.01%    3,720,342        %
  6300 Bridge Point Parkway, Bldg. 2, Suite 500
  Austin, Texas 78730
General Atlantic Partners, L.L.C.(3).................   2,807,143        22.64%    2,807,143        %
  Three Pickwick Plaza
  Greenwich, Connecticut 06830
Resource Investors Management Company(4).............   1,754,464        14.15%    1,754,464        %
  600 Travis Street, Suite 6875
  Houston, Texas 77002
R. Chaney & Co., Inc.(5).............................     635,000         5.12%      635,000        %
  909 Fannin, Suite 1275
  Two Houston Center
  Houston, Texas 77010
Craig M. Fleming(6)..................................      65,477         *           65,477     *
Jon L. Glass(7)......................................      88,798         *           88,798     *
David T. Brigham(8)..................................      66,477         *           66,477     *
A. Lance Langford(9).................................      18,365         *           18,365     *
Harold D. Carter.....................................     341,893         2.76%      341,893        %
Gary J. Milavec(10)..................................          --            --           --       --
Alexis M. Cranberg...................................          --            --           --       --
Stephen P. Reynolds(11)..............................          --            --           --       --
All directors and executive officers as a group
  (11 persons)(6)(7)(8)(9)...........................   4,301,977        34.70%    4,301,977        %
</TABLE>
    
 
---------------
 
                                       62
<PAGE>   64
 
  *  Represents less than 1%.
 
 (1) Beneficial ownership is determined in accordance with the rules of the SEC
     and generally includes voting or disposition power with respect to
     securities.
 
 (2) Includes 1,831,414 shares owned by Ben M. Brigham and 1,831,410 shares
     owned by Anne L. Brigham, who are husband and wife; 28,272 shares owned by
     Ben M. Brigham and Anne L. Brigham as Trustees under Brigham Parental Trust
     I; 28,246 shares owned by Ben M. Brigham and Anne L. Brigham as Trustees
     under Brigham Parental Trust II; and 1,000 shares held by David T. Brigham,
     as custodian for Elizabeth R. Brigham under the Texas Uniform Transfers to
     Minors Act.
 
 (3) Includes 2,679,418 shares held by GAP III; and 127,725 shares held by
     GAP-Brigham Partners, L.P. ("GAP-Brigham"). Stephen P. Reynolds is the
     general partner and a limited partner in GAP-Brigham and is President of
     GAP III Investors, Inc., the general partner of GAP III.
 
 (4) Includes 612,308 shares held by RIMCO Partners, L.P. II, 307,031 shares
     held by RIMCO Partners, L.P. III and 835,125 shares held by RIMCO Partners,
     L.P. IV (collectively, the "RIMCO Partnerships"). RIMCO is the general
     partner of each of the RIMCO Partnerships. The general partner of RIMCO is
     RIMCO Associates, Inc.
 
 (5) Includes 610,000 shares held by R. Chaney & Partners III L.P. ("Fund III")
     and 25,000 shares held by R. Chaney & Partners IV L.P. ("Fund IV"). R.
     Chaney & Partners, Inc. ("Partners") is the sole general partner of Fund
     III, and R. Chaney Investments, Inc. ("Investments") is the sole general
     partner of Fund IV. Mr. Robert H. Chaney is the sole shareholder of
     Partners and Investments.
 
   
 (6) Includes 44,643 shares of restricted stock, which vest as follows: 30% in
     July 1997, 30% in July 1998 and 40% in July 1999; and 20,834 shares of
     Common Stock issuable upon exercise of certain stock options that vested
     July 1, 1998.
    
 
   
 (7) Includes 66,964 shares of restricted stock, which vested as follows: 16.67%
     in February 1997, 28.33% in July 1997, 28.33% in July 1998 and 26.67% in
     July 1999; and 20,834 shares of Common Stock issuable upon exercise of
     certain stock options that vested July 1, 1998.
    
 
   
 (8) Includes 44,643 shares of restricted stock, which vest as follows: 30% in
     July 1997, 30% in July 1998 and 40% in July 1999; 1,000 shares gifted by
     Ben M. Brigham and Anne L. Brigham; and 20,834 shares of Common Stock
     issuable upon exercise of certain stock options that vested July 1, 1998.
    
 
 (9) Includes 17,365 shares of Common Stock issuable upon exercise of certain
     stock options that vest July 1, 1998.
 
(10) Gary J. Milavec is a Managing Director of RIMCO, the general partner of
     each of the RIMCO Partnerships, and is a Vice President of RIMCO
     Associates, Inc., the general partner of RIMCO. As such, Mr. Milavec may be
     deemed to share voting and investment power with respect to the 612,308
     shares held by RIMCO Partners, L.P. II, the 307,031 shares held by RIMCO
     Partners, L.P. III and the 835,125 shares held by RIMCO Partners, L.P. IV.
     Mr. Milavec disclaims beneficial ownership of shares beneficially owned by
     RIMCO and the RIMCO Partnerships.
 
(11) Stephen P. Reynolds is the general partner and a limited partner in
     GAP-Brigham and is President of GAP III Investors, Inc., the general
     partner of GAP III. As such, Mr. Reynolds may be deemed to share voting and
     investment power with respect to the 2,679,418 shares held by GAP III and
     the 127,725 shares held by GAP-Brigham. Mr. Reynolds disclaims beneficial
     ownership of shares owned by GAP III and GAP-Brigham except to the extent
     of his pecuniary interest therein.
 
   
                       DESCRIPTION OF OTHER INDEBTEDNESS
    
 
   
     In January 1998, Brigham entered into the Credit Facility with the Bank of
Montreal and the lenders signatory thereto. For more information, see
"Management's Discussion and Analysis of Financial Condition and Results of
Operations -- Liquidity and Capital Resources."
    
 
                                       63
<PAGE>   65
 
   
                              DESCRIPTION OF NOTES
    
 
   
GENERAL
    
 
   
     The Notes will be issued pursuant to an Indenture between the Company and
Chase Bank of Texas, National Association, as trustee (the "Trustee"). Copies of
the Indenture will be made available to prospective purchasers upon request to
the Company. The Indenture will be subject to the Trust Indenture Act of 1939,
as amended (the "Trust Indenture Act"). The terms of the Notes will include
those stated in the Indenture and those made part of the Indenture by reference
to the Trust Indenture Act. The Notes will be subject to all such terms, and
holders of the Notes are referred to the Indenture and the Trust Indenture Act
for a statement thereof. The following summary of certain provisions of the
Indenture does not purport to be complete and is qualified in its entirety by
reference to the Indenture, including the definitions therein of certain terms
used below. The definitions of certain terms used in the following summary are
set forth below under "-- Certain Definitions."
    
 
   
TERMS OF THE NOTES
    
 
   
     The Notes will be limited in aggregate principal amount to $40 million,
plus any PIK Interest, and will mature on             , 2003. Interest on the
Notes will be payable quarterly, beginning on November 15, 1998. Interest rates
payable on the Notes shall vary depending upon whether accrued interest is paid
in cash or by PIK Interest. Interest shall be paid in cash at interest rates of
  %,   % and   % per annum during years one through three, year four and year
five, respectively, of the term of the Notes; provided, however, that if the
payment in cash of interest accrued on the Notes would cause a "Borrowing Base
Deficiency" under the Senior Credit Agreement or would cause the Company to be
in violation of any covenant or other restriction set forth in any Senior Loan
Document or any Basic Document, the Company may pay PIK Interest at interest
rates of   %,   % and   % per annum during years one through three, year four
and year five, respectively, of the term of the Notes. The Notes may be prepaid
at any time, in whole or in part, without premium or penalty, provided that all
partial prepayments must be pro rata to the various holders of the Notes.
    
 
   
     Interest will be computed on the basis of a 360-day year for the actual
number of days elapsed commencing on the day immediately following any advance
of principal (or interest paid in kind) through and including the date of
payment of any principal amount. Principal, premium, if any, and interest on the
Notes will be payable in cash to holders of the Notes. The Notes will be
registered as to principal and interest in minimum denominations of $1,000 and
integral multiples of $1,000 in excess thereof. Because the parties anticipate
that the Notes, Warrants and Shares will be considered an "investment unit"
under certain United States Treasury Regulations, the aggregate offering price
must be allocated among the three securities. As a result, a portion of the
principal amount of the Notes may be considered "original issue discount"
("OID"). OID would accrue on the Notes on a constant yield basis over the term
of the Notes. Generally, OID accrues in advance of the receipt of cash to which
such OID is attributable regardless of the holder's method of accounting.
    
 
   
     Pursuant to the Securities Purchase Agreement, the initial purchasers of
the Notes will, as long as they and/or their affiliates beneficially own 5% or
more of the Common Stock (including the Warrant Shares, whether exercised or
not), have the right to designate one member of the Board of Directors of the
Company reasonably satisfactory to the Company. If such purchasers elect to
designate a person to serve as a member of the Board of Directors of the Company
(the "Designee"), the Securities Purchase Agreement will require the Company to
(i) expand as required the number of directors constituting the entire board,
(ii) elect such Designee as is reasonably satisfactory to the Company and (iii)
submit the name of such Designee to the Company's stockholders (together with a
recommendation for election) at each meeting of the Company's stockholders at
which directors are elected, until otherwise requested by such purchasers.
    
 
   
SECURITY
    
 
   
     The Obligations and the Subsidiary Guaranty Agreements, as appropriate,
will be secured by the following which, in each case shall be subordinate in
priority only to those liens, security interests or rights
    
 
                                       64
<PAGE>   66
 
   
granted in the same collateral to secure the performance of the Company under
the Senior Loan Documents, in accordance with, but subject to, the terms of the
Subordination Agreement: (i) Security Agreements of the Company, Brigham, Inc.,
Brigham Holdings I, LLC and Brigham Holdings II, LLC granting a security
interest in all of such entity's right, title and interest in and to the Capital
Stock of Brigham, Inc., Brigham Holdings I, LLC, Brigham Holdings II, LLC and
Brigham Oil & Gas, L.P. (the "Partnership"), (ii) a Security Agreement of the
Partnership granting a security interest in all of the Partnership's right,
title and interest in and to all accounts, general intangibles, equipment and
inventory of the Partnership, and (iii) a Mortgage, Deed of Trust, Assignment of
Production, Security Agreement and Financing Statement of the Partnership
covering all of the Property of the Partnership.
    
 
   
RANKING AND SUBORDINATION
    
 
   
     The Notes will be subject to the Subordination Agreement (as defined). See
"Subordination Agreement." As of June 30, 1998, on a pro forma basis, after
giving effect to the application of the estimated net proceeds from the
Offering, the Company would have had $20.5 of Senior Indebtedness outstanding.
The Indenture will limit, subject to certain financial tests, the amount of
additional Debt, including Senior Indebtedness, that the Company and its
Subsidiaries can incur. See "-- Certain Covenants Limitation on Indebtedness."
    
 
   
SUBSIDIARY GUARANTY AGREEMENTS
    
 
   
     Pursuant to the Subsidiary Guaranty Agreements, each Subsidiary Guarantor
will fully and unconditionally guarantee, jointly and severally, the prompt
payment of principal of and interest on the Notes, and all other indebtedness,
obligations and liabilities of the Company under the Securities Purchase
Agreement. Each Subsidiary Guarantor that makes a payment under a Subsidiary
Guaranty Agreement shall be entitled to contribution from each other Subsidiary
Guarantor, subject to such Subsidiary Guarantor's guarantee obligations, in a
pro rata amount based on the net worth of each Subsidiary Guarantor. Financial
statements for the Subsidiary Guarantors are not presented because the Company
has determined that they would not be material to investors.
    
 
   
     The obligations of each Subsidiary Guarantor will be limited to the greater
of (a) the "reasonably equivalent value" or "fair consideration" (or equivalent
concept) received by the Subsidiary Guarantor in exchange for the obligation
incurred under its Subsidiary Guaranty Agreement, within the meaning of any
applicable state or federal fraudulent conveyance or transfer laws; or (b) the
lesser of, after giving effect to the extent allowed by law to its rights of
contribution and subrogation under its Subsidiary Guaranty Agreement, (i) the
maximum amount that will not render the Subsidiary Guarantor insolvent or (ii)
the maximum amount that will not leave the Subsidiary Guarantor with any
property deemed an unreasonably small capital. Each Subsidiary Guarantor that
makes a payment under a Subsidiary Guaranty Agreement shall be entitled to
contribution from each other Subsidiary Guarantor in a pro rata amount based on
the net worth of each Subsidiary Guarantor.
    
 
   
     The rights and remedies of the Noteholders under the Subsidiary Guarantors
will be subject to the Liens created or evidenced by the Senior Loan agreements
and the terms and conditions of the Subordination Agreement. See "Subordination
Agreement."
    
 
   
CERTAIN COVENANTS
    
 
   
     The Indenture will contain certain covenants including, among others, the
following:
    
 
   
  Limitation on Indebtedness
    
 
   
     Neither the Company nor any Subsidiary will incur, create or assume any
Debt, other than Permitted Debt, such that the ratio of the Company's Adjusted
Consolidated Net Tangible Assets (as at the end of the immediately preceding
calendar quarter) to the sum of (a) Company's Consolidated Indebtedness (after
such incurrence, creation or assumption of additional Debt other than Permitted
Debt) plus (b) past due interest on Debt is less than 1.5 to 1.0. This covenant
shall also apply to any such Debt incurred or assumed as a result
    
 
                                       65
<PAGE>   67
 
   
of a merger or consolidation with any other Person. Any such Debt so incurred,
created or assumed (without violation of the Indenture) must be fully
subordinated to the Obligations unless the Agent agrees otherwise, provided
that, so long as certain holders of the Notes have been given a first look and
right to make a proposal for any future subordinated indebtedness, up to
$25,000,000 (less the maximum potential balance at the time in question of the
Schedule 8.02 Payables) in the aggregate of such Debt may be incurred that is
pari passu in right of payment with the Notes. Notwithstanding the foregoing, in
the event of any refinancing of the Senior Loan, which refinancing does not
violate, on a pro forma basis for the four fiscal quarters of the Company after
the refinancing, the interest coverage test described above under "Consolidated
Interest Coverage Ratio" in "Certain Covenants," the current ratio test
described under "Current Ratio," or, provided the amount of such refinanced
Senior Loan is more than $75,000,000, the covenant in the first sentence of this
paragraph, the refinanced Senior Loan shall remain senior to (and shall not be
subordinate to) the Obligations.
    
 
   
     Neither the Company nor any Subsidiary will incur, create, suffer or assume
any accounts payable for the deferred purchase price of Property or services or
any Trade Payables which are more than 75 days past the invoice or billing date,
unless such accounts payable are either (i) being contested in good faith by
appropriate proceedings and reserves as required under GAAP shall have been
established therefor, or (ii) Schedule 8.02 Payables which are not past due.
    
 
   
     Notwithstanding the foregoing, if at any time the ratio of the Company's
Adjusted Consolidated Net Tangible Assets to the sum of (a) Company's
Consolidated Indebtedness plus (b) past due interest on Debt, is less than 1.5
to 1.0, the Agent shall have the right to require, and the Company covenants and
agrees to convey (or cause to be conveyed) to the Trustee or the Agent for the
benefit of the Agent and the Noteholders, such additional Potential Collateral
as the Agent shall require (subject to the Senior Lenders' rights to a first and
prior lien in such Potential Collateral). Such conveyance shall be made within
30 days following receipt of written notice from the Agent and shall be deemed a
pledge of additional Collateral in accordance with Section 7.09 of the
Indenture. As used in this paragraph, "Potential Collateral" means any of the
Company's or any Subsidiary's Oil and Gas Properties (which are not already
Collateral) which are identified as containing proved Hydrocarbon reserves,
whether existing on the date of the Indenture or thereafter acquired.
    
 
   
  Limitation on Liens Securing Indebtedness
    
 
   
     Neither the Company nor any Subsidiary will create, incur, assume or permit
to exist any Lien on any of its Properties (now owned or hereafter acquired),
except (i) Liens securing the Senior Loan; provided the Trustee is granted a
second Lien on such Property securing the payment of the Obligations; (ii) Liens
securing the payment of the Obligations; (iii) Excepted Liens; (iv) Liens
securing leases allowed under clause (iv) of the definition of Excepted Liens
but only on the Property under lease; (v) Liens disclosed on a schedule to the
Securities Purchase Agreement; and (vi) any Permitted Encumbrances as described
in the Mortgage.
    
 
   
  Limitation on Dividends, Distributions and Redemptions
    
 
   
     Neither the Company nor any Subsidiary will declare or pay any dividend,
purchase, redeem or otherwise acquire for value any of its stock now or
hereafter outstanding, return any capital to its stockholders or make any
distribution of its assets to its partners, except to the Company or any
Subsidiary.
    
 
   
  Limitation on Sale/Leaseback Transactions
    
 
   
     Neither the Company nor any Subsidiary will enter into any arrangement,
directly or indirectly, with any Person whereby the Company or any Subsidiary
shall sell or transfer any of its Property, whether now owned or hereafter
acquired, and whereby the Company or any Subsidiary shall then or thereafter
rent or lease as lessee such Property or any part thereof or other Property
which the Company or any Subsidiary intends to use for substantially the same
purpose or purposes as the Property sold or transferred.
    
 
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  Limitation on Mergers and Consolidations
    
 
   
     The Company will not and will not permit any Subsidiary to merge into or
with or consolidate with any other Person (other than the Company or a
Subsidiary) or sell, lease or otherwise dispose of (whether in one transaction
or in a series of transactions) all or substantially all of its Property or
assets to any other Person (other than the Company or a Subsidiary) unless (i)
no Default or Event of Default exists and after giving effect to such merger, no
Default or Event of Default shall exist, (ii) after giving effect to such merger
or consolidation, the surviving entity (as the Company hereunder), or in the
event of a merger or consolidation of a Subsidiary, the Company, would be able
to incur at least $1 in additional Debt (other than Permitted Indebtedness), and
(iii) the surviving entity ratifies and confirms its Obligations under the Basic
Documents and the Notes to the reasonable satisfaction of the Agent and each
Subsidiary Guarantor whose Subsidiary Guarantor is in full force and effect
ratifies and confirms its Subsidiary Guarantor to the reasonable satisfaction of
the Agent.
    
 
   
  Limitation on Transactions with Affiliates
    
 
   
     Neither the Company nor any Subsidiary will enter into any transaction,
including, without limitation, any purchase, sale, lease or exchange of Property
or the rendering of any service, with any Affiliate (other than the Company or a
Subsidiary) unless such transaction (a) is otherwise not in violation of the
Indenture, and (b) unless approved by a majority of the disinterested members of
the Board of Directors, is in the ordinary course of its business and is upon
fair and reasonable terms no less favorable to it than it would obtain in a
comparable arm's length transaction with a Person not an Affiliate.
    
 
   
  Consolidated Interest Coverage Ratio
    
 
   
     As of the last day of each fiscal quarter, the Company will not permit the
Consolidated Interest Coverage Ratio to be less than (i) 1.5 to 1.0 as of the
end of the first four fiscal quarters following the Closing Date and (ii) 2.0 to
1.0 as of the end of each fiscal quarter thereafter.
    
 
   
  Current Ratio
    
 
   
     The Company will not permit its ratio of (i) consolidated current assets of
the Company and its Consolidated Subsidiaries (including without limitation any
unused and available commitments under the Senior Credit Agreement) to (ii)
their consolidated current liabilities (excluding any principal or interest
payments due on the Senior Loan or the Notes), to be less than .8 to 1.0 at any
time.
    
 
   
EVENTS OF DEFAULT AND REMEDIES
    
 
   
     Each of the following will constitute an "Event of Default" for the
purposes of the Indenture and the Notes: (a) the Company shall default in the
payment or prepayment when due of any Obligations, and such default, other than
a default of a payment or prepayment of principal (which shall have no cure
period), shall continue unremedied for a period of 30 days after such
Obligations become due, in the case of interest, or 30 days after the Company
receives notice from the Agent that such Obligations are due, in the case of
Obligations other than principal or interest; or (b) (i) the Company or any
Subsidiary Guarantor shall, as to any Debt (other than the Obligations and the
Senior Loan) aggregating more than $2,000,000, default in the payment when due
of any principal of or interest thereon, or any event specified in any note,
agreement, indenture or other document evidencing or relating to any such Debt
shall occur if the effect of such event is to cause, or (with the giving of any
notice or the lapse of time or both) to permit the holder or holders of such
Debt (or a trustee or agent on behalf of such holder or holders) to cause, such
Debt to become due prior to its stated maturity, or (ii) as to the Senior Loan,
there shall have occurred a default thereunder and the holders of the Senior
Loan shall have elected to accelerate the payment of the Senior Loan (or it
shall be accelerated automatically or otherwise be due and payable in full); or
(c) any representation, warranty or certification made or deemed made in the
Indenture or in any other Basic Document by the Company or any Subsidiary
Guarantor, or any certificate furnished by the Company or any Subsidiary
Guarantor to the Trustee, any Noteholder or the Agent pursuant to the provisions
of the Indenture or any other Basic Document, shall prove
    
 
                                       67
<PAGE>   69
 
   
to have been false or misleading as of the time made or furnished in any
material and adverse respect and such default shall continue unremedied for a
period of 45 days after notice thereof to the Company by the Agent; or (d) the
Company shall default in the performance of any of its obligations pursuant to
the negative covenants in the Indenture which are not capable of being cured, or
under its obligations to provide notice of default or the covenants described
above under "Limitation on Indebtedness," "Consolidated Interest Coverage Ratio"
and "Current Ratio" in "Certain Covenants"; or the Company shall default in the
performance of any of its obligations under the negative covenants in the
Indenture which are capable of being cured (other than obligations described
under "Limitation on Indebtedness," "Consolidated Interest Coverage Ratio" and
"Current Ratio") or any other provision of the Indenture (other than its
obligation to provide notice of default) or under any other Basic Document to
which it is a party (other than the payment of amounts due which shall be
governed by clause (a)) and such default shall continue unremedied for a period
of 45 days after notice thereof to the Company by the Agent; or (e) any
Subsidiary Guarantor shall default in the performance of its obligation to pay
the Liabilities (as defined in the Subsidiary Guaranty Agreements) at maturity,
or any Subsidiary Guarantor shall default in the performance of any of its other
obligations under its Subsidiary Guaranty Agreement and such default shall
continue unremedied for a period of 45 days after notice thereof to the
Subsidiary Guarantor by the Agent; or (f) the Company shall admit in writing its
inability to, or be generally unable to, pay its debts as such debts become due;
or (g) the Company shall (1) apply for a consent to the appointment of, or the
taking of possession by, a receiver, custodian, trustee or liquidator of itself
or of all or a substantial part of its property, (2) make a general assignment
for the benefit of its creditors, (3) commence a voluntary case under the
Federal Bankruptcy Code (as now or hereafter in effect), (4) file a petition
seeking to take advantage of any other law relating to bankruptcy, insolvency,
reorganization, winding-up, liquidation or composition or readjustment of debts,
(5) fail to controvert in a timely and appropriate manner, or acquiesce in
writing to, any petition filed against it in an involuntary case under the
Federal Bankruptcy Code, or (6) take any corporate action for the purpose of
effecting any of the foregoing; or (h) a proceeding or case shall be commenced,
without the application or consent of the Company, in any court of competent
jurisdiction, seeking (1) its liquidation, reorganization, dissolution or
winding-up, or the composition or readjustment of its debt, (2) the appointment
of a trustee, receiver, custodian, liquidator or the like of the Company of all
or any substantial part of its assets, or (3) similar relief in respect of the
Company under any law relating to bankruptcy, insolvency, reorganization,
winding-up, or composition or adjustment of debts, and such proceeding or case
shall continue undismissed, or an order, judgement or decree approving or
ordering any of the foregoing shall be entered and continue unstayed and in
effect, for a period of 60 days; or an order for relief against the Company
shall be entered in an involuntary case under the Federal Bankruptcy Code; or
(i) a judgment or judgments for the payment of money in excess of $2,000,000 in
the aggregate shall be rendered by a court against the Company and the same
shall not be discharged (or provision shall not be made for such discharge), or
a stay of execution thereof shall not be procured, within 45 days from the date
of entry thereof and the Company shall not, within said period of 45 days, or
such longer period during which execution of the same shall have been stayed,
appeal therefrom and cause the execution thereof to be stayed during such
appeal; or (j) any of the Basic Documents after delivery thereof shall for any
reason, except to the extent permitted by the terms thereof, cease to be in full
force and effect and valid, binding and enforceable in all material respects in
accordance with their terms, or cease in any material respect to create a valid
and perfected Lien of the priority required thereby on any of the collateral
purported to be covered thereby, except to the extent permitted by the terms of
the Indenture, or the Company or any Subsidiary Guarantor shall so state in
writing, and such Default shall continue unremedied for a period of 45 days
after notice thereof to the Company by the Agent; or (k) any Subsidiary
Guarantor takes, suffers or permits to exist any of the events or conditions
referred to in clauses (f), (g), (h) or (i) or if any Subsidiary Guaranty
Agreement related thereto shall for any reason cease to be valid and binding on
such Subsidiary Guarantor in all material respects or if such Subsidiary
Guarantor shall so state in writing, and such Default shall continue unremedied
for a period of 45 days after notice thereof to the Subsidiary Guarantor by the
Agent; or (l) there occurs a Change of Control; or (m) any annual audited
financial statement delivered to Agent pursuant to the Indenture is qualified
(as to going concern or similar qualifications).
    
 
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<PAGE>   70
 
   
     During the continuance of any Event of Default specified above (other than
clauses (f), (g) or (h)), or in clause (k) as it relates to clauses (f), (g) or
(h) thereof, the Agent may by written notice to the Company declare the entire
principal amount of all Obligations then outstanding, including interest accrued
thereon, to be immediately due and payable without presentment, demand, protest,
notice of protest or dishonor, notice of intent to accelerate, or other notice
of default of any kind.
    
 
   
     Upon the happening of any Event of Default specified in clauses (f), (g) or
(h), or clause (k) as it relates to clauses (f), (g) or (h), the entire
principal amount of all Obligations then outstanding, including interest accrued
thereon, shall, without notice or action by the Trustee, the Agent or the
Noteholders be immediately due and payable without presentment, demand, protest,
notice of protest or dishonor, notice of intent to accelerate or other notice of
default of any kind.
    
 
   
     In addition to the foregoing, upon the happening of any of the events
described in subsections (a) and (b) above, the Trustee, at the direction of the
Agent may exercise any of the rights or remedies provided in the Collateral
Documents and other Basic Documents or avail itself of any rights or remedies
provided by applicable law. The Trustee's ability to exercise any such rights or
remedies will be subject to any Liens created or evidenced by the Senior Loan
Documents and the Subordination Agreement.
    
 
   
     All proceeds received after maturity of the Notes, whether by acceleration
or otherwise shall be applied first to reimbursement of expenses and indemnities
provided for in the Basic Documents; second to accrued interest on the Notes;
third to fees; fourth pro rata to principal outstanding on the Notes and other
Obligations; and any excess shall be paid to the Company or as otherwise
required by any Governmental Requirement.
    
 
   
     During the continuance of an Event of Default, the Trustee at the direction
of the Agent may (subject to all rights of the Senior Loan Agent and the Senior
Lenders under the Senior Loan Documents) exercise its rights and remedies
granted under the Mortgages and the other Basic Documents, including the rights
and remedies granted under the Mortgages and the other Basic Documents,
including the right to obtain possession of all Production and Proceeds then
held by the Company and such mortgagors and to receive directly from the
purchasers of Hydrocarbons all other Production and Proceeds. In no case shall
any failure by the Trustee to collect directly any such Production and Proceeds
constitute in any way a release of any of its or the Agent's rights under the
Basic Documents.
    
 
   
     No periodic evidence is required to be furnished by the Company as to the
absence of default or as to compliance with the terms of the Indenture. However,
promptly after the Company knows that any Default has occurred, the Company is
required to deliver to the Agent a notice of such Default.
    
 
   
AMENDMENT AND WAIVER
    
 
   
     Except as otherwise provided in the Indenture, no amendment, waiver,
consent, modification, or termination of any provision of the Indenture, the
Notes or any other Basic Document, shall be effective unless signed by the
Company and the Majority Noteholders. Any amendment, supplement or modification
of or to any provision of the Indenture or the Notes or any other Basic
Document, any waiver of any provision of the Indenture, the Notes or any other
Basic Document, and any consent to any departure by the Company from the terms
of any provision of the Indenture, the Notes or any other Basic Document, shall
be effective only in the specific instance and for the specific purpose for
which made or given. Except where notice is specifically required by the
Indenture, no notice to or demand on the Company in any case shall entitle the
Company to any other or further notice or demand in similar or other
circumstances.
    
 
   
CONCERNING THE TRUSTEE
    
 
   
     Chase Bank of Texas, National Association, is to be the Trustee under the
Indenture.
    
 
   
     The Trustee in its individual or any other capacity may become the owner or
pledgee of Notes and may otherwise deal with the Company or its Subsidiaries or
Affiliates with the same rights it would have if it were not Trustee. If,
however, the Trustee acquires any conflicting interest (as defined in the Trust
Indenture Act), it must eliminate such conflict or resign. The Indenture will
provide that if an Event of Default has occurred and is continuing, the Trustee
shall exercise such rights and powers vested in it by the Indenture and use the
    
 
                                       69
<PAGE>   71
 
   
same degree of care and skill in such exercise as a prudent person would
exercise or use under the circumstances in the conduct of such person's own
affairs. The Trustee shall be under no obligation and may refuse to perform any
duty or exercise any right or power unless it receives indemnity satisfactory to
it against any loss, liability or expense
    
 
   
     The Trustee shall not be required to take notice, and shall not be deemed
to have notice, of any Default or Event of Default under the Indenture, unless
the Trustee shall be notified specifically of the Default or Event of Default in
a written instrument or document delivered to it by the Company or any
Subsidiary Guarantor, or by the Agent or the Majority Noteholders. The holders
of the Notes will appoint the Agent (which shall be one of such holders) to act
on their behalf. Thus, the Agent will have authority to on behalf of a majority
of the aggregate principal of the Notes.
    
 
   
GOVERNING LAW
    
 
   
     The Indenture will provide that it will be governed by the laws of the
State of Texas.
    
 
   
CERTAIN DEFINITIONS
    
 
   
     Set forth below are certain defined terms used in the Indenture. Reference
is made to the Indenture for a full definition of all such terms, as well as any
other capitalized terms used herein for which no definition is provided.
    
 
   
     "Adjusted Consolidated Net Tangible Assets" or "ACNTA" means (without
duplication), as of the date of determination, (a) the sum of (i) the discounted
future net revenue from proved crude oil and natural gas reserves of the Company
and its Consolidated Subsidiaries calculated in accordance with Commission
guidelines before any state or federal income taxes, as estimated in the most
current Reserve Report, as increased by, as of the date of determination, the
discounted future net revenue of (A) estimated proved crude oil and natural gas
reserves of the Company and its Consolidated Subsidiaries attributable to
acquisitions consummated since the date of such Reserve Report, and (B)
estimated proved crude oil and natural gas reserves of the Company and its
Consolidated Subsidiaries attributable to extensions, discoveries and other
additions and upward determinations of estimates of proved crude oil and natural
gas reserves due to exploration, development or exploitation, production or
other activities which reserves were not reflected in the most current Reserve
Report which would, in the case of a determination made pursuant to clauses (A)
and (B), in accordance with standard industry practice, result in such
determinations, in each case calculated in accordance with Commission guidelines
(utilizing the Commission guideline prices utilized in the most current Reserve
Report), and decreased by, as of the date of determination, the discounted
future net revenue attributable to (C) estimated proved crude oil and natural
gas reserves of the Company and its Consolidated Subsidiaries reflected in the
most current Reserve Report produced or disposed of since the date of such
Reserve Report and (D) reductions in the estimated proved crude oil and natural
gas reserves of the Company and its Consolidated Subsidiaries reflected in such
Reserve Report since the date of such Reserve Report attributable to downward
determinations of estimates of proved crude oil and natural gas reserves due to
exploration, development or exploitation, production or other activities
conducted or otherwise occurring since the date of the most current Reserve
Report which would, in the case of determinations made pursuant to clauses (C)
and (D), in accordance with standard industry practice, result in such
determinations, in each case calculated in accordance with Commission guidelines
(utilizing the Commission guideline prices utilized in the most current Reserve
Report); provided, however, that, in the case of each of the determinations made
pursuant to clauses (A) through (D), such increases and decreases shall be as
estimated by the Company's engineers, except that if as a result of such
acquisitions, dispositions, discoveries, extensions or revisions, there is a net
increase in the ACNTA which exceeds $10,000,000, the Agent shall have the right
to require that such increases and decreases in the discounted future net
revenue be confirmed in writing by an independent petroleum engineer, at the
Company's expense, (ii) the capitalized costs that are attributable to seismic
and undeveloped oil and gas leases of the Company and its Consolidated
Subsidiaries to which no proved crude oil and natural gas reserves are
attributed, based on the Company's books and records as of a date no earlier
than the date of the Company's latest annual or quarterly financial statements,
(iii) the Net Working Capital on a date no earlier than the date of the
Company's latest annual or quarterly financial statements and (iv) the
    
 
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<PAGE>   72
 
   
greater of (I) the net book value on a date no earlier than the date of the
Company's latest annual or quarterly financial statements and (II) the appraised
value, as estimated by independent appraisers reasonably acceptable to the
Agent, of other tangible assets of the Company and its Consolidated Subsidiaries
as of a date no earlier than the date of the Company's latest audited financial
statements, minus (b) to the extent not otherwise taken into account in the
immediately preceding clause (a), the sum of (i) minority interests, (ii) any
natural gas balancing liabilities and credits of the Company and its
Consolidated Subsidiaries reflected in the Company's latest audited financial
statements, (iii) the discounted future net revenue, calculated in accordance
with Commission guidelines (utilizing the Commission guideline prices utilized
in the Company's most current Reserve Report), attributable to reserves subject
to participation interests, overriding royalty interests or other interests of
third parties, pursuant to participation, partnership, vendor financing or other
agreements then in effect, or which otherwise are required to be delivered to
third parties, (iv) the discounted future net revenue, calculated in accordance
with Commission guidelines (utilizing the Commission guideline prices utilized
in the Company's most current Reserve Report), attributable to reserves that are
required to be delivered to third parties to fully satisfy the obligations of
the Company and its Consolidated Subsidiaries with respect to volumetric
production payments and (v) the discounted future net revenue, calculated in
accordance with Commission guidelines, attributable to reserves subject to
dollar-denominated production payments that, based on the estimates of
production included in determining the discounted future net revenue specified
in the immediately preceding clause (a) (i) (utilizing the Commission guideline
prices utilized in the Company's most current Reserve Report), would be
necessary to satisfy fully the obligations of the Company and its Consolidated
Subsidiaries with respect to dollar-denominated production payments.
    
 
   
     "Affiliate" of any Person means (i) any Person directly or indirectly
controlled by, controlling or under common control with such first Person, (ii)
any director or officer of such first Person or of any Person referred to in
clause (i) above and (iii) if any Person in clause (i) above is an individual,
any member of the immediate family (including parents, spouse and children) of
such individual and any trust whose principal beneficiary is such individual or
one or more members of such immediate family and any Person who is controlled by
any such member or trust. For purposes of this definition, any Person which owns
directly or indirectly 20% or more of the securities having ordinary voting
power for the election of directors or other governing body of a corporation or
20% or more of the partnership or other ownership interests of any other Person
(other than as a limited partner of such other Person) will be deemed to
"control" (including, with its correlative meanings, "controlled by" and "under
common control with") such corporation or other Person.
    
 
   
     "Agent" means the Person appointed and authorized by each Noteholders in
the Indenture as Agent to take such action on behalf of such Noteholder and to
exercise such powers under the Indenture as are delegated to the Agent by the
terms thereof and of the other Basic Documents, together with such powers as are
reasonably incidental thereto.
    
 
   
     "Basic Documents" means, collectively, the Indenture, the Securities
Purchase Agreement and the other Loan Documents.
    
 
   
     "Board of Directors" means the Board of Directors of the Company.
    
 
   
     "Business Day" means any day other than a Saturday, Sunday, or a legal
holiday for commercial banks in Houston, Texas, or New York, New York.
    
 
   
     "Business Opportunities Agreement" means the Corporate Shareholders'
Agreement to be dated as of even date with the Indenture between the purchasers
of the Notes and the Company.
    
 
   
     "Capital Stock" of any Person means any and all shares, interests,
participations, or other equivalents (however designated) of, or rights,
warrants, or options to purchase, corporate stock, partnership interests, or any
other equity interest (however designated) of or in such Person.
    
 
   
     "Change in Control" means (i) a transaction, including any merger or
consolidation of Company with any other Person, in which the shareholders of the
Company immediately prior to such transaction (treating the holders of the
Warrants as holders of voting shares) do not own at least 51.0% of the voting
shares of stock of the Company (or the surviving entity in the case of a merger
or consolidation) immediately following the
    
 
                                       71
<PAGE>   73
 
   
consummation of such transaction, or (ii) a transaction, including any merger or
consolidation of Company with any other Person, in which the members of the
Board of Directors immediately prior to such transaction do not comprise at
least a majority of the board of directors of the Company (or the surviving
entity in the case of a merger or consolidation) for a period of 12 months
immediately following the consummation of such transaction, or (iii) an event,
including any merger or consolidation of Company with any other Person, such
that Mr. Ben Brigham no longer manages the Company (or the surviving entity in
the case of a merger or consolidation), other than as a result of his death or
disability.
    
 
   
     "Closing Date" means the date upon which the Securities Purchase Agreement
is executed.
    
 
   
     "Code" means the Internal Revenue Code of 1986, as amended from time to
time, and any successor statute.
    
 
   
     "Collateral" means the properties, property interests and rights described
in "Security" above, or otherwise covered by the Collateral Documents, as
security for the Obligations.
    
 
   
     "Collateral Documents" means collectively the documents required by the
Agent or the Noteholders to obtain the security interests in the Collateral, as
described in " Security" above, and all other such agreements, documents and
instruments required in the Indenture, as the same may from time to time be
amended or supplemented.
    
 
   
     "Commission" means the United States Securities and Exchange Commission.
    
 
   
     "Common Stock" means the common stock, par value $0.01 per share, of the
Company or such other class of securities as shall, after the date of the
Indenture, constitute the common equity of the Company.
    
 
   
     "Consolidated Indebtedness" means all Debt of the Company and its
Consolidated Subsidiaries.
    
 
   
     "Consolidated Interest Coverage Ratio" means, as of the date of
determination, the ratio of (i) EBITDA for the preceding four calendar quarters
to (ii) Interest Expense for the same four calendar quarters.
    
 
   
     "Consolidated Net Income" means with respect to the Company and its
Consolidated Subsidiaries, for any period, the aggregate of the net income (or
loss) of the Company and its Consolidated Subsidiaries after allowance for taxes
for such period, determined on a consolidated basis in accordance with GAAP;
provided that there shall be excluded from the calculation of such net income
(to the extent otherwise included therein) the following: (i) the net income of
any Person in which Company or any Consolidated Subsidiary has an interest
(which interest does not cause the net income of such other Person to be
consolidated with the net income of Company and its Consolidated Subsidiaries in
accordance with GAAP), except to the extent of the amount of dividends or
distributions actually paid in such period by such other Person to the Company
or to a Consolidated Subsidiary, as the case may be; (ii) the net income (but
not loss) of any Consolidated Subsidiary to the extent that the declaration or
payment of dividends or similar distributions or transfers or loans by that
Consolidated Subsidiary is not at the time permitted by operation of the terms
of its charter or any agreement, instrument or Governmental Requirement
applicable to such Consolidated Subsidiary, or is otherwise restricted or
prohibited, in each case determined in accordance with GAAP; (iii) the net
income (or loss) of any Person acquired in a pooling-of-interests transaction
for any period prior to the date of such transaction; (iv) any extraordinary
gains or losses, including gains or losses attributable to Property sales not in
the ordinary course of business; and (v) the cumulative effect of a change in
accounting principles and any gains or losses attributable to writeups or
writedowns of assets.
    
 
   
     "Consolidated Subsidiaries" means each Subsidiary of the Company (whether
now existing or hereafter created or acquired) the financial statements of which
shall be (or should have been) consolidated with the financial statements of the
Company in accordance with GAAP.
    
 
   
     "Debt" means, for any Person the sum of the following (without
duplication): (i) all obligations of such Person for borrowed money or evidenced
by bonds, debentures, notes or other similar instruments (including principal
and earned but unpaid issuance fees); (ii) all obligations of such Person
(whether contingent or otherwise) in respect of bankers' acceptances, letters of
credit, surety or other bonds and similar instruments; (iii) all obligations of
such Person to pay the deferred purchase price of Property or services (other
than for
    
 
                                       72
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borrowed money) excluding Trade Payables but including Schedule 8.02 Payables;
(iv) all obligations under leases which shall have been, or should have been, in
accordance with GAAP, recorded as capital leases in respect of which such Person
is liable (whether contingent or otherwise); (v) all obligations under leases
(other than capital leases and oil and gas leases) which require such Person or
its Affiliate to make payments exceeding $100,000 (or $500,000 in the aggregate)
over the term of such lease, including payments at termination, which are
substantially equal to at least 80% of the purchase price of the Property
subject to such lease plus interest at an imputed rate of interest; (vi) all
Debt (as described in the other clauses of this definition) of others secured by
a Lien on any asset of such Person, whether or not such Debt is assumed by such
Person; (vii) all Debt (as described in the other clauses of this definition) of
others guaranteed by such Person or in which such Person otherwise assures a
creditor against loss of the Debt of others; (viii) all obligations or
undertakings of such Person to maintain or cause to be maintained the financial
position or covenants of others including without limitation agreements
expressed as an agreement to purchase the Debt or Property of others or
otherwise; (ix) obligations to deliver Hydrocarbons in consideration of advance
payments; (x) obligations to pay for goods or services whether or not such goods
or services are actually received or utilized by such Person; (xi) any capital
stock of such Person in which such Person has a mandatory obligation to redeem
such stock; (xii) any Debt of a Special Entity for which such Person is liable
either by agreement or because of a Governmental Requirement; (xiii) the
undischarged balance of any production payment created by such Person or for the
creation of which such Person directly or indirectly received payment; and (xiv)
all obligations of such Person under Hedging Agreements, provided that "Debt"
shall not include (a) interest or fees (other than earned but unpaid issuance
fees) on any of the foregoing, (b) obligations associated with bid, performance,
surety or appeal bonds (including those required by Governmental Requirements in
connection with Oil and Gas Properties), (c) gas balancing obligations (whether
volumetric or dollar denominated), (d) intercompany obligations among the
Company and its Consolidated Subsidiaries, (e) indemnity obligations which have
not matured into fixed liabilities, and (f) purchase price adjustments and
similar post-closing obligations (but excluding the deferred payment of any
purchase price) incurred in connection with the permitted purchase and sale of
Property or stock, and which is to be determined and payable no later than 180
days following the closing of such purchase and sale.
    
 
   
     "Default" means an Event of Default or an event which with notice or lapse
of time, or both, would become, an Event of Default.
    
 
   
     "Default Rate" means, for any applicable period, an interest rate equal to
the then applicable rate of interest on the Notes (for cash payments of
interest) plus 4.00% per annum, but in no event shall the Default Rate exceed
the Maximum Rate.
    
 
   
     "EBITDA" means, for any period, the sum of Consolidated Net Income for such
period plus the following expenses or charges to the extent deducted from
Consolidated Net Income in such period: interest, taxes, depreciation, depletion
and amortization, and other non-cash charges, minus all non-cash income added to
Consolidated Net Income in such period.
    
 
   
     "Effective Date" means the date the Indenture is executed by all the
parties thereto.
    
 
   
     "Employee Plan" means any employee benefit plan, program or policy with
respect to which the Company or any ERISA Affiliate may have any liability or
any obligation to contribute, other than a Plan or a Multiemployer Plan.
    
 
   
     "Environmental Laws" means any and all Governmental Requirements pertaining
to the environment in effect in any and all jurisdictions in which the Company
or any Subsidiary is conducting or at any time has conducted business, or where
any Property of the Company or any Subsidiary is located, including, without
limitation, the Oil Pollution Act of 1990, as amended, the Clean Air Act, as
amended, the Comprehensive Environmental, Response, Compensation, and Liability
Act of 1980, as amended, the Federal Water Pollution Control Act, as amended,
the Occupational Safety and Health Act of 1970, as amended, the Resource
Conservation and Recovery Act of 1976, as amended, the Safe Drinking Water Act,
as amended, the Toxic Substances Control Act, as amended, the Superfund
Amendments and Reauthorization Act of 1986, as amended, the Hazardous Materials
Transportation Act, as amended, and other environmental conservation or
protection laws. As used in the provisions hereof relating to Environmental
Laws, the term "oil" has the
    
 
                                       73
<PAGE>   75
 
   
meaning specified in OPA; the terms "hazardous substance" and "release" (or
"threatened release") have the meanings specified in CERCLA, and the terms
"solid waste" and "disposal" (or "disposed") have the meanings specified in
RCRA; provided, however, that (i) in the event either OPA, CERCLA or RCRA is
amended so as to broaden the meaning of any term defined thereby, such broader
meaning shall apply subsequent to the effective date of such amendment, and (ii)
to the extent the laws of the state in which any Property of the Company or any
Subsidiary is located establish a meaning for "oil," "hazardous substance,"
"release," "solid waste" or "disposal" which is broader than that specified in
either OPA, CERCLA or RCRA, such broader meaning shall apply.
    
 
   
     "Equity Documents" means the Warrants, the stock certificates representing
the Shares, the New Registration Rights Agreement and the Business Opportunities
Agreement.
    
 
   
     "ERISA" means the Employee Retirement Income Security Act of 1974, as
amended from time to time and any successor statute.
    
 
   
     "ERISA Affiliate" means each trade or business (whether or not
incorporated) which together with the Company or any Subsidiary of the Company
would be deemed to be a "single employer" within the meaning of Section
4001(b)(1) of ERISA or subsections (b), (c), (m) or (o) of section 414 of the
Code.
    
 
   
     "Excepted Liens" means (i) Liens for taxes, assessments or other
governmental charges or levies not yet due or which are being contested in good
faith by appropriate action and for which adequate reserves have been maintained
in accordance with GAAP; (ii) Liens in connection with workman's compensation,
unemployment insurance or other social security, old age pension or public
liability obligations not yet due or which are being contested in good faith by
appropriate action and for which adequate reserves have been maintained in
accordance with GAAP; (iii) operators', vendors', carriers', warehousemen's,
repairmen's, mechanics', workmen's, materialmen's, construction or other like
Liens arising by operation of law in the ordinary course of business or incident
to the exploration, development, operation and maintenance of Oil and Gas
Properties or customary landlord's liens, each of which is in respect of
obligations that have not been outstanding more than 90 days or which are being
contested in good faith by appropriate proceedings and for which adequate
reserves have been maintained in accordance with GAAP; (iv) any Liens reserved
in leases or farmout agreements for rent or royalties and for compliance with
the terms of the farmout agreements or leases in the case of leasehold estates,
to the extent that any such Lien referred to in this clause does not materially
impair the use of the Property covered by such Lien for the purposes for which
such Property is held or materially impair the value of the Property subject
thereto; (v) encumbrances (other than to secure the payment of borrowed money or
the deferred purchase price of Property or services), easements, restrictions,
servitudes, permits, conditions, covenants, exceptions or reservations in any
rights of way or other Property for the purpose of roads, pipelines,
transmission lines, transportation lines, distribution lines for the removal of
gas, oil, coal or other minerals or timber, and other like purposes, or for the
joint or common use of real estate, rights of way, facilities and equipment, and
defects, irregularities, zoning restrictions and deficiencies in title of any
rights of way or other Property which in the aggregate do not materially impair
the use of such rights of way or other Property for the purposes for which such
rights of way and other Property are held or materially imp air the value of
such Property subject thereto; (vi) deposits of cash or securities to secure the
performance of bids, trade, contracts, leases, statutory obligations and other
obligations of a like nature incurred in the ordinary course of business; and
(vii) Liens permitted by the Loan Documents.
    
 
   
     "Federal Funds Rate" means, for any day, a fluctuating interest rate per
annum (rounded upwards, if necessary, to the nearest 1/100 of 1%) equal to the
weighted average of the rates on overnight federal funds transactions with
members of the Federal Reserve System arranged by federal funds brokers on such
day, as published for such day (or, if such day is not a Business Day, for the
next preceding Business Day) by the Federal Reserve Bank of New York, or, if
such rate is not so published for any day which is a Business Day, the average
of the quotations for any such day on such transactions received by the Agent
from three federal funds brokers of recognized standing selected by it.
    
 
   
     "Financial Statements" means the audited consolidated balance sheet of the
Company and its consolidated subsidiaries at December 31, 1997 and the related
consolidated statement of income, stockholders' equity and cash flow of the
Company and its consolidated subsidiaries for the fiscal year then ended, and
the
    
 
                                       74
<PAGE>   76
 
   
unaudited consolidated balance sheet of the Company at June 30, 1998 and its
consolidated subsidiaries and the related consolidated statement of income,
stockholders' equity and cash flow of the Company and its consolidated
subsidiaries for the six-month period then ended.
    
 
   
     "First Reserve Report" means the Reserve Report to be prepared as of
December 31, 1998 or later and furnished by the Company to the Agent pursuant to
the Indenture.
    
 
   
     "GAAP" means generally accepted accounting principles in the United States
of America in effect from time to time.
    
 
   
     "Governmental Authority" includes the country, the state, county, city and
political subdivisions in which any Person or such Person's Property is located
or which exercises valid jurisdiction over any such Person or such Person's
Property, and any court, agency, department, commission, board, bureau or
instrumentality of any of them including monetary authorities which exercises
valid jurisdiction over any such Person or such Person's Property. Unless
otherwise specified, all references to Governmental Authority in the Indenture
shall mean a Governmental Authority having jurisdiction over, where applicable,
the Company, the Subsidiaries or any of their Property or the Agent or any
Noteholder.
    
 
   
     "Hedging Agreements" means any commodity, interest rate or currency swap,
cap, floor, collar, forward agreement or other exchange or protection agreements
or any option with respect to any such transaction.
    
 
   
     "Hydrocarbon Interests" means all rights, titles, interests and estates now
or hereafter acquired in and to oil and gas leases, oil, gas and mineral leases,
or other liquid or gaseous hydrocarbon leases, mineral fee interests, overriding
royalty and royalty interests, net profit interests and production payment
interests, including any reserved or residual interests of whatever nature.
    
 
   
     "Hydrocarbons" means oil, gas, casinghead gas, drip gasoline, natural
gasoline, condensate, distillate, liquid hydrocarbons, gaseous hydrocarbons and
all products refined or separated therefrom.
    
 
   
     "Initial Reserve Report" means the report of Cawley, Gillespie & Associates
with respect to the Oil and Gas Properties of the Partnership as of November 30,
1997.
    
 
   
     "Interest Expense" means, for each applicable period for which EBITDA is to
be calculated, the sum of all required cash payments of interest during such
period on borrowed money. Interest on the Notes, for purposes of this
definition, shall be deemed cash payments, calculated at the cash interest rate,
whether paid in cash or in kind.
    
 
   
     "Lien" means any interest in Property securing an obligation owed to, or a
claim by, a Person other than the owner of the Property, whether such interest
is based on the common law, statute or contract, and whether such obligation or
claim is fixed or contingent, and including but not limited to (i) the lien or
security interest arising from a mortgage, encumbrance, pledge, security
agreement, conditional sale or trust receipt or a lease, consignment or bailment
for security purposes or (ii) production payments and the like payable out of
Oil and Gas Properties. The term "Lien" includes reservations, exceptions,
encroachments, easements, rights of way, covenants, conditions, restrictions,
leases and other title exceptions and encumbrances affecting Property. For the
purpose of the Indenture, a Person shall be deemed to be the owner of any
Property which it has acquired or holds subject to a conditional sale agreement,
or leases under a financing lease or other arrangement pursuant to which title
to the Property has been retained by or vested in some other Person in a
transaction intended to create a financing.
    
 
   
     "Loan Documents" means the Indenture, the Notes, the Structuring Fee
Agreement, the Collateral Documents, and any and all other agreements or
instruments now or hereafter executed and delivered by the Company or any
Subsidiary or Affiliate of the Company (other than the Equity Documents and any
assignments, participation or similar agreements between any Noteholder and any
other lender or creditor with respect to any Obligations pursuant to the
Indenture) in connection with, or as security for the payment or performance of,
the Notes or the Indenture, as such agreements may be amended, supplemented or
restated from time to time.
    
 
                                       75
<PAGE>   77
 
   
     "Majority Noteholders" means, at any time, the Noteholders holding more
than 50% of the outstanding principal balance of the Notes.
    
 
   
     "Material Adverse Effect" means any material and adverse effect on (i) the
assets, liabilities, financial condition, business, operations or affairs of the
Company and its Subsidiaries taken as a whole, from those reflected in the
Financial Statements, or from the facts represented or warranted in any Loan
Document at the time made, or (ii) the ability of the Company and its
Subsidiaries taken as a whole to carry out their business as of the Closing Date
or as proposed as of the Closing Date to be conducted or to meet their
obligations under the Loan Documents on a timely basis.
    
 
   
     "Maximum Rate" means at any particular time in question, the maximum
nonusurious rate of interest, if any, which under applicable law may then be
charged on the Notes. If such maximum rate changes after the date hereof, the
Maximum Rate shall be automatically increased or decreased, as the case may be,
without notice to the Company from time to time as the effective date of each
change in such maximum rate.
    
 
   
     "Mortgage" means a mortgage required by the Indenture to be executed in
favor of the Trustee, as collateral agent for the ratable benefit of the
Noteholders.
    
 
   
     "Mortgaged Property" means the Property owned by the Company and its
Subsidiaries which is subject to the Liens existing and to exist under the Loan
Documents.
    
 
   
     "Multiemployer Plan" means a Plan defined as such in Section 3(37) or
4001(a)(3) of ERISA.
    
 
   
     "NASDAQ" means the National Association of Securities Dealers Automated
Quotation System.
    
 
   
     "Net Working Capital" means, for any Person or group of Persons and as of
any date of its determination, the difference (shown on the balance sheets of
such Person or group as of the end of the most recent fiscal quarter of such
Person or group for which internal financial statements are available) between
(i) all current assets of such Person or group and (ii) all current liabilities
of such Person or group, except the current portion of long-term Debt.
    
 
   
     "Noteholders" means the initial purchasers of the Notes and/or, to the
extent then applicable, each assignee of such purchasers or their respective
successors or assigns in whose name a Note may be registered in the note
register kept for that purpose.
    
 
   
     "Obligations" means any and all amounts, liabilities and obligations owing
from time to time by Company to the Trustee, Agent or the Noteholders, pursuant
to any of the Basic Documents and all renewals, extensions and/or rearrangements
thereof, whether such amounts, liabilities or obligations be liquidated or
unliquidated, now existing or hereafter arising, absolute or contingent.
    
 
   
     "Oil and Gas Properties" means Hydrocarbon Interests; the Properties now or
hereafter pooled or unitized with Hydrocarbon Interests; all presently existing
or future unitization, pooling agreements and declarations of pooled units and
the units created thereby (including without limitation all units created under
orders, regulations and rules of any Governmental Authority) which may affect
all or any portion of the Hydrocarbon Interests; all operating agreements,
contracts and other agreements which relate to any of the Hydrocarbon Interests
or the production, sale, purchase, exchange or processing of Hydrocarbons from
or attributable to such Hydrocarbon Interests; all Hydrocarbons in and under and
which may be produced and saved or attributable to the Hydrocarbon Interests,
including all oil in tanks, the lands covered thereby and all rents, issues,
profits, proceeds, products, revenues and other incomes from or attributable to
the Hydrocarbon Interests; all tenements, hereditaments, appurtenances and
Properties in any manner appertaining, belonging, affixed or incidental to the
Hydrocarbon Interests; and all Properties, rights, titles, interests and estates
described or referred to above, including any and all Property, real or
personal, now owned or hereafter acquired and situated upon, used, held for use
or useful in connection with the operating, working or development of any of
such Hydrocarbon Interests or Property (excluding drilling rights, automotive
equipment or other personal property which may be on such premises for the
purpose of drilling a well or other similar temporary use) and including any and
all oil wells, gas wells, injection wells or other wells, buildings, structures,
fuel separators, liquid extraction plants, plant compressors, pumps, pumping
units, field gathering systems, tanks and tank batteries, fixtures, valves,
fittings, machinery and parts, engines, boilers, meters,
    
 
                                       76
<PAGE>   78
 
   
apparatus, appliances, tools, implements, cables, wires, towers, casing, tubing
and rods, similar equipment, surface leases, rights-of-way, easements and
servitudes together with all additions, substitutions, replacements, accessions
and attachments to any and all of the foregoing.
    
 
   
     "outstanding", when used with reference to Notes, means, as of any
particular time, all Notes authenticated and delivered by the Trustee under the
Indenture, except
    
 
   
          (a) Notes that have been canceled by the Trustee or delivered to the
     Trustee for cancellation;
    
 
   
          (b) Notes for which monies in the necessary amount for payment or
     redemption shall have been deposited in trust with the Trustee or with any
     paying agent (other than the Company), provided that, if such Notes are to
     be redeemed, notice of such redemption shall have been given as provided in
     the Indenture or provision satisfactory to the Trustee shall have been made
     for giving such notice; and
    
 
   
          (c) Notes in lieu of or in substitution for which other Notes shall
     have been authenticated and delivered pursuant to the terms of the
     Indenture.
    
 
   
     "Participation" means, for each Noteholder, such Noteholder's proportionate
share of the Obligations and the Warrants.
    
 
   
     "PBGC" means the Pension Benefit Guaranty Corporation or any entity
succeeding to any or all of its functions.
    
 
   
     "Permitted Debt" means:
    
 
   
          (a) The Senior Loan, up to the lesser of $75,000,000 or the "Borrowing
     Base" under the Senior Credit Agreement;
    
 
   
          (b) The Notes or other Obligations arising under the Loan Documents or
     any guaranty of or suretyship arrangement for the Notes or other
     Obligations arising under the Loan Documents;
    
 
   
          (c) Debt of the Company which is existing on the Closing Date and is
     reflected in the Financial Statements or constitutes Schedule 8.02
     Payables, and any renewals or extensions (but not increases) thereof;
    
 
   
          (d) Accounts payable for the deferred purchase price of Property or
     services (other than Trade Payables) from time to time incurred in the
     ordinary course of business which, if greater than 60 days past the invoice
     or billing date, are being contested in good faith by appropriate
     proceedings if reserves adequate under GAAP shall have been established
     therefor;
    
 
   
          (e) Debt of the Company under capital leases (as required to be
     reported on the financial statements of the Company pursuant to GAAP) not
     to exceed $2,000,000;
    
 
   
          (f) Debt of the Company under Hedging Agreements with a Senior Lender
     or another investment grade counterparty the notional amounts on which do
     not exceed 75% of Company's anticipated oil and/or gas production to be
     produced during the term of such Hedging Agreements entered into as a part
     of its normal business operations as a risk management strategy and/or
     hedge against changes resulting from market conditions related to the
     Company's and its Subsidiaries' operations; and
    
 
   
          (g) Debt of the Company not described in clauses (a) through (f)
     which, in the aggregate, does not exceed $1,000,000 at any one time
     outstanding.
    
 
   
     "Person" means any individual, corporation, company, voluntary association,
partnership, joint venture, trust, limited liability company, unincorporated
organization or government or any agency, instrumentality or political
subdivision thereof, or any other form of entity.
    
 
   
     "Plan" means any employee pension benefit plan, as defined in Section 3(2)
of ERISA, which (i) is currently or hereafter sponsored, maintained or
contributed to by the Company, any Subsidiary or an ERISA Affiliate or (ii) was
at any time during the preceding six calendar years sponsored, maintained or
contributed to, by the Company, any Subsidiary or an ERISA Affiliate.
    
 
                                       77
<PAGE>   79
 
   
     "Property" means any interest in any kind of property or asset, whether
real, personal or mixed, or tangible or intangible.
    
 
   
     "Reportable Event" means an event described in Section 4043(c) of ERISA
with respect to a Plan, other than an event described in paragraphs (1) through
(8) as to which the 30 day notice requirement has been waived by the PBGC.
    
 
   
     "Reserve Report" means a report, in form satisfactory to the Senior Loan
Agent (or if there is no Senior Loan or requirement for a Reserve Report under
the Senior Loan, the Agent), setting forth, as of the dates set forth in the
Indenture (or such other date in the event of an unscheduled redetermination);
(i) the proved oil and gas reserves attributable to the Company's and its
Subsidiaries' Hydrocarbon Interests together with a projection of the rate of
production and future net income, taxes operating expenses and capital
expenditures with respect thereto as of such date, based upon the pricing
assumptions consistent with Commission reporting requirements at the time and
(ii) such other information as the Senior Loan Agent (or, if there is no Senior
Loan, or requirement for a Reserve Report under the Senior Loan, the Agent) may
reasonably request. The term "Reserve Report" shall also include the Initial
Reserve Report, the First Reserve Report, certain supplemental Reserve Reports
described in the Indenture, and certain information to be provided by the
Company with the delivery of each Reserve Report.
    
 
   
     "Schedule 8.02 Payables" means payables owing under the agreements listed
on Schedule 8.02 to the Indenture which are outstanding more than 75 days after
they become fixed and owing, provided that the aggregate amounts of such
payables under each such agreement do not exceed the amount set forth for each
such agreement or such schedule.
    
 
   
     "Scheduled Redetermination Date" means the last Business Day of each
September and March during the term of the Notes, commencing September 1999 .
    
 
   
     "Securities Purchase Agreement" means the Securities Purchase Agreement to
be dated of even date with the Indenture between the purchasers of the Notes and
the Company.
    
 
   
     "Senior Credit Agreement" means the Credit Agreement dated as of January
26, 1998, among the Partnership, the Senior Loan Agent, and the Senior Lenders,
as it may from time to time be amended, modified or supplemented from time to
time, and any Credit Agreement or similar agreement executed with banks or other
financial institutions in connection with any refinancing of the Senior Loan
permitted under the Indenture and under the Subordination Agreement.
    
 
   
     "Senior Lenders" means each of the lenders from time to time under the
Senior Credit Agreement.
    
 
   
     "Senior Loan" shall mean, collectively, any advance or advances of
principal made by the Senior Lenders to the Partnership or the Company under the
Senior Credit Agreement and the other Senior Loan Documents.
    
 
   
     "Senior Loan Agent" means the agent or agents designated under the Senior
Credit Agreement. Bank of Montreal is currently the Senior Loan Agent.
    
 
   
     "Senior Loan Documents" means the Senior Credit Agreement and all
promissory notes, collateral documents and other agreements, documents and
instruments executed or delivered in connection therewith, as such agreements
may be amended, modified or supplemented from time to time.
    
 
   
     "Special Entity" means any joint venture, limited liability company or
partnership, general or limited partnership or any other type of partnership or
company other than a corporation, in which a Person or one or more of its other
Subsidiaries is a member, owner, partner or joint venturer and owns, directly or
indirectly, at least a majority of the equity of such entity or controls such
entity, but excluding any tax partnerships that are not classified as
partnerships under state law. For purposes of the definition, any Person which
owns directly or indirectly an equity investment in another Person which allows
the first Person to manage or elect managers who manage the normal activities of
such second Person will be deemed to "control" such second Person (e.g., a sole
general partner controls a limited partnership).
    
 
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<PAGE>   80
 
   
     "Structuring Fee Agreement" means the agreement between the Company and an
affiliate of the purchasers of the Notes to be dated as of the date of the
Indenture.
    
 
   
     "Subsidiary" means (i) any corporation of which at least a majority of the
outstanding shares of stock having by the terms thereof ordinary voting power to
elect a majority of the board of directors of such corporation (irrespective of
whether or not at the time stock of any other class or classes of such
corporation shall have or might have voting power by reason of the happening of
any contingency) is at the time directly or indirectly owned or controlled by a
Person or one or more of its Subsidiaries or by a Person and one or more of its
Subsidiaries and (ii) any Special Entity. Unless otherwise indicated in the
Indenture, each reference to the term "Subsidiary" shall mean a Subsidiary of
the Company. Quest Resources L.L.C. and Venture Acquisitions L.P., which are not
material, shall not be considered Subsidiaries of the Company.
    
 
   
     "Trade Payables" means customary trade payables incurred in the ordinary
course of business.
    
 
                                       79
<PAGE>   81
 
   
                            SUBORDINATION AGREEMENT
    
 
   
GENERAL
    
 
   
     Pursuant to an Intercreditor and Subordination Agreement (the
"Subordination Agreement") to be entered into by the Trustee, the Noteholders,
the agent for the Noteholders (the "Subordinated Agent"), the Bank of Montreal,
as agent for the lenders ("Senior Lender") under the Credit Facility (the
"Senior Agent"), the Company and certain of its subsidiaries, the Subordinated
Indebtedness (as defined) will be expressly subordinated to the extent and
manner provided in the Subordination Agreement to the Senior Indebtedness,
whether currently outstanding or hereafter created, incurred, assumed or
guaranteed. The following discussion of certain provisions of the Subordination
Agreement does not purport to be complete and is qualified in its entirety by
reference to the Subordination Agreement, including the definitions therein of
certain terms used below. The definitions of certain terms used in the following
summary are set forth below under "-- Certain Definitions." Except for the terms
"Subordination Agreement" and "Senior Indebtedness", the terms defined in this
"Subordination Agreement" section have such meanings only for purposes of this
section.
    
 
   
SUBORDINATION
    
 
   
     The Company and the Subsidiary Guarantors will not be permitted to make any
payment (whether by redemption, purchase, retirement, defeasance, set-off or
otherwise) upon or in respect of the Subordinated Indebtedness, until all
principal and other obligations with respect to the Senior Indebtedness have
been paid in full if: (A) a default in the payment of any principal of or
interest on the Senior Indebtedness occurs; or (B) the payment of the
Subordinated Indebtedness would result in a default or event of default under
the Senior Loan Documents or any other default has occurred and is continuing
with respect to the Senior Indebtedness that permits, or with the giving of
notice or passage of time or both (unless cured or waived) would permit, the
Senior Agent or the Senior Lender to accelerate its maturity and the
Subordinated Agent receives a notice of the default (a "Payment Blockage
Notice") from the Company or any Subsidiary Guarantor, the Senior Agent or any
Senior Lender with regard to the foregoing.
    
 
   
     The Company and each Subsidiary Guarantor will be permitted to resume
payments on and distributions in respect of the Subordinated Indebtedness upon:
(A) in the case of a default referred to in clause (A) in the preceding
paragraph, the date upon which the default is cured or waived, or (B) in the
case of a default referred to in clause (b) of the preceding paragraph, the
earliest of (1) the date on which such nonpayment default is cured or waived or
(2) the expiration of the applicable Payment Blockage Period unless the maturity
of the Senior Indebtedness has been accelerated.
    
 
   
     Upon any payment or distribution of property or securities to creditors of
the Company or any Subsidiary Guarantor in a liquidation or dissolution of such
person or its property, or in an assignment for the benefit of creditors or any
marshaling of its assets and liabilities: (A) the Senior Lender shall be
entitled to receive payment in full of all Senior Indebtedness (including
interest after the commencement of any such proceeding at the rate specified in
the Senior Loan Documents, whether or not a claim for such interest would be
allowed in such proceeding) before the Subordinated Agent and/or Noteholder
shall be entitled to receive any payment with respect to the Subordinated
Indebtedness; and (B) until the Senior Indebtedness is paid in full, any payment
or distribution to which the Subordinated Agent and/or the Noteholders would be
entitled shall be made to the Senior Agent for its benefit and the benefit of
the Senior Lender; and (C) under the circumstances described in this paragraph,
the Company, any Subsidiary Guarantor, or any receiver, trustee in bankruptcy,
liquidating trustee, agent or other similar Person making any payment or
distribution of cash or other property or securities is authorized or instructed
to make any payment or distribution to which the Subordinated Agent and/or the
Noteholders would otherwise be entitled (other than securities that are
subordinated at least to the same extent as the Subordinated Indebtedness)
directly to the Senior Agent for its benefit and the benefit of the Senior
Lender to the extent necessary to pay all Senior Indebtedness in full, after
giving effect to any concurrent payment, distribution or provision therefor to
or for the Senior Agent and the Senior Lender.
    
 
                                       80
<PAGE>   82
 
   
     Liens upon the property of any of the Company or any Subsidiary Guarantor
securing payments of the Subordinated Indebtedness will be and remain inferior
and subordinated to any liens securing payments of the Senior Indebtedness in
such property regardless of whether such encumbrances in favor of the
Subordinated Agent or any Noteholder or the Senior Agent and the Senior Lender
exist on the date of the Subordination Agreement or are thereafter created or
attached and regardless of the date of execution and delivery or the date of
filing or recording. Any obligation of the Company or any Subsidiary Guarantor
under the Subordinated Loan Documents to deliver possession of any property to
the Trustee under the Indenture, the Subordinated Agent or the Noteholders,
whether for purposes of perfection or realization of any rights thereunder shall
be subordinate in all respects to the Company's or any Subsidiary Guarantor's
obligation to deliver possession of any such property to the Senior Loan Agent
or Senior Lender under the Senior Loan Documents for such purposes.
    
 
   
CERTAIN DEFINITIONS
    
 
   
     Set forth below are certain defined terms used in the above summary of
certain provisions of the Subordination Agreement. Except for the terms
"Subordination Agreement" and "Senior Indebtedness", the terms defined in this
"Subordination Agreement" section have such meanings only for purposes of this
section.
    
 
   
     "Hedging Agreement" means the ISDA Master Agreement between the Partnership
and Bank of Montreal now or hereafter entered into, and any hedging transactions
entered into pursuant to the terms thereof.
    
 
   
     "Payment Blockage Period" means the period commencing on (i) the date on
which a default in the payment of any principal of or interest on the Senior
Indebtedness occurs or (ii) the date on which a Payment Blockage Notice is
given, and expiring on the date which is 60 days following the first day of the
Payment Blockage Period.
    
 
   
     "Senior Guaranty Agreements" means Guaranty Agreements executed by the
Company and the Subsidiary Guarantors (other than the Partnership), in favor of
the Senior Agent and the Senior Lender to secure, inter alia, the obligations of
the Partnership under the Credit Facility.
    
 
   
     "Senior Indebtedness" shall mean the principal balance of all loans
advanced to or letters of credit issued for the account of the Partnership
pursuant to the terms and conditions of the Senior Loan Documents, not to exceed
$75,000,000 plus the additional amounts permitted under Section 2.6(a) of the
Subordination Agreement, and accrued but unpaid interest thereon, all fees,
expenses, reimbursement obligations, liabilities, indemnities or other monetary
obligations of the Company or any Subsidiary Guarantor under any Senior Loan
Document, and all swap settlement amounts or other amounts due and payable under
the Hedging Agreement, whether any of the foregoing is (i) absolute or
contingent, direct or indirect, joint, several or independent, (ii) now
outstanding or owing or which may hereafter be existing or incurred, (iii) due
or to become due, or (iv) held or to be held by the Senior Agent or any Senior
Lender, and all renewals, extensions, rearrangements, refundings and
modifications thereof permitted by the terms of the Subordination Agreement.
    
 
   
     "Senior Loan Documents" mean the Credit Facility, the Senior Mortgage, the
Senior Guaranty Agreements, the Senior Parent Security Agreement and those other
documents or instruments given in connection therewith
    
 
   
     "Senior Mortgage" means one or more Mortgage, Deed of Trust, Assignment of
Production, Security Agreement and Financing Statements and one or more Security
Agreements, heretofore or hereafter executed by the Partnership in favor of the
Senior Agent to secure, inter alia, the obligations outstanding under the Credit
Facility.
    
 
   
     "Senior Parent Security Agreement" means the Security Agreement executed by
the Company in favor of the Senior Agent and the Senior Lender to secure, inter
alia, the obligations of the Partnership under the Credit Facility.
    
 
                                       81
<PAGE>   83
 
   
     "Subordinated Indebtedness" shall mean the principal balance of all loans
advanced to the Company pursuant to the terms and conditions of the Subordinated
Loan Documents (including interest paid in kind as permitted by the Subordinated
Loan Documents), and accrued but unpaid interest thereon, and all fees,
expenses, reimbursement obligations, liabilities, indemnities or other monetary
obligations of the Company or any Subsidiary Guarantor under any Subordinated
Loan Document whether any of the foregoing is (i) absolute or contingent, direct
or indirect, joint, several or independent, (ii) now outstanding or owing or
hereafter existing or incurred, (iii) due or to become due, or (iv) held or to
be held by the Subordinated Agent or any Noteholder, and all renewals,
extensions, rearrangements, refundings and modifications thereof permitted by
the terms hereof.
    
 
   
     "Subordinated Loan Documents" means the Indenture, Securities Purchase
Agreement, the Subordinated Mortgage, the Subsidiary Guaranty Agreements, the
Subordinated Parent Security Agreement and those other documents or instruments
given in connection therewith.
    
 
   
     "Subordinated Mortgage" means one or more Mortgage, Deed of Trust,
Assignment of Production, Security Agreement and Financing Statements, executed
by the Partnership granting subordinated liens in the properties subject to the
Senior Mortgage in favor of the Trustee to secure, inter alia, the obligations
outstanding under the Indenture.
    
 
   
     "Subordinated Parent Security Agreement" means the Security Agreement
executed by the Company in favor of the Trustee to secure, inter alia, the
obligations of the Company under the Subordinated Loan Documents.
    
 
   
                            DESCRIPTION OF WARRANTS
    
 
   
GENERAL
    
 
   
     Warrants to purchase shares of Common Stock at an exercise price of $
per share, payable in cash, will be issued pursuant to warrant certificates. The
Warrants will expire on                     , 2005 (the "Warrant Expiration
Date"). The Warrants will entitle the holders thereof to purchase in the
aggregate 1,000,000 shares of Common Stock. The holders of the Warrants (the
"Warrantholders") will be entitled to exercise all or a portion of their
Warrants at any time after issuance of the Warrants and on or prior to the
Warrant Expiration Date at which time all unexercised Warrants will expire. This
summary does not purport to be a complete description of the Warrants and is
subject to the detailed provisions of, and qualified in its entirety by
reference to, the warrant certificates (including the definitions contained
therein).
    
 
   
MERGERS, CONSOLIDATIONS OF THE COMPANY; ANTI-DILUTION ADJUSTMENTS
    
 
   
     In case of any reclassification or change of outstanding securities
issuable upon exercise of the Warrants (other than a change in par value, or
from par value to no par value, or from no par value to par value or as a result
of a subdivision or combination to which a separate provision applies), or in
case of any consolidation or merger of the Company with or into another entity
or other person (other than a merger with another entity or other person in
which the Company is the surviving corporation and which does not result in any
reclassification or change in the securities issuable upon exercise of the
Warrants), provision must be made for Warrantholders to receive, upon the
exercise of Warrants and in lieu of Warrant Shares, such securities or assets as
would be issued or paid in respect of shares of Common Stock upon such
reclassification, change, consolidation or merger.
    
 
   
     If the Company declares a dividend on its Common Stock payable in stock or
other securities of the Company to the holders of its Common Stock, the
Warrantholders shall be entitled to receive upon any exercise of a Warrant, in
addition to the Warrant Shares, the number of shares of stock or other
securities which such holder would have been entitled to receive if he had been
a holder immediately prior to the record date for such dividend (or, if no
record date shall have been established, the payment date for such dividend) of
the number of Warrant Shares purchasable on exercise of such Warrant immediately
prior to such record date or payment date, as the case may be.
    
 
                                       82
<PAGE>   84
 
   
     The number of Warrant Shares issuable upon exercise of a Warrant will also
be adjusted in the event of a combination or subdivision of the Common Stock.
    
 
   
EXERCISE PRICE ADJUSTMENTS
    
 
   
     If the Company issues any additional shares of Common Stock (otherwise than
as described above under "Mergers and Consolidations of the Company;
Anti-Dilution Adjustments") at a price per share less than the average price per
share of Common Stock (with each day's price determined by averaging the high
and low sales prices as reported on the National Association of Securities
Dealers Automated Quotations Systems) for the 20 trading days immediately
preceding the date of the authorization of such issuance (the "Market Price") by
the Board of Directors of the Company, then the exercise price of the Warrants
upon each such issuance shall be adjusted to that price determined by
multiplying the exercise price by a fraction: (A) the numerator of which shall
be the sum of (i) the number of shares of Common Stock outstanding immediately
prior to the issuance of such additional shares of Common Stock multiplied by
the Market Price, and (ii) the consideration, if any, received by the Company
upon the issuance of such additional shares of Common Stock, and (B) the
denominator of which shall be the Market Price multiplied by the total number of
shares of Common Stock outstanding immediately after the issuance of such
additional shares of Common Stock. No such adjustments of the exercise price
shall be made upon the issuance of any additional shares of Common Stock that
(y) are issued pursuant to thrift plans, stock purchase plans, stock bonus
plans, stock option plans, employee stock ownership plans and other incentive or
profit sharing arrangements for the benefit of employees ("Employee Benefit
Plans") that otherwise would cause an adjustment; provided that the aggregate
number of shares of Common Stock so issued (including the shares issued pursuant
to any options, rights or warrants or convertible or exchangeable securities
issued under such Employee Benefit Plans containing the right to purchase shares
of Common Stock) pursuant to Employee Benefit Plans after the date of the
closing of the Company's initial public offering, as adjusted for any stock
splits, stock dividends or subdivisions or combinations of Common Stock prior to
the Warrant Expiration Date, shall not in the aggregate exceed 5% of the
Company's outstanding Common Stock at the time of such issuance; or (z) are
issued pursuant to any Common Stock Equivalent (as defined) (i) if upon the
issuance of any such Common Stock Equivalent, any such adjustments shall
previously have been made pursuant to the provisions described in the following
paragraph or (ii) if no adjustment was required pursuant such provisions.
    
 
   
     If the Company shall issue any security or evidence of indebtedness which
is convertible into or exchangeable for Common Stock ("Convertible Security"),
or any warrant, option or other right to subscribe for or purchase Common Stock
or any Convertible Security, other than pursuant to Employee Benefit Plans
(together with Convertible Securities, "Common Stock Equivalent"), or if, after
any such issuance, the price per share for which additional shares of Common
Stock may be issuable thereunder is amended, then the exercise price upon each
such issuance or amendment shall be adjusted as provided in preceding paragraph
on the basis that (i) the maximum number of additional shares of Common Stock
issuable pursuant to all such Common Stock Equivalents shall be deemed to have
been issued as of the earlier of (a) the date on which the Company shall enter
into a firm contract for the issuance of such Common Stock Equivalent, or (b)
the date of actual issuance of such Common Stock Equivalent; and (ii) the
aggregate consideration for such maximum number of additional shares of Common
Stock shall be deemed to be the minimum consideration received and receivable by
the Company for the issuance of such additional shares of Common Stock pursuant
to such Common Stock Equivalent; provided, however, that no such adjustment
shall be made unless the consideration received and receivable by the Company
per share of Common Stock for the issuance of such additional shares of Common
Stock pursuant to such Common Stock Equivalent is less than the Market Price. No
such adjustment of the exercise price shall be made upon the issuance of any
Convertible Security which is issued pursuant to the exercise of any warrants or
other subscription or purchase rights therefor, if any adjustment shall
previously have been made in the exercise price then in effect upon the issuance
of such warrants or other rights pursuant to the provisions described in this
paragraph. Appropriate readjustments to the purchase price will be made upon the
expiration of the right to convert, exchange or exercise any Common Stock
Equivalent if any such Common Stock Equivalent shall not have been converted,
exercised or exchanged.
    
 
                                       83
<PAGE>   85
 
   
REPORTS
    
 
   
     The Company will cause to be delivered, by first-class mail, postage
prepaid, to the Warrantholders a copy of any reports delivered by the Company to
the holders of Common Stock.
    
 
                          DESCRIPTION OF CAPITAL STOCK
 
   
     The authorized capital stock of the Company consists of 30 million shares
of Common Stock, par value $.01 per share, and 10 million shares of preferred
stock, par value $.01 per share ("Preferred Stock"). As of August 13, 1998, the
Company had outstanding 12,253,574 shares of Common Stock held of record by 67
stockholders and stock options for an aggregate of 935,987 shares.
    
 
COMMON STOCK
 
   
     The holders of Common Stock are entitled to one vote for each share held of
record on all matters submitted to the stockholders. The Certificate of
Incorporation of the Company does not allow the stockholders to take action by
less than unanimous consent. Each share of Common Stock is entitled to
participate equally in dividends, if, as and when declared by the Company's
Board of Directors, and in the distribution of assets in the event of
liquidation, subject in all cases to any prior rights of outstanding shares of
Preferred Stock. The Company has never paid cash dividends on its Common Stock
and is currently restricted from doing so by the Credit Facility, and,
subsequent to the Offering, will be further restricted by the Indenture. The
shares of Common Stock have no preemptive or conversion rights, redemption
rights, or sinking fund provisions. The outstanding shares of Common Stock are,
and the shares of Common Stock offered hereby upon issuance and sale will be,
duly authorized, validly issued, fully paid, and nonassessable.
    
 
PREFERRED STOCK
 
     The Company has no outstanding Preferred Stock. The Company is authorized
to issue 10 million shares of Preferred Stock. The Company's Board of Directors
may establish, without stockholder approval, one or more classes or series of
Preferred Stock having the number of shares, designations, relative voting
rights, dividend rates, liquidation and other rights, preferences, and
limitations that the Board of Directors may designate. The Company believes that
this power to issue Preferred Stock will provide flexibility in connection with
possible corporate transactions. The issuance of Preferred Stock, however, could
adversely affect the voting power of holders of Common Stock and restrict their
rights to receive payments upon liquidation of the Company. It could also have
the effect of delaying, deferring or preventing a change in control of the
Company. The Company does not currently plan to issue Preferred Stock.
 
DELAWARE LAW PROVISIONS
 
     The Company is a Delaware corporation and is subject to Section 203 of the
Delaware General Corporation Law. Generally, Section 203 prohibits the Company
from engaging in a "business combination" (as defined in Section 203) with an
"interested stockholder" (defined generally as a person owning 15% or more of
the Company's outstanding voting stock) for three years following the date that
person becomes an interested stockholder, unless (a) before that person became
an interested stockholder, the Company's Board of Directors approved the
transaction in which the interested stockholder became an interested stockholder
or approved the business combination; (b) upon completion of the transaction
that resulted in the interested stockholder's becoming an interested
stockholder, the interested stockholder owns at least 85% of the voting stock
outstanding at the time the transaction commenced (excluding stock held by
directors who are also officers of the Company and by employee stock plans that
do not provide employees with the right to determine confidentially whether
shares held subject to the plan will be tendered in a tender or exchange offer);
or (c) following the transaction in which that person became an interested
stockholder, the business combination is approved by the Company's Board of
Directors and authorized at a meeting of stockholders by the affirmative vote of
the holders of at least two-thirds of the outstanding voting stock not owned by
the interested stockholder.
 
                                       84
<PAGE>   86
 
     Under Section 203, these restrictions also do not apply to certain business
combinations proposed by an interested stockholder following the announcement or
notification of one of certain extraordinary transactions involving the Company
and a person who was not an interested stockholder during the previous three
years or who became an interested stockholder with the approval of a majority of
the Company's directors, if that extraordinary transaction is approved or not
opposed by a majority of the directors who were directors before any person
became an interested stockholder in the previous three years or who were
recommended for election or elected to succeed such directors by a majority of
such directors then in office.
 
REGISTRATION RIGHTS
 
     The Company has entered into a Registration Rights Agreement with General
Atlantic Partners III, L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P.
II, RIMCO Partners, L.P. III and RIMCO Partners, L.P. IV, Ben M. Brigham, Anne
L. Brigham, Harold D. Carter, Craig M. Fleming, David T. Brigham and Jon L.
Glass. Pursuant to the Registration Rights Agreement, Anne and Ben Brigham,
acting together, the General Atlantic entities, acting together, and the RIMCO
entities, acting together, each may separately require the Company to register
securities, on one occasion, if the shares to be registered have an estimated
aggregate offering price to the public of at least $3 million. One additional
registration is allowed if any registrable securities requested to be included
in a previous registration statement were not disposed of in accordance with
that previous registration. The Registration Rights Agreement also provides
"piggyback" registration rights after the Offering for all registrations of
registrable securities for the Company or another security holder. In an
underwritten offering, however, the Company may exclude all or a portion of the
securities being registered pursuant to "piggyback" registration rights if the
managing underwriter determines that including those securities would raise a
substantial doubt about whether the proposed offering could be consummated. The
Registration Rights Agreement contains customary indemnity by the Company in
favor of persons selling securities in a registration governed by the
Registration Rights Agreement, and by those persons in favor of the Company,
relating to the information included in or omitted from the Registration
Statement.
 
   
     The holders of the Shares and the Warrants will have demand and "piggyback"
registration rights with respect to the Shares and the Warrant Shares,
respectively. See "Registration Rights Relating to the Warrants and Shares."
    
 
TRANSFER AGENT AND REGISTRAR
 
     The Transfer Agent and Registrar for the Common Stock is American Stock
Transfer & Trust Company.
 
   
            REGISTRATION RIGHTS RELATING TO THE WARRANTS AND SHARES
    
 
   
     Pursuant to a New Registration Rights Agreement (the "New Registration
Rights Agreement") to be entered into among the Company and the initial
purchasers of the Warrants and Shares, holders of the Shares, the Warrants, the
Warrant Shares and any other securities issued upon the exercise of the Warrants
(collectively, the "Registrable Securities") collectively owning at least 25% of
the Registrable Securities may require the Company to register (other than
pursuant to a shelf registration on Form S-3) all or any part of the Registrable
Securities held by such holders. In addition, in the event that the Company is
eligible to register securities for resale with the Commission on Form S-3,
holders collectively owning at least a majority of the Registrable Securities
may require the Company to register under Form S-3 all or any portion of the
Registrable Securities held by such holders. The Company shall only be required
under the New Registration Rights Agreement to register Registrable Securities
(including under Form S-3) pursuant to such demand rights on two occasions;
provided that a request will only be "counted" when (i) all the Registrable
Securities requested to be included in the registration statement have been
included, (ii) the corresponding registration statement has become effective and
(iii) the public offering has been consummated and the Registrable Securities
have been sold on the terms and conditions provided therein, provided that in
the event of a shelf registration statement (if the Company is then eligible to
file on Form S-3) the Company shall keep such registration statement effective
for two years from the effective date.
    
 
                                       85
<PAGE>   87
 
   
     If the Company is required to effect a registration pursuant to the New
Registration Rights Agreement, subject to certain exceptions described therein
the Company will be required to file a registration statement with respect to
the applicable securities within 30 days in the case of a shelf registration
statement (if the Company is then eligible to file on Form S-3), or otherwise
within 60 days. The Company will use its best efforts to cause the registration
statement to become and remain effective for the period of the distribution in
order for it to be "counted" as described above.
    
 
   
     Subject to existing registration rights of institutional investors, the
holders of the Registrable Securities will provide "piggyback" registration
rights to the holders of Registrable Securities in the event the Company
registers any of its equity securities for the Company or other security
holders. In an underwritten offering, however, subject to certain provisions
including priority of securities to be registered, the Company may exclude all
or a portion of the Registrable Securities being registered pursuant to
"piggyback" registration rights if in the good faith opinion of the managing
underwriter the inclusion of the shares would raise a substantial doubt as to
whether the proposed offering could successfully be consummated.
    
 
   
     Exercise of the right to convert the Warrants to Warrant Shares shall, at
the election of the holder of the Warrants, be contingent upon the registration
of the Warrant Shares in accordance with the New Registration Rights Agreement
and should such registration not be completed such holder shall have the right
to rescind its election to convert the Warrants.
    
 
   
     The New Registration Rights Agreement will contain customary indemnity by
the Company in favor of persons selling securities in a registration governed by
the New Registration Right Agreement, and by those persons in favor of the
Company, relating to the information included in or omitted from the
registration statement.
    
 
   
     The summary herein of certain provisions of the New Registration Rights
Agreement does not purport to be complete and is subject to, and is qualified in
its entirety by reference to, all the provisions of the New Registration Rights
Agreement form, which is available upon request to the Company.
    
 
                        SHARES ELIGIBLE FOR FUTURE SALE
 
   
     Upon completion of the Offering, the Company will have      shares of
Common Stock outstanding. Of these      shares, the shares of Common Stock
offered hereby will be freely transferable without restriction under the
Securities Act unless they are held by the Company's affiliates, as that term is
used in Rule 144 under the Securities Act. 8,928,574 shares of Common Stock were
issued in reliance on exemptions from the registration requirements of the
Securities Act and are eligible for sale under Rule 144, based on current SEC
rules and subject to compliance with the volume and other requirements of Rule
144. Beginning February 27, 1999, all of those shares of Common Stock will
become eligible for sale under Rule 144(k) if they are not held by affiliates of
the Company.      shares of Common Stock that will be issued in the Offering or
that were sold in the Company's initial public offering are freely tradeable,
except to the extent that they are held by affiliates of the Company.
    
 
   
     In general, under Rule 144 a person (or persons whose sales are
aggregated), including an affiliate, who has beneficially owned shares for at
least one year is entitled to sell in broker transactions, within any three-
month period after the Offering, a number of shares that does not exceed the
greater of (i) 1% of the then outstanding Common Stock (approximately
shares immediately after the Offering) or (ii) the average weekly trading volume
in the Common Stock during the four calendar weeks preceding the sale, subject
to the filing of a Form 144 with respect to the sale and other limitations. In
addition, a person who was not an affiliate of the Company during the three
months preceding a sale and who has beneficially owned the shares proposed to be
sold for at least two years is entitled to sell the shares under Rule 144(k)
without regard to the manner-of-sale, volume and other limitations of Rule 144.
The SEC has proposed modifications to Rule 144 that could change some of these
requirements.
    
 
   
     The holders of 8,421,431 shares of Common Stock and their permitted
transferees are entitled to demand registration of those shares under the
Securities Act, and the holders of 8,928,574 shares of Common Stock are entitled
to "piggyback" registration rights. The holders of the Shares and the Warrants
will have demand
    
                                       86
<PAGE>   88
 
   
and "piggyback" registration rights with respect to the Shares and Warrant
Shares, respectively. See "Description of Capital Stock -- Registration Rights"
and "Registration Rights Relating to the Warrants and Shares."
    
 
   
     Options covering 935,987 shares of Common Stock are outstanding, with an
average exercise price of $7.61 per share, subject to vesting.
    
 
   
     Pursuant to the Offering, Warrants to purchase 1,000,000 shares of Common
Stock at an exercise price of $     per share will be issued and outstanding.
Such Warrants shall be immediately exercisable.
    
 
   
                              PLAN OF DISTRIBUTION
    
 
   
     The Notes, Warrants and shares of Common Stock offered hereby will be
purchased by not more than three institutional "accredited investors", as
defined in Rule 501(a)(1), (2), (3) and (7) under the Securities Act. The
offering price per Share will be based on the average volume-weighted closing
sales price of the Common Stock as reported on the National Association of
Securities Dealers Automated Quotation System over a period of time prior to
closing.
    
 
                                 LEGAL MATTERS
 
   
     Certain legal matters in connection with the securities being offered
hereby will be passed upon for the Company by Thompson & Knight, P.C., Dallas,
Texas.
    
 
                                    EXPERTS
 
   
     The consolidated financial statements of Brigham Exploration Company as of
December 31, 1997 and 1996 and for each of the three years in the period ended
December 31, 1997 included in this Prospectus have been so included in reliance
on the report of PricewaterhouseCoopers LLP, independent accountants, given on
authority of said firm as experts in auditing and accounting.
    
 
     The letter of Cawley, Gillespie & Associates, Inc., independent oil and gas
consultants, set forth in this Prospectus as Appendix A has been included herein
in reliance upon the firm as expert with respect to the matters contained in
that letter. In addition, the information with respect to the reserve reports
prepared by Cawley Gillespie has been included herein in reliance upon by the
firm as experts with respect to such information.
 
                             AVAILABLE INFORMATION
 
     The Company has filed with the Commission a Registration Statement on Form
S-1 (as amended and together with all exhibits thereto, the "Registration
Statement") under the Securities Act, with respect to the shares of Common Stock
offered by this Prospectus. This Prospectus constitutes a part of the
Registration Statement and does not contain all of the information set forth in
the Registration Statement, certain parts of which are omitted from this
Prospectus as permitted by the rules and regulations of the SEC. Statements in
this Prospectus about the contents of any contract or other document are not
necessarily complete; reference is made in each instance to the copy of the
contract or other document filed as an exhibit to the Registration Statement.
Each such statement is qualified in all respects by such reference. The
Registration Statement and accompanying exhibits and schedules may by inspected
and copies may be obtained (at prescribed rates) at the public reference
facilities of the SEC at Judiciary Plaza, 450 Fifth Street, N.W., Room 1024,
Washington, D.C. 20549. Copies of the Registration Statement may also be
inspected at the SEC's regional offices at 7 World Trade Center, Suite 1300, New
York, New York 10048 and Citicorp Center, 500 West Madison Street, Suite 1400,
Chicago, Illinois 60661-2511. In addition, the Common Stock will be listed on
the Nasdaq National Market, 1735 K Street, N.W., Washington, D.C. 20006-1500,
where such material may also be inspected and copied.
 
                                       87
<PAGE>   89
 
     The Company is subject to the information and periodic reporting
requirements of the Securities Exchange Act of 1934, and, in accordance
therewith, files periodic reports, proxy statements and other information with
the SEC. Such periodic reports, proxy statements and other information will be
available for inspection and copying at the public reference facilities and
regional offices referred to above. In addition, these reports, proxy statements
and other information may also be obtained from the web site that the SEC
maintains at http://www.sec.gov.
 
                                       88
<PAGE>   90
 
                     GLOSSARY OF CERTAIN OIL AND GAS TERMS
 
     The following are abbreviations and definitions of certain terms commonly
used in the oil and gas industry and this Prospectus.
 
     Bbl. One stock tank barrel, or 42 U.S. gallons liquid volume, used herein
in reference to oil or other liquid hydrocarbons.
 
     Bcf. One billion cubic feet.
 
     Bcfe. One billion cubic feet of natural gas equivalent. In reference to
natural gas, natural gas equivalents are determined using the ratio of 6 Mcf of
natural gas to 1 Bbl of oil, condensate or natural gas liquids.
 
     Completion. The installation of permanent equipment for the production of
natural gas or oil.
 
     Developed Acreage. The number of acres which are allocated or assignable to
producing wells or wells capable of production.
 
     Development Well. A well drilled within the proved area of natural gas or
an oil reservoir to the depth of a stratigraphic horizon known to be productive.
 
     Drilling Costs. The costs associated with drilling and completing a well
(exclusive of seismic and land acquisition costs for that well and future
development costs associated with proved undeveloped reserves added by the well)
divided by total proved reserve additions.
 
     Dry Well. A well found to be incapable of producing either natural gas or
oil in sufficient quantities to justify completion of natural gas or an oil
well.
 
     Exploratory Well. A well drilled to find and produce natural gas or oil in
an unproved area, to find a new reservoir in a field previously found to be
productive of natural gas or oil in another reservoir, or to extend a known
reservoir.
 
     Finding and Development Costs. Capital costs incurred in the acquisition,
exploration and development of proved natural gas and oil reserves divided by
proved reserve additions.
 
     Gross Acres or Gross Wells. The total acres or wells, as the case may be,
in which the Company has a working interest.
 
     Mbbl. One thousand barrels of oil or other liquid hydrocarbons.
 
     Mcf. One thousand cubic feet of natural gas.
 
     Mcfe. One thousand cubic feet of natural gas equivalent.
 
     MMBbl. One million barrels of oil or other liquid hydrocarbons.
 
     MMBtu. One million Btu, or British Thermal Units. One British Thermal Unit
is the quantity of heat required to raise the temperature of one pound of water
by one degree Fahrenheit.
 
     MMcf. One million cubic feet of natural gas.
 
     MMcfe. One million cubic feet of natural gas equivalent.
 
     Net Acres or Net Wells. Gross acres or wells multiplied, in each case, by
the percentage working interest owned by the Company.
 
     Net Production. Production that is owned by the Company less royalties and
production due others.
 
     Oil. Crude oil or condensate.
 
     Operator. The individual or company responsible for the exploration,
development, and production of natural gas or an oil well or lease.
 
     Present Value of Future Net Revenues or PV-10. The pretax present value of
estimated future revenues to be generated from the production of proved reserves
calculated in accordance with SEC guidelines, net of
 
                                       89
<PAGE>   91
 
estimated production and future development costs, using prices and costs as of
the date of estimation without future escalation, without giving effect to
non-property related expenses such as general and administrative expenses, debt
service and depreciation, depletion and amortization, and discounted using an
annual discount rate of 10%.
 
     Proved Developed Reserves. Reserves that can be expected to be recovered
through existing wells with existing equipment and operating methods.
 
     Proved Reserves. The estimated quantities of crude oil, natural gas and
natural gas liquids which geological and engineering data demonstrate with
reasonable certainty to be recoverable in future years from known reservoirs
under existing economic and operating conditions.
 
     Proved Undeveloped Reserves. Reserves that are expected to be recovered
from new wells on undrilled acreage or from existing wells where a relatively
major expenditure is required for recompletion.
 
     Royalty. An interest in an oil and gas lease that gives the owner of the
interest the right to receive a portion of the production from the leased
acreage (or of the proceeds of the sale thereof), but generally does not require
the owner to pay any portion of the costs of drilling or operating the wells on
the leased acreage. Royalties may be either landowner's royalties, which are
reserved by the owner of the leased acreage at the time the lease is granted, or
overriding royalties, which are usually reserved by an owner of the leasehold in
connection with a transfer to a subsequent owner.
 
     Spud. Start drilling a new well (or restart).
 
     Success Rate. The number of wells on which production casing has been run
for a completion attempt as a percentage of the number of wells drilled.
 
     2-D Seismic. The method by which a cross-section of the earth's subsurface
is created through the interpretation of reflecting seismic data collected along
a single source profile.
 
     3-D Seismic. The method by which a three dimensional image of the earth's
subsurface is created through the interpretation of reflection seismic data
collected over surface grid. 3-D seismic surveys allow for a more detailed
understanding of the subsurface than do conventional surveys and contribute
significantly to field appraisal, development and production.
 
     Working Interest. An interest in an oil and gas lease that gives the owner
of the interest the right to drill for and produce natural gas and oil on the
leased acreage and requires the owner to pay a share of the costs of drilling
and production operations.
 
                                       90
<PAGE>   92
 
                          BRIGHAM EXPLORATION COMPANY
 
                         INDEX TO FINANCIAL STATEMENTS
 
   
<TABLE>
<CAPTION>
                                                              PAGE
                                                              ----
<S>                                                           <C>
Audited Financial Statements
  Report of Independent Accountants.........................   F-2
  Consolidated Balance Sheets as of December 31, 1997 and
     1996...................................................   F-3
  Consolidated Statements of Operations for the Years Ended
     December 31, 1997, 1996, and 1995......................   F-4
  Consolidated Statements of Stockholders' Equity for the
     Years Ended December 31, 1997, 1996, and 1995..........   F-5
  Consolidated Statements of Cash Flows for the Years Ended
     December 31, 1997, 1996, and 1995......................   F-6
  Notes to the December 31, 1997 Consolidated Financial
     Statements.............................................   F-7
Unaudited Financial Statements
  Condensed Consolidated Balance Sheets as of December 31,
     1997 and June 30, 1998.................................  F-20
  Condensed Consolidated Statements of Operations for the
     Six Months Ended June 30, 1997 and 1998................  F-21
  Condensed Consolidated Statements of Cash Flows for the
     Six Months Ended June 30, 1997 and 1998................  F-22
  Notes to the June 30, 1998 Condensed Consolidated
     Financial Statements...................................  F-23
</TABLE>
    
 
                                       F-1
<PAGE>   93
 
                       REPORT OF INDEPENDENT ACCOUNTANTS
 
To the Board of Directors
and Stockholders of Brigham Exploration Company
 
     In our opinion, the accompanying consolidated balance sheets and the
related consolidated statements of operations, of stockholders' equity and of
cash flows present fairly, in all material respects, the financial position of
Brigham Exploration Company and its subsidiaries at December 31, 1997 and 1996,
and the results of their operations and its cash flows for each of the three
years in the period ended December 31, 1997, in conformity with generally
accepted accounting principles. These financial statements are the
responsibility of the Company's management; our responsibility is to express an
opinion on these financial statements based on our audits. We conducted our
audits of these statements in accordance with generally accepted auditing
standards which require that we plan and perform the audit to obtain reasonable
assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements, assessing the
accounting principles used and significant estimates made by management, and
evaluating the overall financial statement presentation. We believe that our
audits provide a reasonable basis for the opinion expressed above.
 
PRICE WATERHOUSE LLP
 
Houston, Texas
March 6, 1998
 
                                       F-2
<PAGE>   94
 
                          BRIGHAM EXPLORATION COMPANY
 
                          CONSOLIDATED BALANCE SHEETS
                                 (IN THOUSANDS)
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                                DECEMBER 31,
                                                              -----------------
                                                               1997      1996
                                                              -------   -------
<S>                                                           <C>       <C>
Current assets:
  Cash and cash equivalents.................................  $ 1,701   $ 1,447
  Accounts receivable.......................................    4,909     2,696
  Prepaid expenses..........................................      280       152
                                                              -------   -------
          Total current assets..............................    6,890     4,295
                                                              -------   -------
Natural gas and oil properties, at cost, net................   84,176    28,005
Other property and equipment, at cost, net..................    1,239       532
Drilling advances paid......................................       78       419
Other noncurrent assets.....................................       18       363
                                                              -------   -------
                                                              $92,401   $33,614
                                                              =======   =======
 
                     LIABILITIES AND STOCKHOLDERS' EQUITY
 
Current liabilities:
  Accounts payable..........................................  $11,892   $ 2,937
  Accrued drilling costs....................................    2,406       915
  Participant advances received.............................      489     1,137
  Other current liabilities.................................      726       628
                                                              -------   -------
          Total current liabilities.........................   15,513     5,617
                                                              -------   -------
Notes payable...............................................   32,000     8,000
Subordinated notes payable -- related party.................       --    16,000
Other noncurrent liabilities................................      507       753
Deferred income tax liability...............................    1,228        --
Stockholders' equity:
  Predecessor capital.......................................       --     3,244
  Preferred stock, $.01 par value, 10 million shares
     authorized, none issued and outstanding................       --        --
  Common stock, $.01 par value, 30 million shares
     authorized, 12,253,574 issued and outstanding..........      123        --
  Additional paid-in capital................................   44,344        --
  Unearned stock compensation...............................   (1,340)       --
  Retained earnings.........................................       26        --
                                                              -------   -------
          Total stockholders' equity........................   43,153     3,244
                                                              -------   -------
                                                              $92,401   $33,614
                                                              =======   =======
</TABLE>
 
  The Company uses the full cost method to account for its natural gas and oil
                                  properties.
 
        See accompanying notes to the consolidated financial statements.
 
                                       F-3
<PAGE>   95
 
                          BRIGHAM EXPLORATION COMPANY
 
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)
 
<TABLE>
<CAPTION>
                                                                YEAR ENDED DECEMBER 31,
                                                              ---------------------------
                                                               1997      1996      1995
                                                              -------   -------   -------
<S>                                                           <C>       <C>       <C>
Revenues:
  Natural gas and oil sales.................................  $ 9,184   $ 6,141   $ 3,578
  Workstation revenue.......................................      637       627       635
                                                              -------   -------   -------
                                                                9,821     6,768     4,213
                                                              -------   -------   -------
Costs and expenses:
  Lease operating...........................................    1,151       726       761
  Production taxes..........................................      549       362       165
  General and administrative................................    3,570     2,199     1,897
  Depletion of natural gas and oil properties...............    2,732     2,323     1,626
  Depreciation and amortization.............................      306       487       533
  Amortization of stock compensation........................      276        --        --
                                                              -------   -------   -------
                                                                8,584     6,097     4,982
                                                              -------   -------   -------
     Operating income (loss)................................    1,237       671      (769)
                                                              -------   -------   -------
Other income (expense):
  Interest income...........................................      145        52       128
  Interest expense..........................................   (1,017)     (373)     (187)
  Interest expense -- related party.........................     (173)     (800)     (749)
                                                              -------   -------   -------
                                                               (1,045)   (1,121)     (808)
                                                              -------   -------   -------
Net income (loss) before income taxes.......................      192      (450)   (1,577)
Income tax expense..........................................   (1,228)       --        --
                                                              -------   -------   -------
  Net loss..................................................  $(1,036)  $  (450)  $(1,577)
                                                              =======   =======   =======
Net loss per share:
  Basic/Diluted.............................................  $ (0.09)  $ (0.05)  $ (0.18)
Common shares outstanding:
  Basic/Diluted.............................................   11,081     8,929     8,929
</TABLE>
 
        See accompanying notes to the consolidated financial statements.
 
                                       F-4
<PAGE>   96
 
                          BRIGHAM EXPLORATION COMPANY
 
                 CONSOLIDATED STATEMENT OF STOCKHOLDERS' EQUITY
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                              COMMON STOCK        ADDITIONAL     UNEARNED
                          ---------------------    PAID-IN        STOCK       RETAINED   PREDECESSOR
                            SHARES      AMOUNTS    CAPITAL     COMPENSATION   EARNINGS     CAPITAL       TOTAL
                          -----------   -------   ----------   ------------   --------   ------------   -------
<S>                       <C>           <C>       <C>          <C>            <C>        <C>            <C>
Balance,
  December 31, 1994.....           --    $ --      $    --       $    --        $--        $ 5,271      $ 5,271
  Net loss..............           --      --           --            --         --         (1,577)      (1,577)
                          -----------    ----      -------       -------        ---        -------      -------
Balance,
  December 31, 1995.....           --      --           --            --         --          3,694        3,694
  Net loss..............           --      --           --            --         --           (450)        (450)
                          -----------    ----      -------       -------        ---        -------      -------
Balance,
  December 31, 1996.....           --      --           --            --         --          3,244        3,244
Consummation of the
  Exchange..............    8,928,574      90       19,580            --         --         (3,244)      16,426
Issuance of stock
  options...............           --      --        1,932        (1,932)        --             --           --
Issuance of common
  stock.................  3,325,000..      33       23,894            --         --             --       23,927
Net loss for period
  ended February 27,
  1997..................           --      --       (4,869)           --         --             --       (4,869)
Net income for period
  from February 27, 1997
  to Dec. 31, 1997......           --      --        3,807            --         26             --        3,833
  (Note 1) Amortization
     of unearned stock
     compensation.......           --      --           --           592         --             --          592
                          -----------    ----      -------       -------        ---        -------      -------
Balance,
  December 31, 1997.....  12,253,574..   $123      $44,344       $(1,340)       $26        $    --      $43,153
                          ===========    ====      =======       =======        ===        =======      =======
</TABLE>
 
        See accompanying notes to the consolidated financial statements.
 
                                       F-5
<PAGE>   97
 
                          BRIGHAM EXPLORATION COMPANY
 
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                                 YEAR ENDED DECEMBER 31,
                                                              ------------------------------
                                                                1997       1996       1995
                                                              --------   --------   --------
<S>                                                           <C>        <C>        <C>
Cash flows from operating activities:
  Net loss..................................................  $ (1,036)  $   (450)  $ (1,577)
  Adjustments to reconcile net loss to cash provided by
     operating activities:
     Depletion of natural gas and oil properties............     2,732      2,323      1,626
     Depreciation and amortization..........................       306        487        533
     Amortization of stock compensation.....................       276         --         --
     Changes in working capital and other items:
       (Increase) decrease in accounts receivable...........    (2,213)    (1,440)       413
       (Increase) decrease in prepaid expenses..............      (128)        25       (107)
       Increase in accounts payable.........................     8,955      1,619        128
       Increase (decrease) in participant advances
          received..........................................      (648)       804         92
       Increase in other current liabilities................        50         60        151
       Increase in deferred interest payable -- related
          party.............................................        53        320        113
       Increase in deferred income tax liability............     1,228         --         --
       Other noncurrent assets..............................       281       (224)       (26)
       Other noncurrent liabilities.........................       (50)       186         37
                                                              --------   --------   --------
          Net cash provided by operating activities.........     9,806      3,710      1,383
                                                              --------   --------   --------
Cash flows from investing activities:
  Additions to natural gas and oil properties...............   (57,170)   (13,612)    (7,935)
  Proceeds from the sale of natural gas and oil
     properties.............................................        74      2,149         --
  Additions to other property and equipment.................      (545)       (41)       (51)
  (Increase) decrease in drilling advances paid.............       341       (292)       (19)
                                                              --------   --------   --------
          Net cash used by investing activities.............   (57,300)   (11,796)    (8,005)
                                                              --------   --------   --------
Cash flows from financing activities:
  Proceeds from issuance of common stock....................    23,927         --         --
  Proceeds from issuance of subordinated notes payable......        --         --     16,000
  Increase in notes payable.................................    37,250      8,000      2,560
  Repayment of notes payable................................   (13,250)        --    (10,510)
  Principal payments on capital lease obligations...........      (179)      (269)      (326)
                                                              --------   --------   --------
          Net cash provided by financing activities.........    47,748      7,731      7,724
                                                              --------   --------   --------
Net increase (decrease) in cash and cash equivalents........       254       (355)     1,102
Cash and cash equivalents, beginning of year................     1,447      1,802        700
                                                              --------   --------   --------
Cash and cash equivalents, end of year......................  $  1,701   $  1,447   $  1,802
                                                              ========   ========   ========
Supplemental disclosure of cash flow information:
  Cash paid during the year for interest....................  $  1,679   $    762   $    654
                                                              ========   ========   ========
Supplemental disclosure of noncash investing and financing
  activities:
  Capital lease asset additions.............................  $    403   $    101   $    208
                                                              ========   ========   ========
</TABLE>
 
        See accompanying notes to the consolidated financial statements.
 
                                       F-6
<PAGE>   98
 
                          BRIGHAM EXPLORATION COMPANY
 
                 NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS
 
1. ORGANIZATION AND NATURE OF OPERATIONS
 
     Brigham Exploration Company is a Delaware corporation formed on February
25, 1997 for the purpose of exchanging its common stock for the common stock of
Brigham, Inc. and the partnership interests of Brigham Oil & Gas, L.P. (the
"Partnership"). Hereinafter, Brigham Exploration Company and the Partnership are
collectively referred to as "the Company." Brigham, Inc. is a Nevada corporation
whose only asset is its ownership interest in the Partnership. The Partnership
was formed in May 1992 to explore and develop onshore domestic natural gas and
oil properties using 3-D seismic imaging and other advanced technologies. Since
its inception, the Partnership has focused its exploration and development of
natural gas and oil properties primarily in the Permian and Hardeman Basins of
West Texas, the Anadarko Basin and the onshore Gulf Coast.
 
     Pursuant to an exchange agreement dated February 26, 1997 (the "Exchange
Agreement") and upon the initial filing on February 27, 1997 of a registration
statement with the Securities and Exchange Commission for the public offering of
common stock (the "Offering"), the shareholders of Brigham, Inc. transferred all
of the outstanding stock of Brigham, Inc. to the Company in exchange for
3,859,821 shares of common stock of the Company. Pursuant to the Exchange
Agreement, the Partnership's other general partner and the limited partners also
transferred all of their partnership interests to the Company in exchange for
3,314,286 shares of common stock of the Company. Furthermore, the holders of the
Partnership's subordinated convertible notes transferred these notes to the
Company in exchange for 1,754,464 shares of common stock. These transactions are
referred to as "the Exchange." In completing the Exchange, the Company issued
8,928,571 shares of common stock to the stockholders of Brigham, Inc., the
partners of the Partnership and the holder of the Partnership's subordinated
notes payable. As a result of the Exchange, the Company now owns all the
partnership interests in the Partnership. In May 1997, the Company sold
3,325,000 shares of its common stock in the Offering at a price of $8.00 per
share. With a portion of the proceeds from the Offering, the Company repaid the
$13.3 million in outstanding borrowings under the existing revolving credit
facility.
 
2. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES
 
  Basis of Accounting
 
     The preparation of financial statements in conformity with generally
accepted accounting principles requires management to make estimates and
assumptions that affect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the date of the financial
statements and the reported amounts of revenues and expenses during the
reporting period. Actual results may differ from those estimates.
 
     The Exchange has been reflected in the consolidated financial statements of
the Company as a reorganization.
 
  Principles of Consolidation
 
     The accompanying financial statements include the accounts of the Company
and its wholly-owned subsidiaries, and its proportionate share of assets,
liabilities and income and expenses of the limited partnerships in which the
Company, or any of its subsidiaries has a participating interest. All
significant intercompany accounts and transactions have been eliminated.
 
  Cash and Cash Equivalents
 
     The Company considers all highly liquid financial instruments with an
original maturity of three months or less to be cash equivalents.
 
                                       F-7
<PAGE>   99
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
  Property and Equipment
 
     The Company uses the full cost method of accounting for its investment in
natural gas and oil properties. Under this method, all acquisition, exploration
and development costs, including certain payroll and other internal costs,
incurred for the purpose of finding natural gas and oil reserves are
capitalized. Costs associated with production and general corporate activities
are expensed in the period incurred.
 
     The capitalized costs of the Company's natural gas and oil properties plus
future development, dismantlement, restoration and abandonment costs (the
"Amortizable Base"), net of estimated of salvage values, are amortized using the
unit-of-production method based upon estimates of total proved reserve
quantities. The Company's capitalized costs of its natural gas and oil
properties, net of accumulated amortization, are limited to the total of
estimated future net cash flows from proved natural gas and oil reserves,
discounted at ten percent, plus the cost of unevaluated properties. There are
many factors, including global events, that may influence the production,
processing, marketing and valuation of natural gas and oil. A reduction in the
valuation of natural gas and oil properties resulting from declining prices or
production could adversely impact depletion rates and ceiling test limitations.
 
     All costs directly associated with the acquisition and evaluation of
unproved properties are initially excluded from the Amortizable Base. Upon the
interpretation by the Company of the 3-D seismic data associated with unproved
properties, the geological and geophysical costs related to acreage that is not
specifically identified as prospective are added to the Amortizable Base.
Geological and geophysical costs associated with prospective acreage, as well as
leasehold costs, are added to the Amortizable Base when the prospects are
drilled. Costs of prospective acreage are reviewed annually for impairment on a
property-by-property basis.
 
     Other property and equipment, which primarily consists of 3-D seismic
interpretation workstations, are depreciated on a straight-line basis over the
estimated useful lives of the assets after considering salvage value. Estimated
useful lives are as follows:
 
<TABLE>
<S>                                                           <C>
Furniture and fixtures......................................  10 years
Machinery and equipment.....................................   5 years
3-D seismic interpretation workstations and software........   3 years
</TABLE>
 
     Betterments and major improvements that extend the useful lives are
capitalized, while expenditures for repairs and maintenance of a minor nature
are expensed as incurred.
 
  Revenue Recognition
 
     The Company recognizes natural gas and oil sales from its interests in
producing wells under the sales method of accounting. Under the sales method,
the Company recognizes revenues based on the amount of natural gas or oil sold
to purchasers, which may differ from the amounts to which the Company is
entitled based on its interest in the properties. Gas balancing obligations as
of December 31, 1995, 1996 and 1997 were not significant. Net realized gains or
losses arising from the Company's crude oil price swaps (see Note 10) are
recognized in the period incurred as a component of natural gas and oil sales.
 
     Industry participants in the Company's seismic programs are charged on an
hourly basis for the work performed by the Company on its 3-D seismic
interpretation workstations. The Company recognizes workstation revenue as
service is provided.
 
  Federal and State Income Taxes
 
     Prior to the consummation of the Exchange, there was no income tax
provision included in the financial statements as the Partnership was not a
taxpaying entity. Income and losses were passed through to its
 
                                       F-8
<PAGE>   100
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
partners on the basis of the allocation provisions established by the
partnership agreement. Upon consummation of the Exchange, the Partnership became
subject to federal income taxes through its ownership by the Company.
 
     In conjunction with the Exchange, the Company recorded a deferred income
tax liability of $5 million to recognize the temporary differences between the
financial statement and tax bases of the assets and liabilities of the
Partnership at the Exchange date, February 27, 1997, given the provisions of
enacted tax laws. Subsequent to this date, the Company elected to record a
step-up in basis of its assets for tax purposes as a result of the Exchange.
Related to this election, the Company recorded a $3.8 million deferred income
tax benefit, resulting in a net $1.2 million deferred income tax charge for the
year ended December 31, 1997.
 
  Earnings Per Share
 
     The Company has adopted Statement of Financial Accounting Standards
("SFAS") No. 128 "Earnings per Share." This statement establishes new standards
for computing and presenting earnings per share ("EPS") and requires restatement
of all prior-period EPS information.
 
  Recent Pronouncements
 
     In June 1997, the Financial Accounting Standards Board issued SFAS No. 130,
"Reporting Comprehensive Income," which will become effective for the Company in
1998. SFAS No. 130 will require companies to present certain items as separate
components of stockholders' equity. Management does not believe that the effect
of implementing this standard will materially impact the Company's financial
statements.
 
3. ACQUISITION
 
     On November 12, 1997, the Company acquired a 50% interest in certain
producing properties in Grady County, Oklahoma (the "Acquisition"). These
properties were formerly owned by Mobil and were acquired by Ward Petroleum. The
acquisition has been accounted for as a purchase and the results of operations
of the properties acquired are included in the Company's results of operations
effective September 1, 1997. The purchase price of $13.4 million was financed
primarily through the Company's existing revolving credit facility and was based
on the Company's determination of the fair value of the assets acquired.
 
  Pro Forma Information
 
     The following unaudited pro forma statement of operations information has
been prepared to give effect to the Acquisition as if the transaction had
occurred at the beginning of 1996 and 1997. The historical results of operations
have been adjusted to reflect (i) the difference between the acquired
properties' historical depletion and such expense calculated based on the value
allocated to the acquired assets, (ii) the increase in interest expense
associated with the debt issued in the transaction, and (iii) the increase in
federal income taxes related to historical net income attributable to the
properties acquired. The pro forma amounts do not
 
                                       F-9
<PAGE>   101
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
purport to be indicative of the results of operations that would have been
reported had the Acquisition occurred as of the dates indicated, or that may be
reported in the future (in thousands).
 
<TABLE>
<CAPTION>
                                                                 PRO FORMA
                                                                 YEAR ENDED
                                                                DECEMBER 31,
                                                              ----------------
                                                               1997      1996
                                                              -------   ------
<S>                                                           <C>       <C>
Revenues....................................................  $11,194   $8,516
Costs and expenses:
  Lease operating and production taxes......................    1,864    1,300
  General and administrative................................    3,570    2,199
  Depletion of natural gas and oil properties...............    3,307    2,791
  Depreciation and amortization.............................      582      487
  Interest expense, net.....................................    2,235    2,355
                                                              -------   ------
  Total costs and expenses..................................   11,558    9,132
                                                              -------   ------
Net loss before income taxes................................     (364)    (616)
  Income tax expense........................................    1,039       --
                                                              -------   ------
Net loss....................................................  $(1,403)  $ (616)
                                                              =======   ======
Net loss per share:
  Basic/Diluted.............................................  $ (0.13)  $(0.07)
                                                              =======   ======
Common shares outstanding:
  Basic/Diluted.............................................   11,081    8,929
                                                              =======   ======
</TABLE>
 
4. PROPERTY AND EQUIPMENT
 
     Property and equipment, at cost, are summarized as follows (in thousands):
 
<TABLE>
<CAPTION>
                                                                DECEMBER 31,
                                                              -----------------
                                                               1997      1996
                                                              -------   -------
<S>                                                           <C>       <C>
Natural gas and oil properties..............................  $96,458   $37,555
Accumulated depletion.......................................  (12,282)   (9,550)
                                                              -------   -------
                                                               84,176    28,005
                                                              -------   -------
Other property and equipment:
  3-D seismic interpretation workstations and software......    1,693     1,456
  Office furniture and equipment............................    1,095       384
  Accumulated depreciation..................................   (1,549)   (1,308)
                                                              -------   -------
                                                                1,239       532
                                                              -------   -------
                                                              $85,415   $28,537
                                                              =======   =======
</TABLE>
 
     The Company sold its interest in certain producing properties for $2.1
million and $74,000 during 1996
and 1997, respectively. No gain or loss was recognized on these transaction
because the Company applies the full cost method of accounting for its
investment in natural gas and oil properties.
 
     The Company capitalizes certain payroll and other internal costs directly
attributable to acquisition, exploration and development activities as part of
its investment in natural gas and oil properties over the periods benefited by
these activities. During the years ended December 31, 1995, 1996 and 1997,
certain payroll and other internal costs incurred of $1,640,196, $1,826,013 and
$3,330,518, respectively, were capitalized.
 
                                      F-10
<PAGE>   102
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
5. NOTES PAYABLE AND SUBORDINATED NOTES PAYABLE
 
     In April 1996, the Company entered into a revolving credit facility with
Bank One, Texas, NA (the "Bank One Facility") which provided for borrowings up
to $25 million. On November 10, 1997, the Bank One Facility was amended and the
amount available under the agreement was increased to $75 million. The Company's
borrowings under the Bank One Facility were limited to a borrowing base
determined periodically by the lender. This determination was based upon the
Company's proved net gas and oil properties.
 
     The amounts outstanding under the revolving credit facility, excluding a
$5.4 million special advance made November 12, 1997, bore interest, at the
borrower's option, at the Base Rate or (i) LIBOR plus 1.75% if the principal
outstanding is less than or equal to 50% of the borrowing base, (ii) LIBOR plus
2.0% if the principal outstanding is less than or equal to 75% but more than 50%
of the borrowing base, and (iii) LIBOR plus 2.25% if the principal outstanding
is greater than 75% of the borrowing base. The Base Rate is the fluctuating rate
of interest per annum established from time to time by the lender. Interest
accrued on the $5.4 million special advance at 11.50% per annum. The Company
also paid a quarterly commitment fee of 0.5% per annum for the unused portion of
the borrowing base.
 
     In January 1998, the Company entered into a reserve-based revolving credit
facility with the Bank of Montreal (the "Bank of Montreal Facility"). The Bank
of Montreal Facility provides for borrowings up to $75 million until January 31,
1999, at which time the borrowing available will be redetermined by the Bank of
Montreal based on the Company's proved reserve value at that time. The Company
may elect, at its option, to have the borrowing availability redetermined based
on the Company's proved reserve value at any time prior to January 31, 1999.
Amounts outstanding under the Bank of Montreal Facility bear interest at either
the lender's Base Rate or LIBOR plus 2.25%, at the Company's option. The
Company's obligations under the Bank of Montreal Facility are secured by
substantially all of the natural gas and oil properties of the Company. A
portion of the funds available under the Bank of Montreal Facility were used to
repay in full the Bank One Facility.
 
     The subordinated notes payable bore interest at 5% per annum and were due
in 2002. The notes were convertible into a 20% interest in the Company at any
time prior to maturity and were unsecured. Interest payments of 3% were due
semi-annually and the remaining 2% was deferred until maturity. Pursuant to the
Exchange (see Note 1), the holders of these notes exchanged the notes and
related deferred interest for shares of the Company's common stock.
 
6. CAPITAL LEASE OBLIGATIONS
 
     Property under capital leases consists of the following (in thousands):
 
<TABLE>
<CAPTION>
                                                              DECEMBER 31,
                                                              -------------
                                                              1997    1996
                                                              -----   -----
<S>                                                           <C>     <C>
3-D seismic interpretation workstations and software........  $ 497   $ 525
Office furniture and equipment..............................    204      17
                                                              -----   -----
                                                                701     542
Accumulated depreciation and amortization...................   (241)   (305)
                                                              -----   -----
                                                              $ 460   $ 237
                                                              =====   =====
</TABLE>
 
                                      F-11
<PAGE>   103
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
     The obligations under capital leases are at fixed interest rates ranging
from 9% to 17% and are collateralized by property, plant and equipment. The
future minimum lease payments under the capital leases and the present value of
the net minimum lease payments at December 31, 1997 are as follows (in
thousands):
 
<TABLE>
<S>                                                            <C>
1998........................................................   $ 261
1999........................................................     185
2000........................................................      99
2001........................................................      40
2002........................................................      24
                                                               -----
Total minimum lease payments................................     609
  Estimated executory costs included in capital leases......     (73)
                                                               -----
Net minimum lease payments..................................     536
  Amounts representing interest.............................     (81)
                                                               -----
Present value of net minimum lease payments.................     455
Less: current portion.......................................    (181)
                                                               -----
Noncurrent portion..........................................   $ 274
                                                               =====
</TABLE>
 
7. INCOME TAXES
 
     The provision for income taxes consists of the following (in thousands):
 
<TABLE>
<CAPTION>
                                                               YEAR ENDED
                                                              DECEMBER 31,
                                                                  1997
                                                              ------------
<S>                                                           <C>
Current income taxes:
  Federal...................................................     $   --
  State.....................................................         --
Deferred income taxes:
  Federal...................................................      1,228
  State.....................................................         --
                                                                 ------
                                                                 $1,228
                                                                 ======
</TABLE>
 
     The difference in income taxes provided and the amounts determined by
applying the federal statutory tax rate to income before income taxes result
from the following (in thousands):
 
<TABLE>
<CAPTION>
                                                               YEAR ENDED
                                                              DECEMBER 31,
                                                                  1997
                                                              ------------
<S>                                                           <C>
Tax at statutory rate.......................................     $   65
Add (deduct) the effect of:
  January and February income, not taxable..................        (44)
  Nondeductible expenses....................................         14
  Tax effect of Exchange....................................      1,193
                                                                 ------
                                                                 $1,228
                                                                 ======
</TABLE>
 
                                      F-12
<PAGE>   104
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
     The components of deferred income tax assets and liabilities are as follows
(in thousands):
 
<TABLE>
<CAPTION>
                                                               DECEMBER 31,
                                                                   1997
                                                               ------------
<S>                                                            <C>
Deferred tax assets:
  Net operating loss carryforwards..........................     $ 5,563
  Amortization of stock compensation........................          94
  Other.....................................................           3
                                                                 -------
                                                                   5,660
Deferred tax liability:
  Depreciable and depletable property.......................      (6,888)
                                                                 -------
                                                                 $(1,228)
                                                                 =======
</TABLE>
 
     The Company has regular and alternative minimum tax net operating loss
carryforwards of approximately $16,361 million and $8,441 million, respectively,
each including separate return limitation year carryovers of approximately
$1,352 million, which expire by December 31, 2012.
 
8. EARNINGS PER SHARE
 
     Earnings per share have been calculated in accordance with the provisions
of SFAS No. 128. The implementation of the standard has resulted in the
presentation of a basic EPS calculation in the consolidated financial statements
as well as a diluted EPS calculation. Basic EPS is computed by dividing net
income (loss) applicable to common shareholders by the weighted average number
of common shares outstanding during each period. Diluted EPS is computed by
dividing net income (loss) applicable to common shareholders by the weighted
average number of common shares and common share equivalents outstanding (if
dilutive), during each period. The number of common share equivalents
outstanding is computed using the treasury stock method.
 
     Historical earnings per common share for 1996 and 1995 is based on shares
issued upon consummation of the Exchange, assuming such shares has been
outstanding for all periods presented. Earnings per share for 1997 is presented
giving effect to the shares issued pursuant to the Exchange as well as shares
issued in the initial public offering.
 
     At December 31, 1997, options to purchase 644,097 shares of common stock
were outstanding but were not included in the computation of diluted earnings
per share due to the anti-dilutive effect they would have on EPS if converted.
 
     In January 1998, the Company granted 309,247 stock options under the 1997
incentive plan (the "1997 Incentive Plan") with an exercise price of $12.88.
 
9. COMMITMENTS AND CONTINGENCIES
 
     The Company is, from time to time, party to certain lawsuits and claims
arising in the ordinary course of business. While the outcome of lawsuits and
claims cannot be predicted with certainty, management does not expect these
matters to have a materially adverse effect on the financial condition, results
of operations or cash flows of the Company.
 
                                      F-13
<PAGE>   105
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
     The Company leases office equipment and space under operating leases
expiring at various dates through 2007. The future minimum annual rental
payments under the noncancelable terms of these leases at December 31, 1997, are
as follows (in thousands):
 
<TABLE>
<S>                                                   <C>
1998................................................  $  765
1999................................................     763
2000................................................     684
2001................................................     684
2002................................................     342
                                                      ------
                                                      $3,238
                                                      ======
</TABLE>
 
     Rental expense for the years ended December 31, 1995, 1996 and 1997 was
$239,715, $253,112 and $606,173, respectively.
 
     Since the Company's major products are commodities, significant changes in
the prices of natural gas and oil could have a significant impact on the
Company's results of operations for any particular year.
 
     As of December 31, 1997, there were no known environmental or other
regulatory matters related to the Company's operations which are reasonably
expected to result in a material liability to the Company. Compliance with
environmental laws and regulations has not had, and is not expected to have, a
material adverse effect on the Company's capital expenditures, earnings or
competitive position.
 
     During 1997, approximately 14% and 12% of the Company's natural gas and oil
production was sold to two separate customers. During 1996, approximately 16%,
12% and 10% of the Company's natural gas and oil production was sold to three
separate customers. During 1995, approximately 14%, 11%, 10% and 10% of the
Company's natural gas and oil production was sold to four separate customers.
However, due to the availability of other markets, the Company does not believe
that the loss of any one of these individual customers would adversely affect
the Company's result of operations.
 
10. FINANCIAL INSTRUMENTS
 
     The Company periodically enters into commodity price swap agreements which
require payments to (or receipts from) counterparties based on the differential
between a fixed price and a variable price for a fixed quantity of natural gas
or crude oil without the exchange of the underlying volumes. The notional
amounts of these derivative financial instruments are based on planned
production from existing wells. The Company uses these derivative financial
instruments to manage market risks resulting from fluctuations in commodity
prices. Commodity price swaps are effective in minimizing these risks by
creating essentially equal and offsetting market exposures. The derivative
financial instruments held by the Company are not leveraged and are held for
purposes other than trading.
 
     At December 31, 1996, the Company was a party to crude oil swap based on an
average notional volume of 7,550 barrels of crude oil per month and a fixed
price of $22.70 per barrel. The contract expired in May 1997. The fair market
value of the crude oil price swap at December 31, 1996, based on the market
price of crude oil in December 1996, was $41,902. The Company was not a party to
any swap agreements at December 31, 1997.
 
     In February 1998, the Company entered into a hedging contract whereby
natural gas is purchased and sold subject to a fixed price swap agreement for
monthly periods from April 1998 through October 1999. Total natural gas subject
to this hedging contract is 2,750,000 MMBtu in 1998 and 3,040,000 MMBtu in 1999.
 
     The Company's non-derivative financial instruments include cash and cash
equivalents, accounts receivable, accounts payable and long-term debt. The
carrying amount of cash and cash equivalents, accounts
 
                                      F-14
<PAGE>   106
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
receivable and accounts payable approximate fair value because of their
immediate or short maturities. The carrying value of the Company's revolving
credit facility (see Note 5) approximates its fair market value since it bears
interest at floating market interest rates. At December 31, 1996, the carrying
amount of the Company's subordinated notes payable exceeded the fair market
value by $1.9 million, based on current rates offered to the Company for debt of
the same remaining maturity.
 
     The Company's accounts receivable relate to natural gas and oil sales to
various industry companies, amounts due from industry participants for
expenditures made by the Company on their behalf and workstation revenues.
Credit terms, typical of industry standards, are of a short-term nature and the
Company does not require collateral. The Company's accounts receivable at
December 31, 1997 do not represent significant credit risks as they are
dispersed across many counterparties. Counterparties to the crude oil price
swaps are investment grade financial institutions.
 
11. EMPLOYEE BENEFIT PLANS
 
  Retirement Savings Plan
 
     During 1996 the Company adopted a defined contribution 401(k) plan for
substantially all of its employees. Eligible employees may contribute up to 15%
of their compensation to this plan. The 401(k) plan provides that the Company
may, at its discretion, match employee contributions. The Company did not match
employee contributions in 1997 or 1996.
 
  Stock Compensation
 
     In 1994 three employees were granted restricted interests in the Company
which vest in increments through July 1999. At the date of grant, the value of
these interests was immaterial. On February 26, 1997, in connection with the
Exchange (see Note 1), the three employees transferred these company interests
to the Company in exchange for 156,250 shares of restricted common stock of the
Company. The terms of the restricted stock and the restricted company interests
are substantially the same. The shares vest over a three-year period ending in
1999. No compensation expense will result from this exchange.
 
     The Company adopted an incentive plan, effective upon completion of the
Exchange (see Note 1), which provides for the issuance of stock options, stock
appreciation rights, stock, restricted stock, cash or any combination of the
foregoing. The objective of this plan is to reward key employees whose
performance may have a significant effect on the success of the Company. An
aggregate of 1,588,170 shares of the Company's common stock was reserved for
issuance pursuant to this plan. The Compensation Committee of the Board of
Directors will determine the type of awards made to each participant and the
terms, conditions and limitations applicable to each award.
 
     The Company granted 644,097 stock options as of March 4, 1997. These
options were granted under the 1997 Incentive Plan established as part of the
Exchange (Note 1). These options have contractual lives of 7.3 years and have an
exercise price of $5.00 compared to the public offering price of $8.00. This
grant resulted in noncash compensation expense which is recognized over the
appropriate vesting period. None of these options were exercisable at December
31, 1997.
 
     As provided under SFAS 123, the Company estimates that the fair value of
these options on their grant date, using the Black-Scholes Option Pricing Model,
was $3.4 million ($5.32 per option). This valuation was determined using the
following assumptions: risk free interest rate of 6.24%; volatility factor of
the expected market prices of the Company's common stock of 38%; no expected
dividends; and weighted average option lives of 7.3 years. If this valuation
method were elected for accounting purposes, the estimated fair value of $3.4
million would be amortized over the appropriate vesting periods of the options
through 2003, resulting in a pro forma net loss for the year ended December 31,
1997 of $1.3 million, or $0.11 per common share.
 
                                      F-15
<PAGE>   107
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
12. RELATED PARTY TRANSACTIONS
 
     During the years ended December 31, 1995, 1996 and 1997, the Company paid
approximately $382,000, $596,000 and $837,000 respectively, in fees for land
acquisition services performed by a company owned by a brother of the Company's
President and Chief Executive Officer. Other participants in the Company's 3-D
seismic projects reimbursed the Company for a portion of these amounts.
 
     The Company also participated in various industry projects with affiliates
of the holder of the subordinated notes payable (see Note 5). During 1996 and
1997, the Company received approximately $123,000 and $50,000, respectively, for
workstation and geoscientists' time spent interpreting 3-D seismic data and
workstation use. In 1997, the Company paid approximately $214,000 for an
interest in an exploration project sold by the affiliates. The Company billed
the affiliates $197,000 in 1997 for their proportionate share of the costs
related to this and other projects in which the affiliates participate. The
Company also sold to an affiliate of the holders of the subordinated notes
payable an interest in (i) a 3-D project for approximately $75,000 in 1995 and
(ii) two 3-D delineated potential drilling locations and 3-D seismic data for
approximately $83,000 in 1996.
 
     In 1996 and 1997, the Company paid $110,000 and $18,000 for working
interests in natural gas and oil properties owned by affiliates of a member of
the Company's board of directors/management committee. The Company billed the
affiliates $13,000 and $68,000 in 1995 and 1996, respectively, for their
proportionate share of the costs related to this project.
 
     A limited partner and member of the Company's management committee served
as a consultant to the Company on various aspects of the Company's business and
strategic issues. Fees paid for these services by the Company were $72,000,
$79,200 and $86,580 for the twelve month periods ended December 31, 1995, 1996
and 1997, respectively. Additional disbursements totaling approximately $13,000
were made during 1997 for the reimbursement of certain expenses.
 
13. NATURAL GAS AND OIL EXPLORATION AND PRODUCTION ACTIVITIES
 
     The tables presented below provide supplemental information about natural
gas and oil exploration and production activities as defined by SFAS No. 69,
"Disclosures about Oil and Gas Producing Activities."
 
  Results of Operations for Natural Gas and Oil Producing Activities (in
thousands)
 
<TABLE>
<CAPTION>
                                                             YEAR ENDED DECEMBER 31,
                                                             ------------------------
                                                              1997     1996     1995
                                                             ------   ------   ------
<S>                                                          <C>      <C>      <C>
Natural gas and oil sales..................................  $9,184   $6,141   $3,578
Costs and expenses:
  Lease operating..........................................   1,151      726      761
  Production taxes.........................................     549      362      165
  Depletion of natural gas and oil properties..............   2,732    2,323    1,626
  Income taxes.............................................   1,322       --       --
                                                             ------   ------   ------
Total costs and expenses...................................   5,754    3,411    2,552
                                                             ------   ------   ------
                                                             $3,430   $2,730   $1,026
                                                             ======   ======   ======
Depletion per physical unit of production (equivalent Mcf
  of gas)..................................................  $ 0.87   $ 1.13   $ 1.22
                                                             ======   ======   ======
</TABLE>
 
     Natural gas and oil sales reflect the market prices of net production sold
or transferred, with appropriate adjustments for royalties, net profits interest
and other contractual provisions. Lease operating expenses include lifting costs
incurred to operate and maintain productive wells and related equipment,
including such costs as operating labor, repairs and maintenance, materials,
supplies and fuel consumed. Production taxes
 
                                      F-16
<PAGE>   108
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
include production and severance taxes. No provision was made for income taxes
for 1995 and 1996 since these taxes are the responsibility of the partners (see
Note 2). Depletion of natural gas and oil properties relates to capitalized
costs incurred in acquisition, exploration and development activities. Results
of operations do not include interest expense and general corporate amounts.
 
  Costs Incurred and Capitalized Costs
 
     The costs incurred in natural gas and oil acquisition, exploration and
development activities follow (in thousands):
 
<TABLE>
<CAPTION>
                                                                 DECEMBER 31,
                                                          ---------------------------
                                                           1997      1996      1995
                                                          -------   -------   -------
<S>                                                       <C>       <C>       <C>
Costs incurred for the year:
  Exploration...........................................  $29,421   $10,527   $ 6,893
  Property acquisition..................................   26,922     6,195     1,885
  Development...........................................    2,953     1,328       713
  Proceeds from participants............................     (319)   (4,111)   (1,296)
                                                          -------   -------   -------
                                                          $58,977   $13,939   $ 8,195
                                                          =======   =======   =======
</TABLE>
 
     Costs incurred represent amounts incurred by the Company for exploration,
property acquisition and development activities. Periodically, the Company will
receive proceeds from participants subsequent to project initiation for an
assignment of an interest in the project. These payments are represented by
proceeds from participants.
 
     Capitalized costs related to natural gas and oil acquisition, exploration
and development activities follow (in thousands):
 
<TABLE>
<CAPTION>
                                                                 DECEMBER 31,
                                                              ------------------
                                                                1997      1996
                                                              --------   -------
<S>                                                           <C>        <C>
Cost of natural gas and oil properties at year-end:
  Proved....................................................  $ 67,615   $30,487
  Unproved..................................................    28,843     7,068
                                                              --------   -------
  Total capitalized costs...................................    96,458    37,555
  Accumulated depletion.....................................   (12,282)   (9,550)
                                                              --------   -------
                                                              $ 84,176   $28,005
                                                              ========   =======
</TABLE>
 
     Following is a summary of costs (in thousands) excluded from depletion at
December 31, 1997, by year incurred. At this time, the Company is unable to
predict either the timing of the inclusion of these costs and the related
natural gas and oil reserves in its depletion computation or their potential
future impact on depletion rates.
 
<TABLE>
<CAPTION>
                                                 DECEMBER 31,
                                            -----------------------   PRIOR
                                             1997      1996    1995   YEARS     TOTAL
                                            -------   ------   ----   ------   -------
<S>                                         <C>       <C>      <C>    <C>      <C>
Property acquisition......................  $17,382   $2,515   $694   $1,852   $22,443
Exploration...............................    4,393    1,242    234      531     6,400
                                            -------   ------   ----   ------   -------
Total.....................................  $21,775   $3,757   $928   $2,383   $28,843
                                            =======   ======   ====   ======   =======
</TABLE>
 
                                      F-17
<PAGE>   109
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
14. NATURAL GAS AND OIL RESERVES AND RELATED FINANCIAL DATA (UNAUDITED)
 
     Information with respect to the Company's natural gas and oil producing
activities is presented in the following tables. Reserve quantities as well as
certain information regarding future production and discounted cash flows were
determined by the Company's independent petroleum consultants and internal
petroleum reservoir engineer.
 
  Natural Gas and Oil Reserve Data
 
     The following tables present the Company's estimates of its proved natural
gas and oil reserves. The Company emphasizes that reserve estimates are
approximates and are expected to change as additional information becomes
available. Reservoir engineering is a subjective process of estimating
underground accumulations of natural gas and oil that cannot be measured in an
exact way, and the accuracy of any reserve estimate is a function of the quality
of available data and of engineering and geological interpretation and judgment.
Accordingly, there can be no assurance that the reserves set forth herein will
ultimately be produced nor can there be assurance that the proved undeveloped
reserves will be developed within the periods anticipated. A substantial portion
of the reserve balances were estimated utilizing the volumetric method, as
opposed to the production performance method.
 
<TABLE>
<CAPTION>
                                                              NATURAL
                                                                GAS       OIL
                                                              (MMCF)    (MBBLS)
                                                              -------   -------
<S>                                                           <C>       <C>
Proved reserves at December 31, 1994........................   3,579     1,022
  Revisions to previous estimates...........................  (1,600)     (214)
  Extensions, discoveries and other additions...............   2,555     1,055
  Sales of minerals-in-place................................      (6)      (14)
  Production................................................    (271)     (177)
                                                              ------     -----
Proved reserves at December 31, 1995........................   4,257     1,672
  Revisions to previous estimates...........................  (1,005)     (232)
  Extensions, discoveries and other additions...............   7,742       996
  Purchase of minerals-in-place.............................     260         3
  Sales of minerals-in-place................................    (299)     (272)
  Production................................................    (698)     (227)
                                                              ------     -----
Proved reserves at December 31, 1996........................  10,257     1,940
  Revisions of previous estimates...........................  (3,044)     (447)
  Extensions, discoveries and other additions...............  33,721       735
  Purchase of minerals-in-place.............................  13,718     1,244
  Sales of minerals-in-place................................     (40)       --
  Production................................................  (1,382)     (291)
                                                              ------     -----
Proved reserves at December 31, 1997........................  53,230     3,181
                                                              ======     =====
Proved developed reserves at December 31:
  1995......................................................   3,819     1,274
  1996......................................................   6,034     1,453
  1997......................................................  30,677     2,665
</TABLE>
 
     Proved reserves are estimated quantities of crude natural gas and oil which
geological and engineering data indicate with reasonable certainty to be
recoverable in future years from known reservoirs under existing economic and
operating conditions. Proved developed reserves are proved reserves which can be
expected to be recovered through existing wells with existing equipment and
operating methods.
 
                                      F-18
<PAGE>   110
                          BRIGHAM EXPLORATION COMPANY
 
         NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
  Standardized Measure of Discounted Future Net Cash Inflows and Changes Therein
 
     The following table presents a standardized measure of discounted future
net cash inflows (in thousands) relating to proved natural gas and oil reserves.
Future cash flows were computed by applying year end prices of natural gas and
oil relating to the Company's proved reserves to the estimated year-end
quantities of those reserves. Future price changes were considered only to the
extent provided by contractual agreements in existence at year-end. Future
production and development costs were computed by estimating those expenditures
expected to occur in developing and producing the proved natural gas and oil
reserves at the end of the year, based on year-end costs. Actual future cash
inflows may vary considerably and the standardized measure does not necessarily
represent the fair value of the Company's natural gas and oil reserves.
 
<TABLE>
<CAPTION>
                                                                DECEMBER 31,
                                                       ------------------------------
                                                         1997       1996       1995
                                                       --------   --------   --------
<S>                                                    <C>        <C>        <C>
Future cash inflows..................................  $165,156   $ 84,987   $ 38,333
Future development and production costs..............   (40,923)   (20,998)   (12,543)
Future income taxes..................................   (22,919)        --         --
                                                       --------   --------   --------
Future net cash inflows..............................  $101,314   $ 63,989   $ 25,790
                                                       ========   ========   ========
Future net cash inflow before income taxes,
  discounted at 10% per annum........................  $ 69,249   $ 44,506   $ 18,222
                                                       ========   ========   ========
Standardized measure of future net cash inflows
  discounted at 10% per annum........................  $ 64,274   $ 44,506   $ 18,222
                                                       ========   ========   ========
</TABLE>
 
     The average natural gas and oil prices used to calculate the future net
cash inflows at December 31, 1997 were $16.64 per barrel and $2.11 per Mcf,
respectively. At December 31, 1997, the NYMEX price for natural gas was $2.26
per MMBtu and the NYMEX price for oil was $17.64 per barrel. From January 1,
1998 to March 24, 1997, the NYMEX price for natural gas ranged from $2.00 per
MMBtu to $2.38 per MMBtu and the NYMEX price for oil ranged from $13.21 per
barrel to $17.82 per barrel.
 
     Changes in the future net cash inflows discounted at 10% per annum follow:
 
<TABLE>
<CAPTION>
                                                                 DECEMBER 31,
                                                         ----------------------------
                                                           1997      1996      1995
                                                         --------   -------   -------
<S>                                                      <C>        <C>       <C>
Beginning of period....................................  $ 44,506   $18,222   $10,240
  Sales of natural gas and oil produced, net of
     production costs..................................    (7,484)   (5,053)   (2,652)
  Development costs incurred...........................     1,955       246       169
  Extensions and discoveries...........................    38,016    29,457    11,669
  Purchases of minerals-in-place.......................    16,965       384        --
  Sales of minerals-in-place...........................       (94)   (2,380)     (198)
  Net change of prices and production costs............   (20,466)    7,023     1,394
  Change in future development costs...................       319       303       419
  Changes in production rates and other................    (1,954)     (342)     (364)
  Revisions of quantity estimates......................    (6,964)   (5,176)   (3,479)
  Accretion of discount................................     4,450     1,822     1,024
  Change in income taxes...............................    (4,975)       --        --
                                                         --------   -------   -------
End of period..........................................  $ 64,274   $44,506   $18,222
                                                         ========   =======   =======
</TABLE>
 
                                      F-19
<PAGE>   111
 
                          BRIGHAM EXPLORATION COMPANY
 
                             CONDENSED CONSOLIDATED
                                 BALANCE SHEETS
                                 (IN THOUSANDS)
 
                                     ASSETS
 
   
<TABLE>
<CAPTION>
                                                              DECEMBER 31,    JUNE 30,
                                                                  1997          1998
                                                              ------------   -----------
                                                                             (UNAUDITED)
<S>                                                           <C>            <C>
Current assets:
  Cash and cash equivalents.................................    $ 1,701       $  3,106
  Accounts receivable.......................................      4,909          7,934
  Prepaid expenses..........................................        280            217
                                                                -------       --------
          Total current assets..............................      6,890         11,257
                                                                -------       --------
Natural gas and oil properties, at cost, net................     84,176        114,454
Other property and equipment, at cost, net..................      1,239          1,603
Drilling advances paid......................................         78            603
Deferred loan fees..........................................         --          1,645
Other noncurrent assets.....................................         18            137
                                                                -------       --------
                                                                $92,401       $129,699
                                                                =======       ========
 
                          LIABILITIES AND STOCKHOLDERS' EQUITY
 
Current liabilities:
  Accounts payable..........................................    $11,892       $  7,837
  Accrued drilling costs....................................      2,406          5,206
  Participant advances received.............................        489            442
  Other current liabilities.................................        726          4,748
                                                                -------       --------
          Total current liabilities.........................     15,513         18,233
                                                                -------       --------
Notes payable...............................................     32,000         68,000
Other noncurrent liabilities................................        507            526
Deferred income tax liability...............................      1,228            606
Stockholders' equity:
  Preferred stock, $.01 par value, 10 million shares
     authorized, none issued and outstanding................         --             --
  Common stock, $.01 par value, 30 million shares
     authorized, 12,253,574 issued and outstanding..........        123            123
  Additional paid-in capital................................     44,344         44,292
  Unearned stock compensation...............................     (1,340)          (880)
  Retained earnings (accumulated deficit)...................         26         (1,201)
                                                                -------       --------
          Total stockholders' equity........................     43,153         42,334
                                                                -------       --------
                                                                $92,401       $129,699
                                                                =======       ========
</TABLE>
    
 
   See accompanying notes to the condensed consolidated financial statements.
 
                                      F-20
<PAGE>   112
 
                          BRIGHAM EXPLORATION COMPANY
 
                             CONDENSED CONSOLIDATED
                            STATEMENTS OF OPERATIONS
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)
                                  (UNAUDITED)
 
   
<TABLE>
<CAPTION>
                                                                 SIX MONTHS
                                                               ENDED JUNE 30,
                                                              -----------------
                                                               1997      1998
                                                              -------   -------
<S>                                                           <C>       <C>
Revenues:
  Natural gas and oil sales.................................  $ 3,854   $ 7,130
  Workstation revenue.......................................      324       247
                                                              -------   -------
                                                                4,178     7,377
                                                              -------   -------
Costs and expenses:
  Lease operating...........................................      470       978
  Production taxes..........................................      219       450
  General and administrative................................    1,455     2,293
  Depletion of natural gas and oil properties...............    1,395     2,784
  Depreciation and amortization.............................      172       175
  Amortization of stock compensation........................      115       190
                                                              -------   -------
                                                                3,826     6,870
                                                              -------   -------
     Operating income.......................................      352       507
                                                              -------   -------
Other income (expense):
  Interest income...........................................       81        77
  Interest expense..........................................     (372)   (2,432)
  Interest expense -- related party.........................     (174)       --
                                                              -------   -------
                                                                 (465)   (2,355)
                                                              -------   -------
Net loss before income taxes................................     (113)   (1,848)
Income tax (expense) benefit................................   (4,813)      621
                                                              -------   -------
  Net loss..................................................  $(4,926)  $(1,227)
                                                              =======   =======
Net loss per share:
  Basic/Diluted.............................................  $ (0.50)  $ (0.10)
Weighted average common shares outstanding:
  Basic/Diluted.............................................    9,890    12,254
</TABLE>
    
 
   See accompanying notes to the condensed consolidated financial statements.
 
                                      F-21
<PAGE>   113
 
                          BRIGHAM EXPLORATION COMPANY
 
                             CONDENSED CONSOLIDATED
                            STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
                                  (UNAUDITED)
 
   
<TABLE>
<CAPTION>
                                                                  SIX MONTHS
                                                                ENDED JUNE 30,
                                                              -------------------
                                                                1997       1998
                                                              --------   --------
<S>                                                           <C>        <C>
Cash flows from operating activities:
  Net loss..................................................  $ (4,926)  $ (1,227)
  Adjustments to reconcile net loss to cash provided by
     operating activities:
     Depletion of natural gas and oil properties............     1,395      2,784
     Depreciation and amortization..........................       172        175
     Amortization of stock compensation.....................       115        190
     Amortization of deferred loan fees.....................        --        266
     Changes in deferred income tax liability...............     4,813       (622)
     Changes in working capital and other items.............    (1,764)    (3,258)
                                                              --------   --------
          Net cash used by operating activities.............      (195)    (1,692)
                                                              --------   --------
Cash flows from investing activities:
  Additions to natural gas and oil properties...............   (11,796)   (30,044)
  Additions to other property and equipment.................      (183)      (315)
  Increase in drilling advances paid........................      (126)      (525)
                                                              --------   --------
       Net cash used by investing activities................   (12,105)   (30,884)
                                                              --------   --------
Cash flows from financing activities:
  Proceeds from issuance of common stock....................    23,929         --
  Increase in notes payable.................................     5,250     70,800
  Repayment of notes payable................................   (13,250)   (34,800)
  Principal payments on capital lease obligations...........       (87)      (108)
  Deferred loan fees........................................        --     (1,911)
                                                              --------   --------
       Net cash provided by financing activities............    15,842     33,981
                                                              --------   --------
Net increase in cash and cash equivalents...................     3,542      1,405
Cash and cash equivalents, beginning of period..............     1,447      1,701
                                                              --------   --------
Cash and cash equivalents, end of period....................  $  4,989   $  3,106
                                                              ========   ========
</TABLE>
    
 
   See accompanying notes to the condensed consolidated financial statements.
 
                                      F-22
<PAGE>   114
 
                          BRIGHAM EXPLORATION COMPANY
 
                      NOTES TO THE CONDENSED CONSOLIDATED
                              FINANCIAL STATEMENTS
                                  (UNAUDITED)
 
1. ORGANIZATION AND NATURE OF OPERATIONS
 
   
     Brigham Exploration Company (the "Company") is a Delaware corporation
formed on February 25, 1997 for the purpose of exchanging its common stock for
the common stock of Brigham, Inc. and the partnership interests of Brigham Oil &
Gas, L.P. (the "Partnership"). Brigham, Inc. is a Texas corporation whose only
asset is its ownership interest in the Partnership. The Partnership was formed
in May 1992 to explore and develop onshore domestic natural gas and oil
properties using 3-D seismic imaging and other advanced technologies. Since its
inception, the Partnership has focused its exploration and development of
natural gas and oil properties in West Texas, the Anadarko Basin and the onshore
Gulf Coast.
    
 
   
     Pursuant to an exchange agreement dated February 26, 1997 (the "Exchange
Agreement") and upon the initial filing on February 27, 1997 of a registration
statement with the Securities and Exchange Commission for the public offering of
common stock (the "Offering"), the shareholders of Brigham, Inc. transferred all
of the outstanding stock of Brigham, Inc. to the Company in exchange for
3,859,821 shares of common stock of the Company. Pursuant to the Exchange
Agreement, the Partnership's other general partner and the limited partners also
transferred all of their partnership interests to the Company in exchange for
3,314,286 shares of common stock of the Company. Furthermore, the holders of the
Partnership's subordinated convertible notes transferred these notes to the
Company in exchange for 1,754,464 shares of common stock. These transactions are
referred to as the "Exchange." In completing the Exchange, the Company issued
8,928,571 shares of common stock to the stockholders of Brigham, Inc., the
partners of the Partnership and the holder of the Partnership's subordinated
notes payable. As a result of the Exchange, the Company now owns all the
partnership interests in the Partnership.
    
 
   
     In May 1997, the Company sold 3,325,000 shares of its common stock in the
Offering at a price of $8.00 per share. With a portion of the proceeds from the
Offering, the Company repaid the then outstanding borrowings ($13.3 million)
under the Company's revolving credit facility.
    
 
   
2. BASIS OF PRESENTATION
    
 
   
     The unaudited condensed consolidated balance sheets at December 31, 1997
and June 30, 1998 reflect the consolidated accounts of the Company. The
unaudited condensed consolidated statements of operations and of cash flows for
the six months ended June 30, 1997 and 1998 include the results of operations
and of cash flows of the Partnership for the period from January 1, 1997 to
February 27, 1997 and of the Company for the period from February 25, 1997, the
date of its inception, to June 30, 1997 and for the six months ended June 30,
1998. As the Exchange was the conversion of a partnership to a corporation, the
Exchange was accounted for by the Company as a reorganization.
    
 
   
     The accompanying condensed consolidated financial statements are unaudited,
and in the opinion of management, reflect all adjustments that are necessary for
a fair presentation of the financial position and results of operations for the
periods presented. All such adjustments are of a normal and recurring nature.
The results of operations for the periods presented are not necessarily
indicative of the results to be expected for the entire year. The unaudited
condensed consolidated financial statements should be read in conjunction with
the Company's 1997 Annual Report on Form 10-K pursuant to Section 13 or 15(d) of
the Securities Exchange Act of 1934.
    
 
   
3. NOTES PAYABLE
    
 
   
     In January 1998, the Company entered into a reserve based revolving credit
facility (the "Credit Facility"). The Credit Facility provides for borrowings up
to $75 million, all of which was immediately available for borrowing to fund
capital expenditures, until January 31, 1999, at which time the borrowing
    
 
                                      F-23
<PAGE>   115
                          BRIGHAM EXPLORATION COMPANY
 
                      NOTES TO THE CONDENSED CONSOLIDATED
                      FINANCIAL STATEMENTS -- (CONTINUED)
 
   
availability will be redetermined by the lender based on the Company's proved
reserve value at that time. The Company may elect, at its option, to have the
borrowing availability redetermined based on the Company's proved reserve value
at any time prior to January 31, 1999. Amounts outstanding under the Credit
Facility bear interest at either the lender's Base Rate or LIBOR plus 2.25%, at
the Company's option. The Company's obligations under the Credit Facility are
secured by substantially all of the natural gas and oil properties of the
Company. A portion of the funds borrowed under the Credit Facility were used to
repay in full the debt outstanding under the Company's previous revolving credit
facility.
    
 
   
     In connection with the origination of the Credit Facility, certain bank
fees and other expenses totaling approximately $1.9 million were recorded as
deferred costs and will be amortized over the life of the loan which matures
January 26, 2001.
    
 
   
4. INCOME TAXES
    
 
   
     Prior to the consummation of the Exchange, the Partnership was not subject
to federal income taxes. Income and losses were passed through to its partners
on the basis of the allocation provisions established by the partnership
agreement. Upon consummation of the Exchange, the Partnership's net income
became subject to federal income taxes through its ownership by the Company.
Also, in conjunction with the Exchange, the Company recorded a deferred income
tax liability of $5 million to recognize the temporary differences between the
financial statement and tax bases of the assets and liabilities of the
Partnership at the Exchange date, February 27, 1997, given the provisions of
enacted tax laws. Subsequent to this date, the Company elected to record a
step-up in basis of its assets for tax purposes as a result of the Exchange. As
a result of this election, the Company recorded a $3.8 million deferred income
tax benefit in the fourth quarter of 1997, which resulted in a net $1.2 million
non-cash deferred income tax charge for the year ended December 31, 1997.
    
 
   
5. EARNINGS PER SHARE
    
 
   
     Earnings per share have been calculated in accordance with the provisions
of Statement of Financial Accounting Standards ("SFAS") No. 128. The
implementation of this standard has resulted in the presentation of a basic EPS
calculation in the consolidated financial statements as well as a diluted EPS
calculation. Basic EPS is computed by dividing net income (loss) applicable to
common shareholders by the weighted average number of common shares outstanding
during each period. Diluted EPS is computed by dividing net income (loss)
applicable to common shareholders by the weighted average number of common
shares and common share equivalents outstanding, if dilutive, during each
period. The number of common share equivalents outstanding is computed using the
treasury stock method.
    
 
   
     Historical earnings per share for the six months ended June 30, 1997 is
based on shares of common stock issued upon consummation of the Exchange (Note
1). At June 30, 1997 and 1998, options to purchase 644,097 and 935,987,
respectively, shares of common stock were outstanding but were not included in
the computation of diluted EPS due to the anti-dilutive effect they would have
on EPS if converted.
    
 
   
6. REPORTING COMPREHENSIVE INCOME
    
 
   
     In June 1997, the Financial Accounting Standards Board ("FASB") issued SFAS
No. 130, "Reporting Comprehensive Income." The new standard, which is effective
for financial statements issued for periods ending after December 15, 1997,
established standards for reporting, in addition to net income, comprehensive
income and its components including, as applicable, foreign currency items,
minimum pension liability adjustments and unrealized gains and losses on certain
investments in debt and equity securities. Upon adoption, the Company is also
required to reclassify financial statements for earlier periods provided for
    
 
                                      F-24
<PAGE>   116
                          BRIGHAM EXPLORATION COMPANY
 
                      NOTES TO THE CONDENSED CONSOLIDATED
                      FINANCIAL STATEMENTS -- (CONTINUED)
 
   
comparative purposes. The Company adopted this standard in the first quarter of
1998. There is no difference between the Company's net income as reported and
comprehensive income.
    
 
   
7. SEGMENT REPORTING
    
 
   
     In June 1997, the FASB issued SFAS No. 131, "Disclosure about Segments of
an Enterprise and Related Information," which the Company adopted in the first
quarter of 1998. The standard established requirements for reporting information
about operating segments in interim financial reports issued to shareholders. It
also established standards for related disclosures about products and services,
geographic areas and major customers. Under SFAS No. 131, operating segments are
to be determined consistent with management's organization and evaluation of
financial information internally for making operating decisions and assessing
performance. The disclosure provisions of this standard are not applicable for
interim periods in the year of adoption. The adoption of this new standard is
not expected to have a material impact on the Company's consolidated balance
sheet or statement of operations.
    
 
   
8. ACCOUNTING FOR DERIVATIVE INSTRUMENTS AND HEDGING ACTIVITIES
    
 
   
     In June, 1998, the FASB issued SFAS No. 133, "Accounting for Derivative
Instruments and Hedging Activities." The new standard is effective for fiscal
years beginning after June 15, 1999, but earlier application is permitted. SFAS
No. 133 requires that all derivatives be recognized on the balance sheet as
either assets or liabilities and measured at fair value regardless of any hedge
relationship that exists. The corresponding gains and losses should be reported
based on the hedge relationship that exists. The adoption of this new standard
is not expected to have a material impact on the Company's consolidated balance
sheet or statement of operations.
    
 
                                      F-25
<PAGE>   117
 
                                  May 26, 1998
 
Brigham Exploration Company
6300 Bridge Point Parkway
Building Two, Suite 500
Austin, Texas 78730
 
Re:     Evaluation
       BRIGHAM EXPLORATION COMPANY
       Proved Reserves
       As of December 31, 1997
 
       Pursuant to the Guidelines of the Securities
       and Exchange Commission for Reporting
       Corporate Reserves and Future Net Revenue
 
Gentlemen:
 
     As requested, we are submitting our estimated proven reserves and future
net cash flows, as of December 31, 1997, attributable to the interest of Brigham
Exploration Company in certain natural gas and oil properties. The evaluated
properties are located in various counties in Kansas, New Mexico, Oklahoma and
Texas. This report was prepared using constant prices and costs and conforms to
the guidelines of the Securities and Exchange Commission (SEC).
 
     Composite forecasts for the total proved, proved developed producing,
proved developed non-producing and proved undeveloped estimates are presented by
category in Tables I-P, I-PDP, I-PDNP and I-PUD, respectively. The proved
reserves and economics for all three groups are summarized as follows:
 
<TABLE>
<CAPTION>
                                         NET RESERVES             FUTURE NET CASH FLOW
                                    -----------------------   ----------------------------
                                       OIL          GAS                      PRESENT WORTH
CATEGORY                            (BARRELS)      (MCF)         TOTAL          AT 10%
--------                            ---------   -----------   ------------   -------------
<S>                                 <C>         <C>           <C>            <C>
Proved Developed:
  Producing......................   2,146,422    26,002,050   $ 67,895,820    $44,240,260
  Non-Producing..................     518,606     4,674,717     14,544,070      3,980,896
Proved Undeveloped...............     516,290    22,552,930     41,783,310     21,028,250
                                    ---------   -----------   ------------    -----------
     Total Proved................   3,181,318    53,229,700   $124,233,200    $69,249,406
                                    =========   ===========   ============    ===========
</TABLE>
 
     Future revenue is prior to deducting state production taxes and ad valorem
taxes. Future net cash flow is after deducting these taxes, future capital costs
and operating expenses, but before consideration of federal income taxes. In
accordance with SEC guidelines, the future net cash flow has been discounted at
an annual rate of ten percent to determine its "present worth". The present
worth is shown to indicate the effect of time on the value of money and should
not be construed as being the fair market value of the properties.
 
     The oil reserves include oil and condensate. Oil volumes are expressed in
barrels (42 U.S. gallons). Gas volumes are expressed in thousands of standard
cubic feet (Mcf) at contract temperature and pressure base.
 
     Our estimates are for proved reserves only and do not include any probable
or possible reserves nor have any values been attributed to interest in acreage
beyond the location for which undeveloped reserves have been estimated.
 
     Oil and gas prices being received at December 31, 1997 were utilized as
furnished. Direct lease operating expenses are based on 1996 and 1997 historical
data and do not include general and administrative overhead. Investments are
capital costs for pumping unit installations, work-overs and drilling costs and
were utilized as furnished. All economic factors were held constant in
accordance with SEC guidelines.
 
     An on-site field inspection of the properties has not been performed nor
have the mechanical operation or condition of the wells and their related
facilities been examined nor have the wells been tested by Cawley, Gillespie &
Associates, Inc. Possible environmental liability related to the properties has
not been investigated
 
                                       A-1
<PAGE>   118
 
nor considered. The cost of plugging and the salvage value of equipment at
abandonment have not been included.
 
     The reserve classifications and the economic considerations used herein
conform to the criteria of the Securities and Exchange Commission. The reserves
and economics are predicated on regulatory agency classifications, rules,
policies, laws, taxes and royalties currently in effect except as noted herein.
The possible effects of changes in legislation or other Federal or State
restrictive actions which could affect the reserves and economics have not been
considered.
 
     The proved reserve estimates and forecasts were based upon interpretations
of data furnished by your office and available from our files. All estimates
represent our best judgment based on the data available at the time of
preparation. It should be realized that the reserve estimates, the reserves
actually recovered, the revenue derived therefrom and the actual cost incurred
could be more or less than the estimated amounts. Additionally, the prices and
costs may vary from those utilized which may increase or decrease both the
volume and future net revenue.
 
     Ownership was accepted as furnished and has not been independently
confirmed. We are independent registered professional engineers and geologists.
We do not own an interest in the properties or Brigham Exploration Company and
are not employed on a contingent basis. Our work-papers and related data
utilized in the preparation of these estimates are available in our office.
 
                                            Yours very truly,
 
                                            Cawley, Gillespie & Associates, Inc.
 
                                                    /s/ AARON CAWLEY
 
                                            ------------------------------------
                                                     Aaron Cawley, P.E.
                                                  Executive Vice President
AC:rkf
 
                                       A-2
<PAGE>   119
 
------------------------------------------------------
------------------------------------------------------
 
   
    NO DEALER, SALESPERSON OR OTHER PERSON HAS BEEN AUTHORIZED TO GIVE ANY
INFORMATION OR TO MAKE ANY REPRESENTATIONS OTHER THAN THOSE CONTAINED IN THIS
PROSPECTUS IN CONNECTION WITH THE OFFER MADE BY THIS PROSPECTUS AND, IF GIVEN OR
MADE, SUCH INFORMATION OR REPRESENTATIONS MUST NOT BE RELIED UPON AS HAVING BEEN
AUTHORIZED BY THE COMPANY. THIS PROSPECTUS DOES NOT CONSTITUTE AN OFFER TO SELL
OR THE SOLICITATION OF ANY OFFER TO BUY ANY SECURITIES OTHER THAN THE NOTES,
WARRANTS AND SHARES OFFERED BY THIS PROSPECTUS, NOR DOES IT CONSTITUTE AN OFFER
TO SELL OR A SOLICITATION OF ANY OFFER TO BUY THE NOTES, WARRANTS AND SHARES BY
ANYONE IN ANY JURISDICTION IN WHICH SUCH OFFER OR SOLICITATION IS NOT
AUTHORIZED, OR IN WHICH THE PERSON MAKING SUCH OFFER OR SOLICITATION IS NOT
QUALIFIED TO DO SO, OR TO ANY PERSON TO WHOM IT IS UNLAWFUL TO MAKE SUCH OFFER
OR SOLICITATION. NEITHER THE DELIVERY OF THIS PROSPECTUS NOR ANY SALE MADE
HEREUNDER SHALL, UNDER ANY CIRCUMSTANCES, CREATE ANY IMPLICATION THAT THE
INFORMATION CONTAINED HEREIN IS CORRECT AS OF ANY TIME SUBSEQUENT TO THE DATE
HEREOF.
    
 
                             ---------------------
 
                               TABLE OF CONTENTS
 
   
<TABLE>
<CAPTION>
                                            PAGE
                                            ----
<S>                                         <C>
Prospectus Summary........................    3
Disclosure Regarding Forward-Looking
  Statements..............................   14
Risk Factors..............................   14
The Company...............................   23
Use of Proceeds...........................   24
Price Range of Common Stock and Dividend
  Policy..................................   24
Capitalization............................   25
Selected Financial Data...................   26
Management's Discussion and Analysis of
  Financial Condition and Results of
  Operations..............................   28
Business and Properties...................   36
Management................................   53
Certain Transactions......................   60
Principal Stockholders....................   62
Description of Other Indebtedness.........   63
Description of Notes......................   64
Subordination Agreement...................   80
Description of Warrants...................   82
Description of Capital Stock..............   84
Registration Rights Relating to the
  Warrants and Shares.....................   85
Shares Eligible for Future Sale...........   86
Plan of Distribution......................   87
Legal Matters.............................   87
Experts...................................   87
Available Information.....................   87
Glossary of Certain Oil and Gas Terms.....   89
Index to Financial Statements.............  F-1
Letter of Cawley, Gillespie & Associates,
  Inc.....................................  A-1
</TABLE>
    
 
                             ---------------------
   
    UNTIL         , 1998 (25 DAYS AFTER THE DATE OF THIS PROSPECTUS), ALL
DEALERS EFFECTING TRANSACTIONS IN THE NOTES, WARRANTS AND SHARES, WHETHER OR NOT
PARTICIPATING IN THIS DISTRIBUTION, MAY BE REQUIRED TO DELIVER A PROSPECTUS.
THIS IS IN ADDITION TO THE OBLIGATION OF DEALERS TO DELIVER A PROSPECTUS WHEN
ACTING AS UNDERWRITERS AND WITH RESPECT TO THEIR UNSOLD ALLOTMENTS OR
SUBSCRIPTIONS.
    
------------------------------------------------------
------------------------------------------------------
------------------------------------------------------
------------------------------------------------------
 
   
                                  $40,000,000
    
   
                          SENIOR SUBORDINATED SECURED
    
   
                                 NOTES DUE 2003
    
 
   
                              WARRANTS TO PURCHASE
    
   
                        1,000,000 SHARES OF COMMON STOCK
    
 
   
                                     SHARES OF COMMON STOCK
    
   
                          BRIGHAM EXPLORATION COMPANY
    
 
                                ----------------
 
                                   PROSPECTUS
                                ----------------
                                            , 1998
 
------------------------------------------------------
------------------------------------------------------
<PAGE>   120
 
                                    PART II
 
                     INFORMATION NOT REQUIRED IN PROSPECTUS
 
ITEM 13. OTHER EXPENSES OF ISSUANCE AND DISTRIBUTION
 
     The estimated expenses payable by Brigham Exploration Company (the
"Registrant" or the "Company") in connection with the registration of the
securities offered hereby, other than underwriting discounts and commissions,
are as follows:
 
   
<TABLE>
<S>                                                           <C>
SEC Registration Fee........................................  $ 17,700
NASD Filing Fee.............................................     5,100
Nasdaq National Market Listing Fee..........................    17,500
Accounting Fees and Expenses................................    35,000
Legal Fees and Expenses.....................................   125,000
Engineering Fees and Expenses...............................        --
Transfer Agent and Registrar Fees...........................     1,500
Printing and Engraving Expenses.............................    85,000
Miscellaneous...............................................    63,200
                                                              --------
          Total.............................................  $350,000
                                                              ========
</TABLE>
    
 
---------------
 
* To be provided by amendment.
 
ITEM 14. INDEMNIFICATION OF DIRECTORS AND OFFICERS
 
     In accordance with Section 102(b)(7) of the Delaware General Corporation
Law ("DGCL"), the Company's Certificate of Incorporation includes a provision
that, to the fullest extent permitted by law, eliminates the personal liability
of members of its Board of Directors to the Company or its stockholders for
monetary damages for breach of fiduciary duty as a director. Such provision does
not eliminate or limit the liability of a director (1) for any breach of a
director's duty of loyalty to the Company or its stockholders, (2) for acts or
omissions not in good faith or which involve intentional misconduct or a knowing
violation of a law, (3) for paying an unlawful dividend or approving an illegal
stock repurchase (as provided in Section 174 of the DGCL) or (4) for any
transaction from which the director derived an improper personal benefit.
 
     Under Section 145 of the DGCL, the Registrant has the power to indemnify
any person who was or is a party or is threatened to be made a party to any
threatened, pending or completed action, suit or proceeding (other than an
action by or in the right of the corporation) by reason of the fact that the
person is or was a director, officer, employee or agent of any corporation,
partnership, joint venture, trust or other enterprise, reasonably incurred in
connection with such action, suit or proceeding. The power to indemnify applies
only if the person acted in good faith and in a manner the person reasonably
believed to be in or not opposed to the best interests of the corporation, and
with respect to any criminal action or proceeding, had no reasonable cause to
believe the person's conduct was unlawful.
 
     In the case of an action by or in the right of the Registrant, no
indemnification may be made with respect to any claim, issue or matter as to
which such person shall have been adjudged to be liable to the Registrant unless
and only to the extent that the court of chancery or the court in which such
action or suit was brought shall determine that despite the adjudication of
liability such person is fairly and reasonably entitled to indemnity for such
expenses which the court shall deem proper. Section 145 of the DGCL further
provides that to the extent a director or officer of the Registrant has been
successful in the defense of any action, suit or proceeding referred to above or
in the defense of any claim, issue or matter therein, that person shall be
indemnified against expenses (including attorney's fees) actually and reasonably
incurred in connection therewith.
 
     The Registrant also has the power to purchase and maintain insurance on
behalf of any person covering any liability incurred in that person's capacity
as a director, officer, employee or agent of the corporation, or
 
                                      II-1
<PAGE>   121
 
arising out of that person's status as such, whether or not the corporation
would have the power to indemnify against the liability.
 
     The Certificate of Incorporation and Bylaws provide that the Registrant
will indemnify its officers and directors and former officers and directors
against any expenses, judgments or settlement payments sustained or paid by such
persons as a result of having acted as an officer or director of the Registrant,
or, at the request of the Registrant, as an officer, director, agent or employee
of another business entity. The Certificate of Incorporation and Bylaws further
provide that the Registrant may, by action of its Board of Directors, provide
indemnification to employees and agents of the Registrant, individually or as a
group, with the same scope and effect as the indemnification of directors and
officers.
 
     The form of Indemnity Agreement contained in Exhibit 10.23 provides for the
indemnification in certain instances against liability and expenses incurred in
connection with proceedings brought by or in the right of the Company or by
third parties by reason of a person serving as an officer or director of the
Company.
 
   
ITEM 15. RECENT SALES OF UNREGISTERED SECURITIES
    
 
   
     The following information relates to all securities issued or sold by the
Registrant since inception and not registered under the Securities Act of 1933
(the "Securities Act").
    
 
     Unless otherwise specifically provided, each of the transactions described
below was conducted in reliance upon the exemption from registration provided in
Section 4(2) of the Securities Act and the rules and regulations promulgated
thereunder. Furthermore, each of the certificates representing the Registrant's
securities issued in connection with such transactions contains a restrictive
legend, as appropriate, requiring each person acquiring such securities from the
Registrant to furnish investment representations to the Registrant and stating
that no underwriters participated in such transactions.
 
     The Registrant was formed on February 25, 1997. On February 26, 1997, the
Company sold three shares of the Registrant's Common Stock to Ben M. Brigham,
President of the Company. Pursuant to the terms of an Agreement and Plan of
Reorganization dated February 26, 1997 (the "Exchange Agreement") the Company
became the holding company for Brigham Oil & Gas, L.P., which conducts the
Registrant's operations and was formed in May 1992 (the "Partnership"). Pursuant
to the terms of the Exchange Agreement, the limited partners of the Partnership
received 634,868 shares of the Registrant's common stock. In addition, the
general partners or their stockholders received 6,539,239 shares of the
Registrant's common stock for each share of common stock of the general partner
owned by such stockholder. Each certificate issued in connection with such
exchange contained an appropriate restrictive legend.
 
     In August 1995, the Registrant issued $16 million principal amount of its
5% convertible subordinated notes (the "Notes") to Resource Investment
Management Company. Immediately after the consummation of the exchange described
above, RIMCO converted the Notes into 1,759,464 shares of the Registrant's
common stock. Each certificate issued in connection with that conversion
contained an appropriate restrictive legend.
 
     The Registrant and its predecessor have granted options that remain
outstanding to purchase an aggregate of 935,987 shares of Common Stock, subject
to vesting, and issued 156,250 shares of restricted stock to officers and key
employees.
 
                                      II-2
<PAGE>   122
 
ITEM 16. EXHIBITS AND FINANCIAL STATEMENT SCHEDULES
 
     (a) Exhibits:
 
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         2.1             -- Exchange Agreement (filed as Exhibit 2.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         3.1             -- Certificate of Incorporation (filed as Exhibit 3.1 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         3.2             -- Bylaws (filed as Exhibit 3.2 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         4.1             -- Form of Common Stock Certificate (filed as Exhibit 4.1 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         4.2+            -- Form of Indenture
         4.3+            -- Form of Warrant Certificate
         4.4+            -- Form of Senior Subordinated Secured Note due 2003
         4.5+            -- Form of Registration Rights Agreement
         5+              -- Opinion of Thompson & Knight, A Professional Corporation
        10.1             -- Agreement of Limited Partnership of Venture Acquisitions,
                            L.P., dated September 23, 1994, by and between Quest
                            Resources, L.L.C. and RIMCO Energy, Inc. as general
                            partners, and RIMCO Production Company, Inc., RIMCO
                            Exploration Partners, L.P. I and RIMCO Exploration
                            Partners, L.P. II, as limited partners (filed as Exhibit
                            10.2 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.2             -- Regulations of Quest Resources, L.L.C. (filed as Exhibit
                            10.3 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.3             -- Management and Ownership Agreement, dated September 23,
                            1994, by and among Brigham Oil & Gas, L.P., Brigham
                            Exploration Company, General Atlantic Partners III, L.P.,
                            Harold D. Carter, Ben M. Brigham and GAP-Brigham
                            Partners, L.P. (filed as Exhibit 10.4 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.4*++          -- Consulting Agreement, dated May 1, 1997, by and between
                            Brigham Oil & Gas, L.P. and Harold D. Carter.
        10.5*            -- Employment Agreement, by and between Brigham Exploration
                            Company and Ben M. Brigham (filed as Exhibit 10.7 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.6*            -- Form of Confidentiality and Noncompete Agreement between
                            the Registrant and each of its executive officers (filed
                            as Exhibit 10.8 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.7*            -- 1997 Incentive Plan of Brigham Exploration Company (filed
                            as Exhibit 10.9 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
</TABLE>
    
 
                                      II-3
<PAGE>   123
 
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.7.1*          -- Form of Option Agreement for certain executive officers
                            (filed as Exhibit 10.9.1 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.7.2*          -- Option Agreement dated as of March 4, 1997, by and
                            between Brigham Exploration Company and Jon L. Glass
                            (filed as Exhibit 10.9.2 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.8*            -- Incentive Bonus Plan dated as of February 28, 1997 of
                            Brigham, Inc. and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.10 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.9.1++         -- First Amendment to Two Bridge Point Lease Agreement dated
                            April 11, 1997 between Investors Life Insurance Company
                            of North America and Brigham Oil & Gas, L.P.
        10.9.2++         -- Second Amendment to Two Bridge Point Lease Agreement
                            dated October 13, 1997 between Investors Life Insurance
                            Company of North America and Brigham Oil & Gas, L.P.
        10.9.3++         -- Letter dated April 17, 1998 exercising Right of First
                            Refusal to Lease "3rd Option Space."
        10.9             -- Two Bridge Point Lease Agreement, dated September 30,
                            1996, by and between Investors Life Insurance Company of
                            North America and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.14 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.10            -- Anadarko Basin Seismic Operations Agreement, dated
                            February 15, 1996, by and between Brigham Oil & Gas, L.P.
                            and Veritas Geophysical, Ltd. (filed as Exhibit 10.15 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.10.1          -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement, dated June 10, 1996, between Brigham Oil &
                            Gas, L.P. and Veritas Geophysical, Ltd. (filed as Exhibit
                            10.15.1 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
        10.11            -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Gasco
                            Limited Partnership. (filed as Exhibit 10.16 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.11.1          -- Amendment to Expense Allocation and Participation
                            Agreement, dated October 21, 1996, between Brigham Oil &
                            Gas, L.P. and Gasco Limited Partnership (filed as Exhibit
                            10.16.1 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
        10.12            -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Middle
                            Bay Oil Company, Inc. (filed as Exhibit 10.17 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.12.1          -- Amendment to Expense Allocation and Participation
                            Agreement, dated September 26, 1996, between Brigham Oil
                            & Gas, L.P. and Middle Bay Oil Company, Inc. (filed as
                            Exhibit 10.17.1 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
</TABLE>
    
 
                                      II-4
<PAGE>   124
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.12.2          -- Letter Amendment to Expense Allocation and Participation
                            Agreement, dated May 20, 1996, between Brigham Oil & Gas,
                            L.P. and Middle Bay Oil Company, Inc. (filed as Exhibit
                            10.17.2 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
        10.13            -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and among Stephens Production Company and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.18 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.14            -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and between Vintage Petroleum, Inc. and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.19 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.15            -- Processing Alliance Agreement, dated July 20, 1993,
                            between Veritas Seismic Ltd. and Brigham Oil & Gas, L.P.
                            (filed as Exhibit 10.20 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333- 22491), and
                            incorporated herein by reference).
        10.15.1          -- Letter Amendment to Processing Alliance Agreement, dated
                            November 3, 1994, between Veritas Seismic Ltd. and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.20.1 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.16            -- Agreement and Assignment of Interest, West Bradley
                            Project, dated September 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P. (filed as Exhibit 10.21 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.17            -- Agreement and Assignment of Interests in lands located in
                            Grady County, Oklahoma, West Bradley Project, dated
                            December 1, 1995, by and between Aspect Resources Limited
                            Liability Company, Brigham Oil & Gas, L.P. and Venture
                            Acquisitions, L.P. (filed as Exhibit 10.22 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.18            -- Agreement and Assignment of Interests, West Bradley
                            Project, dated December 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P. (filed as Exhibit 10.23 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.19            -- Geophysical Exploration Agreement, Hardeman Project,
                            Hardeman and Wilbarger Counties, Texas and Jackson
                            County, Oklahoma, dated March 15, 1993 by and among
                            General Atlantic Resources, Inc., Maynard Oil Company,
                            Ruja Muta Corporation, Tucker Scully Interests Ltd., JHJ
                            Exploration, Ltd., Cheyenne Petroleum Company, Antrim
                            Resources, Inc., and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.24 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.20            -- Agreement and Partial Assignment of Interests in OK13-P
                            Prospect Area, Jackson County, Oklahoma (Hardeman
                            Project), dated August 1, 1995, by and between Brigham
                            Oil & Gas, L.P. and Aspect Resources Limited Liability
                            Company (filed as Exhibit 10.25 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
</TABLE>
 
                                      II-5
<PAGE>   125
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.21            -- Agreement and Partial Assignment of Interests in Q140-E
                            Prospect Area, Hardeman County, Texas (Hardeman Project),
                            dated August 1, 1995, by and between Brigham Oil & Gas,
                            L.P. and Aspect Resources Limited Liability Company
                            (filed as Exhibit 10.26 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.22            -- Agreement and Partial Assignment of Interests in Hankins
                            #1 Chappel Prospect Agreement, Jackson County, Oklahoma
                            (Hardeman Project), dated March 21, 1996, by and between
                            Brigham Oil & Gas, L.P., NGR, Ltd. and Aspect Resources
                            Limited Liability Company (filed as Exhibit 10.27 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.23            -- Form of Indemnity Agreement between the Registrant and
                            each of its executive officers (filed as Exhibit 10.28 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.24            -- Registration Rights Agreement dated February 26, 1997 by
                            and among Brigham Exploration Company, General Atlantic
                            Partners III L.P., GAP-Brigham Partners, L.P., RIMCO
                            Partners, L.P. II, RIMCO Partners L.P. III, and RIMCO
                            Partners, L.P. IV, Ben M. Brigham, Anne L. Brigham,
                            Harold D. Carter, Craig M. Fleming, David T. Brigham and
                            Jon L. Glass (filed as Exhibit 10.29 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.25            -- 1997 Director Stock Option Plan (filed as Exhibit 10.30
                            to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.26            -- Form of Employee Stock Ownership Agreement (filed as
                            Exhibit 10.31 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.27            -- Agreement and Assignment of Interest in Geophysical
                            Exploration Agreement, Esperson Dome Project, dated
                            November 1, 1994, by and between Brigham Oil & Gas, L.P.
                            and Vaquero Gas Company (filed as Exhibit 10.33 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.28            -- Geophysical Exploration Agreement, Southwest Danbury
                            Project, Brazoria County, Texas, dated as of July 1,
                            1996, by and among UNEXCO, Inc. and Brigham Oil & Gas,
                            L.P. (filed as Exhibit 10.34 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.29            -- Geophysical Exploration Agreement, Welder Project, Duval
                            County, Texas, dated as of October 1, 1996, by and among
                            UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.35 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.30            -- Proposed Trade Structure, RIMCO/Tigre Project, Vermillion
                            Parish, Louisiana, among Brigham Oil & Gas, L.P., Tigre
                            Energy Corporation and Resource Investors Management
                            Company (filed as Exhibit 10.36.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
</TABLE>
 
                                      II-6
<PAGE>   126
 
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.30.1          -- Letter relating to Proposed Trade Structure, RIMCO/Tigre
                            Project, dated January 31, 1997, from Resource Investors
                            Management Company to Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.36.1 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.31            -- Anadarko Basin Seismic Operations Agreement II, dated as
                            of April 1, 1997, by and between Brigham Oil & Gas, L.P.
                            (filed as Exhibit 10.37 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.31.1          -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement II, dated March 20, 1997, between Brigham Oil &
                            Gas, L.P. and Veritas DGC Land, Inc. (filed as Exhibit
                            10.37 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.32            -- Expense Allocation and Participation Agreement II, dated
                            April 1, 1997, between Brigham Oil & Gas, L.P., and Gasco
                            Limited Partnership (filed as Exhibit 10.31 to the
                            Company's Quarterly Report on Form 10-Q for the quarter
                            ended June 30, 1997, and incorporated herein by
                            reference).
        10.33            -- Credit Agreement dated as of January 26, 1998 among
                            Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and
                            the lenders signatory thereto (filed as Exhibit 10.36 to
                            the Company's Annual Report on Form 10-K for the year
                            ended December 31, 1997, and incorporated herein by
                            reference).
        10.33.1++        -- Guaranty Agreement dated January 26, 1998 by Brigham
                            Exploration Company in favor of Bank of Montreal, as
                            Agent, and each of the Lenders party to the Credit
                            Agreement.
        10.33.2++        -- First Amendment to Guaranty Agreement dated as of March
                            30, 1998 between Brigham Exploration Company and Bank of
                            Montreal, as agent for the Lenders party to the Credit
                            Agreement.
        10.34+           -- Form of Securities Purchase Agreement
        10.35+           -- Form of First Amendment to Credit Agreement among Brigham
                            Oil & Gas, L.P., Bank of Montreal, as Agent, and the
                            Lenders signatory thereto.
        10.36+           -- Form of Second Amendment to Guaranty Agreement between
                            Brigham Exploration Company and Bank of Montreal, as
                            agent for the Lenders party to the Credit Agreement.
        12+              -- Computation of Ratio of Earnings to Fixed Charges
        21++             -- Subsidiaries of the Registrant.
        23.1+            -- Consent of Thompson & Knight, A Professional Corporation
                            (included in Exhibit 5 above).
        23.2+            -- Consent of PricewaterhouseCoopers LLP, independent
                            accountants.
        23.3+            -- Consent of Cawley, Gillespie & Associates, Inc.,
                            independent petroleum engineers.
        24.1++           -- Powers of Attorney.
        25+              -- Statement of eligibility of trustee
</TABLE>
    
 
---------------
 
*    Management contract or compensatory plan.
 
+    Filed herewith.
 
++   Previously filed.
 
     (b) Financial Statement Schedules: None.
 
                                      II-7
<PAGE>   127
 
ITEM 17. UNDERTAKINGS
 
     The undersigned Registrant hereby undertakes to provide to the Underwriters
at the closing specified in the Underwriting Agreements, certificates in such
denominations and registered in such names as required by the particular
Underwriter, to permit prompt delivery to each purchaser.
 
     The undersigned Registrant also hereby undertakes that:
 
          (1) For purposes of determining any liability under the Securities
     Act, the information omitted from the form of prospectus filed as part of
     this Registration Statement in reliance upon Rule 430A and contained in a
     form of prospectus filed by the registrant pursuant to Rule 424(b)(1) or
     (4) or 497(h) under the Securities Act shall be deemed to be part of this
     Registration Statement as of the time it was declared effective.
 
          (2) For the purpose of determining any liability under the Securities
     Act, each post-effective amendment that contains a form of prospectus shall
     be deemed to be a new registration statement relating to the securities
     offered therein, and the offering of such securities at that time shall be
     deemed to be the initial bona fide offering thereof.
 
     Insofar as indemnification for liabilities arising under the Securities Act
may be permitted to directors, officers and controlling persons of the
Registrant pursuant to the foregoing provisions, or otherwise, the registrant
has been advised that in the opinion of the Securities and Exchange Commission
such indemnification is against public policy as expressed in the Securities Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the registrant of expenses
incurred or paid by a director, officer or controlling person of the registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.
 
                                      II-8
<PAGE>   128
 
                                   SIGNATURES
 
   
     Pursuant to the requirements of the Securities Act of 1933, each of the
undersigned registrants has duly caused this Registration Statement to be signed
on its behalf by the undersigned, thereunto duly authorized, in Austin, Texas,
on August 14, 1998.
    
 
   
                                            BRIGHAM EXPLORATION COMPANY
    
 
   
                                            By:     /s/ BEN M. BRIGHAM
    
   
 
                                              ----------------------------------
                                                        Ben M. Brigham
                                              President, Chief Executive Officer
                                                              and
                                                    Chairman of the Board
    
 
   
                                            BRIGHAM, INC.
    
 
   
                                            By:     /s/ BEN M. BRIGHAM
    
   
                                              ----------------------------------
                                                               Ben M. Brigham
                                                      President and Chairman of
                                                the Board
                                            BRIGHAM OIL & GAS, L.P.
    
 
   
                                            By: Brigham, Inc., its General
                                                Partner
    
 
   
                                                By:  /s/ BEN M. BRIGHAM
    
   
 
                                                --------------------------------
                                                               Ben M. Brigham
                                                      President and Chairman of
    
   
                                                    the Board
    
 
                                      II-9
<PAGE>   129
 
   
     Pursuant to the requirements of the Securities Act of 1933, each of the
undersigned registrants has duly caused this Registration Statement to be signed
on its behalf by the undersigned, thereunto duly authorized, in Oklahoma City,
Oklahoma, on August 14, 1998.
    
 
   
                                            BRIGHAM HOLDINGS I, LLC
    
 
   
                                            By:     /s/ BEN M. BRIGHAM
    
 
                                              ----------------------------------
   
                                                        Ben M. Brigham
    
   
                                                    Manager and President
    
 
   
                                            BRIGHAM HOLDINGS II, LLC
    
 
   
                                            By:     /s/ BEN M. BRIGHAM
    
   
 
                                              ----------------------------------
                                                        Ben M. Brigham
    
   
                                                    Manager and President
    
 
                                      II-10
<PAGE>   130
 
   
                          BRIGHAM EXPLORATION COMPANY
    
 
   
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
    
 
   
<TABLE>
<CAPTION>
                      SIGNATURE                                   TITLE                   DATE
                      ---------                                   -----                   ----
<C>                                                    <S>                           <C>
 
                 /s/ BEN M. BRIGHAM                    President, Chief Executive    August 14, 1998
-----------------------------------------------------  Officer and Chairman of the
                   Ben M. Brigham                      Board (principal executive
                                                       officer)
 
                /s/ ANNE L. BRIGHAM*                   Executive Vice President and  August 14, 1998
-----------------------------------------------------  Director
                   Anne L. Brigham
 
                /s/ CRAIG M. FLEMING*                  Chief Financial Officer,      August 14, 1998
-----------------------------------------------------  Vice President -- Finance
                  Craig M. Fleming                     and Treasurer (principal
                                                       financial and accounting
                                                       officer)
 
                  /s/ JON L. GLASS*                    Vice                          August 14, 1998
-----------------------------------------------------  President -- Exploration and
                    Jon L. Glass                       Director
 
                /s/ HAROLD D. CARTER*                  Director                      August 14, 1998
-----------------------------------------------------
                  Harold D. Carter
 
                /s/ GARY J. MILAVEC*                   Director                      August 14, 1998
-----------------------------------------------------
                   Gary J. Milavec
 
               /s/ ALEXIS M. CRANBERG*                 Director                      August 14, 1998
-----------------------------------------------------
                 Alexis M. Cranberg
 
              /s/ STEPHEN P. REYNOLDS*                 Director                      August 14, 1998
-----------------------------------------------------
                 Stephen P. Reynolds
 
               *By: /s/ BEN M. BRIGHAM
  ------------------------------------------------
                   Ben M. Brigham
                  Attorney-in-fact
</TABLE>
    
 
                                      II-11
<PAGE>   131
 
                                 BRIGHAM, INC.
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned directors and officers
of Brigham, Inc., a Nevada corporation, which is filing a Registration Statement
on Form S-1 with the Securities and Exchange Commission, Washington D.C. 20549
under the provisions of the Securities Act of 1933, as amended (the "Securities
Act"), hereby constitute and appoint Ben M. Brigham and Craig M. Fleming, and
each of them, the individual's true and lawful attorneys-in-fact and agents,
with full power of substitution and resubstitution, for the person and in his
other name, place and post-effective amendments, to the Registration Statement
and any or all amendments, including post-effective amendments, to the
Registration Statement, including a Prospectus or an amended Prospectus therein
and any registration statement for the same offering that is to be effective
upon filing pursuant to Rule 462(b) under the Securities Act, and all other
documents in connection therewith to be filed with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents, and each of them,
full power and authority to do and perform each and every act and thing
requisite and necessary to be done in and about the premises, as fully to all
intents and purposes as he might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact as agents or any of them, or their
substitute or substitutes, may lawfully door cause to be done by virtue hereof.
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
 
   
<TABLE>
<CAPTION>
                      SIGNATURE                                     TITLE                    DATE
                      ---------                                     -----                    ----
<C>                                                    <S>                              <C>
 
                 /s/ BEN M. BRIGHAM                    President and Chairman of the    August 14, 1998
-----------------------------------------------------  Board (principal executive
                   Ben M. Brigham                      officer)
 
                /s/ CRAIG M. FLEMING                   Chief Financial Officer, Vice    August 14, 1998
-----------------------------------------------------  President -- Finance, Treasurer
                  Craig M. Fleming                     and Director (principal
                                                       financial and accounting
                                                       officer)
</TABLE>
    
 
                                      II-12
<PAGE>   132
 
                            BRIGHAM HOLDINGS I, LLC
 
                               POWER OF ATTORNEY
 
   
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned managers and officers
of Brigham Holdings I, LLC, a Nevada limited liability company, which is filing
a Registration Statement on Form S-1 with the Securities and Exchange
Commission, Washington D.C. 20549 under the provisions of the Securities Act of
1933, as amended (the "Securities Act"), hereby constitute and appoint Ben M.
Brigham and Craig M. Fleming, and each of them, the individual's true and lawful
attorneys-in-fact and agents, with full power of substitution and
resubstitution, for the person and in his other name, place and post-effective
amendments, to the Registration Statement and any or all amendments, including
post-effective amendments, to the Registration Statement, including a Prospectus
or an amended Prospectus therein and any registration statement for the same
offering that is to be effective upon filing pursuant to Rule 462(b) under the
Securities Act, and all other documents in connection therewith to be filed with
the Securities and Exchange Commission, granting unto said attorneys-in-fact and
agents, and each of them, full power and authority to do and perform each and
every act and thing requisite and necessary to be done in and about the
premises, as fully to all intents and purposes as he might or could do in
person, hereby ratifying and confirming all that said attorneys-in-fact as
agents or any of them, or their substitute or substitutes, may lawfully door
cause to be done by virtue hereof.
    
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
 
   
<TABLE>
<CAPTION>
                      SIGNATURE                                     TITLE                    DATE
                      ---------                                     -----                    ----
<C>                                                    <S>                              <C>
 
                 /s/ BEN M. BRIGHAM                    President and Manager            August 14, 1998
-----------------------------------------------------  (principal executive officer)
                   Ben M. Brigham
 
                /s/ CRAIG M. FLEMING                   Vice President, Treasurer and    August 14, 1998
-----------------------------------------------------  Manager (principal financial
                  Craig M. Fleming                     and accounting officer)
</TABLE>
    
 
                                      II-13
<PAGE>   133
 
                            BRIGHAM HOLDINGS II, LLC
 
                               POWER OF ATTORNEY
 
   
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned managers and officers
of Brigham Holdings II, LLC, a Nevada limited liability company, which is filing
a Registration Statement on Form S-1 with the Securities and Exchange
Commission, Washington D.C. 20549 under the provisions of the Securities Act of
1933, as amended (the "Securities Act"), hereby constitute and appoint Ben M.
Brigham and Craig M. Fleming, and each of them, the individual's true and lawful
attorneys-in-fact and agents, with full power of substitution and
resubstitution, for the person and in his other name, place and post-effective
amendments, to the Registration Statement and any or all amendments, including
post-effective amendments, to the Registration Statement, including a Prospectus
or an amended Prospectus therein and any registration statement for the same
offering that is to be effective upon filing pursuant to Rule 462(b) under the
Securities Act, and all other documents in connection therewith to be filed with
the Securities and Exchange Commission, granting unto said attorneys-in-fact and
agents, and each of them, full power and authority to do and perform each and
every act and thing requisite and necessary to be done in and about the
premises, as fully to all intents and purposes as he might or could do in
person, hereby ratifying and confirming all that said attorneys-in-fact as
agents or any of them, or their substitute or substitutes, may lawfully door
cause to be done by virtue hereof.
    
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
 
   
<TABLE>
<CAPTION>
                      SIGNATURE                                     TITLE                    DATE
                      ---------                                     -----                    ----
<C>                                                    <S>                              <C>
 
                 /s/ BEN M. BRIGHAM                    President and Manager            August 14, 1998
-----------------------------------------------------  (principal executive officer)
                   Ben M. Brigham
 
                /s/ CRAIG M. FLEMING                   Vice President, Treasurer and    August 14, 1998
-----------------------------------------------------  Manager (principal financial
                  Craig M. Fleming                     and accounting officer)
</TABLE>
    
 
                                      II-14
<PAGE>   134
 
                            BRIGHAM OIL & GAS, L.P.
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned officers of Brigham
Oil & Gas, L.P., a Nevada limited partnership, and directors of Brigham, Inc.,
the general partner of Brigham Oil & Gas, L.P., which is filing a Registration
Statement on Form S-1 with the Securities and Exchange Commission, Washington
D.C. 20549 under the provisions of the Securities Act of 1933, as amended (the
"Securities Act"), hereby constitute and appoint Ben M. Brigham and Craig M.
Fleming, and each of them, the individual's true and lawful attorneys-in-fact
and agents, with full power of substitution and resubstitution, for the person
and in his other name, place and post-effective amendments, to the Registration
Statement and any or all amendments, including post-effective amendments, to the
Registration Statement, including a Prospectus or an amended Prospectus therein
and any registration statement for the same offering that is to be effective
upon filing pursuant to Rule 462(b) under the Securities Act, and all other
documents in connection therewith to be filed with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents, and each of them,
full power and authority to do and perform each and every act and thing
requisite and necessary to be done in and about the premises, as fully to all
intents and purposes as he might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact as agents or any of them, or their
substitute or substitutes, may lawfully door cause to be done by virtue hereof.
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
 
   
<TABLE>
<CAPTION>
                      SIGNATURE                                     TITLE                    DATE
                      ---------                                     -----                    ----
<C>                                                    <S>                              <C>
 
                 /s/ BEN M. BRIGHAM                    President of the Registrant and  August 14, 1998
-----------------------------------------------------  Director of its General Partner
                   Ben M. Brigham                      (principal executive officer)
 
                /s/ CRAIG M. FLEMING                   Chief Financial Officer of the   August 14, 1998
-----------------------------------------------------  Registrant and Director of its
                  Craig M. Fleming                     General Partner (principal
                                                       financial and accounting
                                                       officer)
</TABLE>
    
 
                                      II-15
<PAGE>   135
 
                               INDEX TO EXHIBITS
 
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
 
         2.1             -- Exchange Agreement (filed as Exhibit 2.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         3.1             -- Certificate of Incorporation (filed as Exhibit 3.1 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         3.2             -- Bylaws (filed as Exhibit 3.2 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
         4.1             -- Form of Common Stock Certificate (filed as Exhibit 4.1 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
         4.2+            -- Form of Indenture
         4.3+            -- Form of Warrant Certificate
         4.4+            -- Form of Senior Subordinated Secured Note due 2003
         4.5+            -- Form of Registration Rights Agreement
         5+              -- Opinion of Thompson & Knight, A Professional Corporation
        10.1             -- Agreement of Limited Partnership of Venture Acquisitions,
                            L.P., dated September 23, 1994, by and between Quest
                            Resources, L.L.C. and RIMCO Energy, Inc. as general
                            partners, and RIMCO Production Company, Inc., RIMCO
                            Exploration Partners, L.P. I and RIMCO Exploration
                            Partners, L.P. II, as limited partners (filed as Exhibit
                            10.2 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.2             -- Regulations of Quest Resources, L.L.C. (filed as Exhibit
                            10.3 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.3             -- Management and Ownership Agreement, dated September 23,
                            1994, by and among Brigham Oil & Gas, L.P., Brigham
                            Exploration Company, General Atlantic Partners III, L.P.,
                            Harold D. Carter, Ben M. Brigham and GAP-Brigham
                            Partners, L.P. (filed as Exhibit 10.4 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.4*++          -- Consulting Agreement, dated May 1, 1997, by and between
                            Brigham Oil & Gas, L.P. and Harold D. Carter.
        10.5*            -- Employment Agreement, by and between Brigham Exploration
                            Company and Ben M. Brigham (filed as Exhibit 10.7 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.6*            -- Form of Confidentiality and Noncompete Agreement between
                            the Registrant and each of its executive officers (filed
                            as Exhibit 10.8 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.7*            -- 1997 Incentive Plan of Brigham Exploration Company (filed
                            as Exhibit 10.9 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.7.1*          -- Form of Option Agreement for certain executive officers
                            (filed as Exhibit 10.9.1 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
</TABLE>
    
<PAGE>   136
 
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.7.2*          -- Option Agreement dated as of March 4, 1997, by and
                            between Brigham Exploration Company and Jon L. Glass
                            (filed as Exhibit 10.9.2 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.8*            -- Incentive Bonus Plan dated as of February 28, 1997 of
                            Brigham, Inc. and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.10 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.9.1++         -- First Amendment to Two Bridge Point Lease Agreement dated
                            April 11, 1997 between Investors Life Insurance Company
                            of North America and Brigham Oil & Gas, L.P.
        10.9.2++         -- Second Amendment to Two Bridge Point Lease Agreement
                            dated October 13, 1997 between Investors Life Insurance
                            Company of North America and Brigham Oil & Gas, L.P.
        10.9.3++         -- Letter dated April 17, 1998 exercising Right of First
                            Refusal to Lease "3rd Option Space."
        10.9             -- Two Bridge Point Lease Agreement, dated September 30,
                            1996, by and between Investors Life Insurance Company of
                            North America and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.14 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.10            -- Anadarko Basin Seismic Operations Agreement, dated
                            February 15, 1996, by and between Brigham Oil & Gas, L.P.
                            and Veritas Geophysical, Ltd. (filed as Exhibit 10.15 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.10.1          -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement, dated June 10, 1996, between Brigham Oil &
                            Gas, L.P. and Veritas Geophysical, Ltd. (filed as Exhibit
                            10.15.1 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
        10.11            -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Gasco
                            Limited Partnership. (filed as Exhibit 10.16 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.11.1          -- Amendment to Expense Allocation and Participation
                            Agreement, dated October 21, 1996, between Brigham Oil &
                            Gas, L.P. and Gasco Limited Partnership (filed as Exhibit
                            10.16.1 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
        10.12            -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Middle
                            Bay Oil Company, Inc. (filed as Exhibit 10.17 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.12.1          -- Amendment to Expense Allocation and Participation
                            Agreement, dated September 26, 1996, between Brigham Oil
                            & Gas, L.P. and Middle Bay Oil Company, Inc. (filed as
                            Exhibit 10.17.1 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.12.2          -- Letter Amendment to Expense Allocation and Participation
                            Agreement, dated May 20, 1996, between Brigham Oil & Gas,
                            L.P. and Middle Bay Oil Company, Inc. (filed as Exhibit
                            10.17.2 to the Company's Registration Statement on Form
                            S-1 (Registration No. 333-22491), and incorporated herein
                            by reference).
</TABLE>
    
<PAGE>   137
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.13            -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and among Stephens Production Company and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.18 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.14            -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and between Vintage Petroleum, Inc. and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.19 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.15            -- Processing Alliance Agreement, dated July 20, 1993,
                            between Veritas Seismic Ltd. and Brigham Oil & Gas, L.P.
                            (filed as Exhibit 10.20 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333- 22491), and
                            incorporated herein by reference).
        10.15.1          -- Letter Amendment to Processing Alliance Agreement, dated
                            November 3, 1994, between Veritas Seismic Ltd. and
                            Brigham Oil & Gas, L.P. (filed as Exhibit 10.20.1 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.16            -- Agreement and Assignment of Interest, West Bradley
                            Project, dated September 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P. (filed as Exhibit 10.21 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.17            -- Agreement and Assignment of Interests in lands located in
                            Grady County, Oklahoma, West Bradley Project, dated
                            December 1, 1995, by and between Aspect Resources Limited
                            Liability Company, Brigham Oil & Gas, L.P. and Venture
                            Acquisitions, L.P. (filed as Exhibit 10.22 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.18            -- Agreement and Assignment of Interests, West Bradley
                            Project, dated December 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P. (filed as Exhibit 10.23 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.19            -- Geophysical Exploration Agreement, Hardeman Project,
                            Hardeman and Wilbarger Counties, Texas and Jackson
                            County, Oklahoma, dated March 15, 1993 by and among
                            General Atlantic Resources, Inc., Maynard Oil Company,
                            Ruja Muta Corporation, Tucker Scully Interests Ltd., JHJ
                            Exploration, Ltd., Cheyenne Petroleum Company, Antrim
                            Resources, Inc., and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.24 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.20            -- Agreement and Partial Assignment of Interests in OK13-P
                            Prospect Area, Jackson County, Oklahoma (Hardeman
                            Project), dated August 1, 1995, by and between Brigham
                            Oil & Gas, L.P. and Aspect Resources Limited Liability
                            Company (filed as Exhibit 10.25 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.21            -- Agreement and Partial Assignment of Interests in Q140-E
                            Prospect Area, Hardeman County, Texas (Hardeman Project),
                            dated August 1, 1995, by and between Brigham Oil & Gas,
                            L.P. and Aspect Resources Limited Liability Company
                            (filed as Exhibit 10.26 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
</TABLE>
<PAGE>   138
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.22            -- Agreement and Partial Assignment of Interests in Hankins
                            #1 Chappel Prospect Agreement, Jackson County, Oklahoma
                            (Hardeman Project), dated March 21, 1996, by and between
                            Brigham Oil & Gas, L.P., NGR, Ltd. and Aspect Resources
                            Limited Liability Company (filed as Exhibit 10.27 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.23            -- Form of Indemnity Agreement between the Registrant and
                            each of its executive officers (filed as Exhibit 10.28 to
                            the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.24            -- Registration Rights Agreement dated February 26, 1997 by
                            and among Brigham Exploration Company, General Atlantic
                            Partners III L.P., GAP-Brigham Partners, L.P., RIMCO
                            Partners, L.P. II, RIMCO Partners L.P. III, and RIMCO
                            Partners, L.P. IV, Ben M. Brigham, Anne L. Brigham,
                            Harold D. Carter, Craig M. Fleming, David T. Brigham and
                            Jon L. Glass (filed as Exhibit 10.29 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.25            -- 1997 Director Stock Option Plan (filed as Exhibit 10.30
                            to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.26            -- Form of Employee Stock Ownership Agreement (filed as
                            Exhibit 10.31 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.27            -- Agreement and Assignment of Interest in Geophysical
                            Exploration Agreement, Esperson Dome Project, dated
                            November 1, 1994, by and between Brigham Oil & Gas, L.P.
                            and Vaquero Gas Company (filed as Exhibit 10.33 to the
                            Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.28            -- Geophysical Exploration Agreement, Southwest Danbury
                            Project, Brazoria County, Texas, dated as of July 1,
                            1996, by and among UNEXCO, Inc. and Brigham Oil & Gas,
                            L.P. (filed as Exhibit 10.34 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.29            -- Geophysical Exploration Agreement, Welder Project, Duval
                            County, Texas, dated as of October 1, 1996, by and among
                            UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.35 to the Company's Registration Statement on
                            Form S-1 (Registration No. 333-22491), and incorporated
                            herein by reference).
        10.30            -- Proposed Trade Structure, RIMCO/Tigre Project, Vermillion
                            Parish, Louisiana, among Brigham Oil & Gas, L.P., Tigre
                            Energy Corporation and Resource Investors Management
                            Company (filed as Exhibit 10.36.1 to the Company's
                            Registration Statement on Form S-1 (Registration No.
                            333-22491), and incorporated herein by reference).
        10.30.1          -- Letter relating to Proposed Trade Structure, RIMCO/Tigre
                            Project, dated January 31, 1997, from Resource Investors
                            Management Company to Brigham Oil & Gas, L.P. (filed as
                            Exhibit 10.36.1 to the Company's Registration Statement
                            on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
        10.31            -- Anadarko Basin Seismic Operations Agreement II, dated as
                            of April 1, 1997, by and between Brigham Oil & Gas, L.P.
                            (filed as Exhibit 10.37 to the Company's Registration
                            Statement on Form S-1 (Registration No. 333-22491), and
                            incorporated herein by reference).
</TABLE>
<PAGE>   139
 
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.31.1          -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement II, dated March 20, 1997, between Brigham Oil &
                            Gas, L.P. and Veritas DGC Land, Inc. (filed as Exhibit
                            10.37 to the Company's Registration Statement on Form S-1
                            (Registration No. 333-22491), and incorporated herein by
                            reference).
        10.32            -- Expense Allocation and Participation Agreement II, dated
                            April 1, 1997, between Brigham Oil & Gas, L.P., and Gasco
                            Limited Partnership (filed as Exhibit 10.31 to the
                            Company's Quarterly Report on Form 10-Q for the quarter
                            ended June 30, 1997, and incorporated herein by
                            reference).
        10.33            -- Credit Agreement dated as of January 26, 1998 among
                            Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and
                            the lenders signatory thereto (filed as Exhibit 10.36 to
                            the Company's Annual Report on Form 10-K for the year
                            ended December 31, 1997, and incorporated herein by
                            reference).
        10.33.1++        -- Guaranty Agreement dated January 26, 1998 by Brigham
                            Exploration Company in favor of Bank of Montreal, as
                            Agent, and each of the Lenders party to the Credit
                            Agreement.
        10.33.2++        -- First Amendment to Guaranty Agreement dated as of March
                            30, 1998 between Brigham Exploration Company and Bank of
                            Montreal, as agent for the Lenders party to the Credit
                            Agreement.
        10.34+           -- Form of Securities Purchase Agreement
        10.35+           -- Form of First Amendment to Credit Agreement among Brigham
                            Oil & Gas, L.P., Bank of Montreal, as Agent, and the
                            Lenders signatory thereto.
        10.36+           -- Form of Second Amendment to Guaranty Agreement between
                            Brigham Exploration Company and Bank of Montreal, as
                            agent for the Lenders party to the Credit Agreement.
        12+              -- Computation of Ratio of Earnings to Fixed Charges
        21++             -- Subsidiaries of the Registrant.
        23.1+            -- Consent of Thompson & Knight, A Professional Corporation
                            (included in Exhibit 5 above).
        23.2+            -- Consent of PricewaterhouseCoopers LLP, independent
                            accountants.
        23.3+            -- Consent of Cawley, Gillespie & Associates, Inc.,
                            independent petroleum engineers.
        24.1++           -- Powers of Attorney.
        25+              -- Statement of eligibility of trustee
</TABLE>
    
 
---------------
 
*    Management contract or compensatory plan.
 
+    Filed herewith.
 
++   Previously filed.