<PAGE>   1
                                                                   EXHIBIT 10.38

 


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                         SECURITIES PURCHASE AGREEMENT

                                    BETWEEN

                          BRIGHAM EXPLORATION COMPANY

                                      AND

                     ENRON CAPITAL & TRADE RESOURCES CORP.
                                      AND
                    JOINT ENERGY DEVELOPMENT INVESTMENTS II
                              LIMITED PARTNERSHIP

                          DATED AS OF AUGUST 20, 1998



            $50,000,000 SENIOR SUBORDINATED SECURED NOTES DUE 2003,

            Warrants to Purchase 1,000,000 Shares of Common Stock;

                                      AND

                ACQUISITION OF 1,052,632 SHARES OF COMMON STOCK

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<PAGE>   2
 
                                 TABLE OF CONTENTS
<TABLE>
<S>                 <C>                                                     <C>
ARTICLE I
     DEFINITIONS..........................................................    1
     Section 1.01    Definitions..........................................    1
     Section 1.02    Accounting Procedures and Interpretation.............   10
 
ARTICLE II
     ISSUANCE OF SECURITIES; RIGHTS OF PURCHASERS.........................   10
     Section 2.01    Issuance of Securities...............................   10
     Section 2.02    The Closing; Funding Date............................   11
     Section 2.03    Delivery.............................................   11
     Section 2.04    Payment..............................................   11
     Section 2.05    Tax Matters..........................................   11
     Section 2.06    Rights of Purchasers.................................   12
 
ARTICLE III
     SECURITY FOR THE OBLIGATIONS.........................................   12
     Section 3.01    Security.............................................   12
 
ARTICLE IV
     REPRESENTATIONS AND WARRANTIES OF THE SELLER.........................   12
     Section 4.01    Corporate Existence..................................   12
     Section 4.02    Financial Condition..................................   13
     Section 4.03    Litigation...........................................   13
     Section 4.04    No Breach............................................   13
     Section 4.05    Authority............................................   14
     Section 4.06    Approvals............................................   14
     Section 4.07    Use of Loans.........................................   14
     Section 4.08    ERISA................................................   14
     Section 4.09    Taxes................................................   15
     Section 4.10    Titles, etc..........................................   15
     Section 4.11    No Material Misstatements............................   16
     Section 4.12    Investment Company Act...............................   17
     Section 4.13    Public Utility Holding Company Act...................   17
     Section 4.14    Subsidiaries.........................................   17
     Section 4.15    Location of Business and Offices.....................   17
     Section 4.16    Defaults.............................................   17
     Section 4.17    Environmental Matters................................   17
     Section 4.18    Compliance with the Law..............................   18
     Section 4.19    Insurance............................................   19
     Section 4.20    Hedging Agreements...................................   19
     Section 4.21    Restriction on Liens.................................   20
</TABLE> 

                                      -i-
<PAGE>   3
 
<TABLE>
<S>                  <C>                                                     <C>
     Section 4.22    Material Agreements..................................   20
     Section 4.23    Gas Imbalances.......................................   20
     Section 4.24    Capitalization.......................................   20
     Section 4.25    Acquired Shares......................................   20
     Section 4.26    Warrant Shares.......................................   21
     Section 4.27    No Restrictions......................................   21
     Section 4.28    Certain Fees.........................................   21
 
ARTICLE V
     REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS.....................   21
     Section 5.01    Investment...........................................   21
     Section 5.02    Nature of Purchasers.................................   22
     Section 5.03    Receipt of Information; Authorization................   22
 
ARTICLE VI
     CONDITIONS PRECEDENT TO FUNDING......................................   22
     Section 6.01    Conditions Precedent to Obligations of the Purchasers   22
     Section 6.02    Conditions Precedent to Obligations of the Seller....   25
     Section 6.03    Conditions Precedent to the Obligations of
                     Purchasers and Seller................................   26
 
ARTICLE VII
     AFFIRMATIVE COVENANTS................................................   26
     Section 7.01    Warrants.............................................   26
     Section 7.02    Hart-Scott -Rodino Compliance........................   26
     Section 7.03    Board Representation.................................   27
     Section 7.04    Common Stock; Dividends; Voting Rights...............   27
 
ARTICLE VIII
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE IX
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE X
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE XI
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE XII
     MISCELLANEOUS........................................................   28
     Section 12.01   INTERPRETATION AND SURVIVAL OF PROVISIONS............   28
     Section 12.02   COSTS, EXPENSES AND TAXES............................   28
     Section 12.03   NO WAIVER; MODIFICATIONS IN WRITING..................   30
</TABLE>


                                      -ii-
<PAGE>   4


<TABLE>
<S>                  <C>                                                     <C>
     Section 12.04   BINDING EFFECT; ASSIGNMENT...........................   30
     Section 12.05   REPLACEMENT SECURITIES...............................   30
     Section 12.06   COMMUNICATIONS.......................................   31
     Section 12.07   GOVERNING LAW........................................   31
     Section 12.08   ARBITRATION..........................................   31
     Section 12.09   EXECUTION IN COUNTERPARTS............................   32 

Exhibits:

Exhibit A  -  Form of Warrants


Schedules:

Schedule 4.02  -  Liabilities
Schedule 4.03  -  Litigation
Schedule 4.09  -  Taxes
Schedule 4.10  -  Titles, Etc.
Schedule 4.14  -  Subsidiaries and Addresses
Schedule 4.19  -  Insurance
Schedule 4.20  -  Hedging Agreements
Schedule 4.22  -  Material Agreements
Schedule 4.23  -  Gas Imbalances
Schedule 4.24  -  Voting Agreements; Registration Rights
</TABLE>

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<PAGE>   5
 
                         SECURITIES PURCHASE AGREEMENT


     SECURITIES PURCHASE AGREEMENT, dated as of August 20, 1998 (this
"Agreement"), among BRIGHAM EXPLORATION COMPANY, a Delaware corporation, ENRON
CAPITAL & TRADE RESOURCES CORP., a Delaware corporation ("ECT") and JOINT ENERGY
DEVELOPMENT INVESTMENTS II LIMITED PARTNERSHIP, a Delaware limited partnership
("JEDI-II").

     In consideration of the mutual covenants and agreements set forth herein
and for good and valuable consideration, the receipt of which is hereby
acknowledged, the parties agree as follows:

                                   ARTICLE I
                                  DEFINITIONS

     Section 1.01  DEFINITIONS.  As used in this Agreement, and unless the
context requires a different meaning, the following terms have the meanings
indicated:

     "Acquired Shares" means 1,052,632 shares of Common Stock acquired by the
Purchasers on the Funding Date in accordance with Section 2.01 and any
additional shares of Common Stock of the Seller issued to the Purchasers after
the Funding Date in accordance with Section 2.01(ii).

     "Affiliate" of any Person shall mean (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 is
the sole general partner of a limited partnership, or 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" is defined in the Indenture.

     "Average Share Price" means $9.50.

     "Basic Documents" means, collectively, this Agreement, the other Loan
Documents, the Structuring Fee Agreement and the Equity Documents.

     "Board of Directors" means the Board of Directors of the Seller.

     "BOG" means Brigham Oil & Gas, L.P., a Delaware limited partnership.

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<PAGE>   6
 
     "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 Opportunities
Shareholders' Agreement dated as of even date herewith between the Purchasers
and the Seller.

     "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.

     "Closing" has the meaning provided therefor in Section 2.02.

     "Closing Date" means the date upon which the Closing occurs as provided in
Section 2.02.

     "Code" means the Internal Revenue Code of 1986, as amended from time to
time, and any successor statute.

     "Collateral" is defined in the Indenture.

     "Collateral Documents" is defined in the Indenture.

     "Commission" means the United States Securities and Exchange Commission.

     "Common Stock" means the common stock, par value $0.01 per share, of the
Seller or such other class of securities as shall, after the date of this
Agreement, constitute the common equity of the Seller.

     "Consolidated Subsidiaries" shall mean each Subsidiary of the Seller
(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 Seller 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 past due 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 borrowed money) excluding Trade 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
eighty percent (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

                                      -2-
<PAGE>   7
 
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 and fees (other than past due 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 Seller
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.

     "Designee" shall have the meaning set forth in Section 7.03.

     "Effective Date" means the date this Agreement is executed by all the
parties hereto.

     "Employee Plan" means any employee benefit plan, program or policy with
respect to which the Seller 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 Seller or
any Subsidiary is conducting or at any time has conducted business, or where any
Property of the Seller or any Subsidiary is located, including, without
limitation, the Oil Pollution Act of 1990 ("OPA"), as amended, the Clean Air
Act, as amended, the Comprehensive Environmental, Response, Compensation, and
Liability Act of 1980 ("CERCLA"), 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 ("RCRA"), 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 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

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<PAGE>   8
 
"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 Seller 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 Acquired Shares, the 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" shall mean each trade or business (whether or not
incorporated) which together with the Seller or any Subsidiary of the Seller
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 impair the value of such
Property subject thereto; (vi) deposits of cash or securities to secure the
performance of bids, trade, contracts, leases, statutory

                                      -4-
<PAGE>   9
 
obligations and other obligations of a like nature incurred in the ordinary
course of business; and (vii) Liens permitted by the Loan Documents.

     "Financial Statements" means the financial statement or statements
described or referred to in Section 4.02.

     "Financing Agreement" means an agreement between the Seller and ECT
Securities Corp. pursuant to which the Seller grants to ECT Securities Corp. the
right and option to participate during the three years following the Closing
Date for up to 20% on any public or private (e.g. 144A) high yield debt offering
by the Seller with gross proceeds in excess of $50,000,000.

  "Funding Date" means the first Business Day following the date all of the
conditions precedent to funding in Article VI have been satisfied.

     "GAAP" means generally accepted accounting principles in the United States
of America in effect from time to time.

     "Governmental Authority" shall include 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 herein shall mean
a Governmental Authority having jurisdiction over, where applicable, the Seller,
the Subsidiaries or any of their Property or any Purchaser.

     "Government Requirement" means any law, statute, code, ordinance, order,
determination, rule, regulation, judgment, decree, injunction, franchise,
permit, certificate, license, authorization or other directive or requirement
(in the case of banking regulatory authorities whether or not having the force
of law), including without limitation, Environmental Laws, energy regulations
and occupational, safety and health standards or controls of any Governmental
Authority.

     "Guarantors" means Brigham, Inc., Brigham Holdings I, LLC, Brigham Holdings
II, LLC, BOG and any other Person who becomes party to a Guaranty Agreement
pursuant to the terms of the Loan Documents.

     "Guaranty Agreements" means the agreements executed by the Guarantors in
form and substance satisfactory to the Trustee and the Purchasers guarantying,
unconditionally, payment of the Obligations, as the same may be amended,
modified or supplemented from time to time.

     "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.

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<PAGE>   10
 
     "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.

     "Indenture" means that certain Indenture dated as of August 20, 1998,
executed by Seller.

     "Investment Unit" has the meaning provided therefor in Section 2.05 of this
Agreement.

     "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" shall include reservations, exceptions,
encroachments, easements, rights of way, covenants, conditions, restrictions,
leases and other title exceptions and encumbrances affecting Property.  For the
purpose of this Agreement, 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 this Agreement, 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 Seller
or any Subsidiary or Affiliate of the Seller (other than the Equity Documents
and any assignments, participation or similar agreements between any Purchaser
and any other lender or creditor with respect to any Obligations pursuant to
this Agreement) in connection with, or as security for the payment or
performance of, the Notes or this Agreement, as such agreements may be amended,
supplemented or restated from time to time.

     "Majority Purchasers" means, at any time, the Purchasers holding more than
50% of the  Warrants.

     "Material Adverse Effect" means any material and adverse effect on (i) the
assets, liabilities, financial condition, business, operations or affairs of the
Seller 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 Seller 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.

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<PAGE>   11
 
     "Mortgage" is defined in the Indenture.

     "Mortgaged Property" means the Property owned by the Seller 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.

     "Notes" means the Senior Subordinated Secured Notes issued pursuant to
Section 2.03 of this Agreement and the Indenture, in the aggregate face amount
of $50,000,000, dated as of the date hereof, made by the Seller and initially
payable to the order of the Purchasers in their respective Participations.

     "Noteholders" means, from time to time, the holders of the Notes.

     "Obligations" means any and all amounts, liabilities and obligations owing
from time to time by Seller to the Agent or the Noteholders, pursuant to any of
the Loan 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, apparatus, appliances,
tools, implements, cables, wires, towers, casing, tubing and rods, similar
equipment, surface leases, rights-

                                      -7-
<PAGE>   12
 
of-way, easements and servitudes together with all additions, substitutions,
replacements, accessions and attachments to any and all of the foregoing.

     "Participation" means, for each Purchaser, such Purchaser's proportionate
share of the Obligations and the Warrants.  As of the Effective Date, ECT's
Participation shall be 25% and JEDI-II's Participation shall be 75%.

     "PBGC" means the Pension Benefit Guaranty Corporation or any entity
succeeding to any or all of its functions.

     "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 Seller, 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 Seller, any Subsidiary or an ERISA Affiliate.

     "Property" means any interest in any kind of property or asset, whether
real, personal or mixed, or tangible or intangible.

     "Purchasers" means ECT and JEDI-II and/or, to the extent then applicable,
each assignee of ECT or JEDI-II or their respective successors or assigns
pursuant to Section 12.04.

     "Registration Rights Agreement" means the Registration Rights Agreement
dated as of the date hereof, made by the Seller in favor of the Purchasers
relating to the Warrants, the Warrant Shares and the Acquired Shares.

     "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" is defined in the Indenture.

     "Responsible Officer" means, as to any Person, the Chief Executive Officer,
the President or any Vice President of such Person and the Chief Financial
Officer of such Person.  Unless otherwise specified, all references to a
Responsible Officer herein shall mean a Responsible Officer of the Seller.

     "Securities" means the Notes, the Warrants and the Acquired Shares.

     "Securities Act" means the Securities Act of 1933, as amended from time to
time, and the rules and regulations of the Commission promulgated thereunder.

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<PAGE>   13
 
     "Seller" means Brigham Exploration Company, a Delaware corporation.

     "Senior Credit Agreement" means the Credit Agreement dated as of January
26, 1998, among BOG, 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 in connection with any
refinancing of the Senior Loan permitted hereunder and under the Subordination
Agreement.

     "Senior Loan Agent" means the agent or agents designated under the Senior
Credit Agreement.  Bank of Montreal is the Senior Loan Agent as of the date
hereof.

     "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 BOG under the Senior Credit Agreement
and the other Senior Loan Documents.

     "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 this 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).

     "Structuring Fee Agreement" means the agreement between the Seller and ECT
Securities Corp. dated as of the date hereof.

     "Subordination Agreement" means the Intercreditor and Subordination
Agreement dated as of even date herewith, by and among the Senior Loan Agent,
the Agent, the Purchasers, the Seller and certain Subsidiaries, as the same may
be supplemented or amended from time to time.

     "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 

                                      -9-
<PAGE>   14
 
its Subsidiaries or by a Person and one or more of its Subsidiaries and (ii) any
Special Entity. Unless otherwise indicated herein, each reference to the term
"Subsidiary" shall mean a Subsidiary of the Seller. Quest Resources L.L.C. and
Venture Acquisitions L.P. shall not be considered Subsidiaries of Seller.

     "Trade Payables" means customary trade payables incurred in the ordinary
course of business.

     "Trustee" means the Trustee as defined in the Indenture.

     "Warrant Shares" means the shares of Common Stock and other securities
receivable upon exercise of the Warrants.

     "Warrants" means the Warrants issued by the Seller to the Purchasers in
their respective Participations pursuant to Section 2.03, for the purchase of an
aggregate of 1,000,000 shares of Common Stock, and any Warrants issued upon the
transfer thereof or in substitution therefor, pursuant to the Warrant
Certificates to be issued to ECT and JEDI-II, forms of which are attached hereto
as Exhibit A.

     Section  1.02.  ACCOUNTING PROCEDURES AND INTERPRETATION.  Unless otherwise
specified herein, all accounting terms used herein shall be interpreted, all
determinations with respect to accounting matters hereunder shall be made, and
all financial statements and certificates and reports as to financial matters
required to be furnished by the Seller hereunder shall be prepared, in
accordance with GAAP, applied on a basis consistent with the Financial
Statements (except for changes concurred with by the Seller's independent public
accountants).

                                  ARTICLE II
                 ISSUANCE OF SECURITIES; RIGHTS OF PURCHASERS

     Section 2.01  ISSUANCE OF SECURITIES.  Subject to the terms and
conditions herein set forth, the Seller agrees that it will issue the Securities
to the Purchasers and the Purchasers agree that they shall each purchase the
Securities from the Seller for an aggregate 
cash consideration of $50,000,000,
as follows:

               (i)  The Notes and the Warrants will be purchased by the
          Purchasers in their respective participations and sold for an
          aggregate cash consideration of $40,000,000.

               (ii)  The Acquired Shares will be purchased by the Purchasers or
          their respective Affiliates for a total cash consideration of
          $10,000,000.  The number of Acquired Shares to be purchased and sold
          on the Funding Date shall be determined by dividing the $10,000,000
          purchase price by the Average Share Price.  If within 180 days
          following the Funding Date the Seller enters into an agreement to
          issue or issues new Common Stock for a price per share that is less
          than the Average Share

                                      -10-
<PAGE>   15
 
          Price (a "Post Funding Sale Price"), the Seller shall,
          contemporaneously with the issuance of such new Common Stock, issue
          and deliver to the Purchasers or their respective Affiliates
          additional shares of Common Stock (which shall be deemed additional
          Acquired Shares) such that, after issuance and delivery of such
          additional Acquired Shares, the total number of Acquired Shares
          received by the Purchasers or their respective Affiliates multiplied
          by the Post Funding Date Sale Price, shall aggregate $10,000,000.

     Section 2.02  THE CLOSING; FUNDING DATE.

          (a)  The execution of the Basic Documents and all other instruments
required pursuant to Section 6.01 will take place at a closing (the "Closing")
to be held at the offices of Bracewell & Patterson, L.L.P. on such date as the
Seller and the Purchasers shall agree.  The date and time at which the Closing
occurs is the "Closing Date".

          (b)  Delivery of the Securities by the Seller to the Purchasers, and
payment by the Purchasers to the Seller of the consideration therefor as set
forth in Section 2.01, shall occur on the Funding Date.

     Section 2.03  DELIVERY.   Delivery of the Securities pursuant to this
Agreement shall be made on the Funding Date by the Seller delivering to the
Purchasers, against payment of the purchase price therefor, as follows: (i) one
Note executed by the Seller in the face amount of $12,500,000.00, payable to the
order of ECT and one Note executed by the Seller in the face amount of
$37,500,000.00, payable to the order of JEDI-II, (ii) one certificate executed
by the Seller representing ECT's Participation in the Warrants and one
certificate executed by the Seller representing JEDI-II's Participation in the
Warrants, registered in the names of ECT and JEDI-II, respectively (or such
other Person as either Purchaser may have designated in writing to the Seller at
least three Business Days prior to the Funding Date) and (iii) a certificate or
certificates of Common Stock executed by the Seller representing the Purchasers
and/or their respective Affiliates share of the Acquired Shares registered in
the name(s) of the Purchasers and/or their respective Affiliates (or such other
Person as either Purchaser may have designated in writing to the Seller at least
three Business Days prior to the Funding Date).

     Section 2.04  PAYMENT.  Payment of the consideration for the Securities
shall be made on the Funding Date by wire transfer of immediately available
funds to such account of the Seller as shall have been designated to ECT at
least two Business Days prior to the Funding Date.

     Section 2.05 TAX MATTERS. The Seller and the Purchasers agree as follows:
(i) Purchasers' acquisition of the Securities constitutes the purchase of an
"investment unit" (the "Investment Unit") for purposes of Treas. Reg. (S)1.1273-
2(h)(1); (ii) the issue price of the Investment Unit is $50,000,000, as
determined in accordance with Treas. Reg. (S)1.1273-2(a)(1); (iii) the issue
price for the Investment Unit shall be allocated among the Notes, the Warrants,
and the Acquired Shares in accordance with their relative fair market values, as
required by Treas. Reg. (S)1.1273-2(h)(1); and 

                                      -11-
<PAGE>   16
 
(iv) the parties agree that the issue price shall be allocated among the Notes,
the Warrants, and the Acquired Shares as follows and the parties shall be bound
by such allocation for all tax-related purposes:

<TABLE>
<S>           <C>                   <C> 
               Notes:                $39,900,000
               Warrants:             $   100,000
               Acquired Shares:      $10,000,000
</TABLE>

     Section 2.06  RIGHTS OF PURCHASERS.  The Purchasers shall have such
rights with respect to the registration of the Warrant Shares and the Acquired
Shares under the Securities Act and state securities laws as are set forth in
the Registration Rights Agreement, which shall be executed by the Seller and the
Purchasers at the Closing.

                                  ARTICLE III
                         SECURITY FOR THE OBLIGATIONS

     Section 3.01  SECURITY.  The Obligations shall be secured by the
Collateral and the Collateral Documents in accordance with the Indenture.

                                  ARTICLE IV
                 REPRESENTATIONS AND WARRANTIES OF THE SELLER

     The Seller represents and warrants to the Purchasers, for the benefit of
each of the holders of the Notes, the holders of the Warrants and the holders of
the Acquired Shares, which representations and warranties shall survive the
execution of any Basic Document, that as of the date of this Agreement:

     Section 4.01  CORPORATE EXISTENCE.  The Seller: (i) is a corporation duly
organized, legally existing and in good standing under the laws of the State of
Delaware; (ii) has all requisite power, and has all material governmental
licenses, authorizations, consents and approvals necessary to own its assets and
carry on its business as now being or as proposed to be conducted; and (iii) is
qualified to do business in all jurisdictions in which the nature of the
business conducted by it makes such qualifications necessary and where failure
so to qualify would have a Material Adverse Effect.  Brigham, Inc.: (i) is a
corporation duly organized, legally existing and in good standing under the laws
of the State of Nevada; (ii) has all requisite power, and has all material
governmental licenses, authorizations, consents and approvals necessary to own
its assets and carry on its business as now being or as proposed to be
conducted; and (iii) is qualified to do business in all jurisdictions in which
the nature of the business conducted by it makes such qualifications necessary
and where failure so to qualify would have a Material Adverse Effect.  Each of
Brigham Holdings I, LLC and Brigham Holdings II, LLC:  (i) is a limited
liability company duly organized, legally existing and in good standing under
the laws of the State of Nevada; (ii) has all requisite power, and has all
material governmental licenses, authorizations, consents and approvals necessary
to own its assets and carry on its business as now being or as proposed to be
conducted; and (iii) is qualified to do business in all jurisdictions in which
the nature of the business conducted by it makes such qualifications 

                                      -12-
<PAGE>   17
 
necessary and where failure so to qualify would have a Material Adverse Effect.
Brigham Oil & Gas, L.P.: (i) is a limited partnership duly organized, legally
existing and in good standing under the laws of the State of Delaware; (ii) has
all requisite power, and has all material governmental licenses, authorizations,
consents and approvals necessary to own its assets and carry on its business as
now being or as proposed to be conducted; and (iii) is qualified to do business
in all jurisdictions in which the nature of the business conducted by it makes
such qualifications necessary and where failure so to qualify would have a
Material Adverse Effect.

     Section  4.02  FINANCIAL CONDITION.  The audited consolidated balance
sheet of the Seller and its Consolidated Subsidiaries as at December 31, 1997
and the related consolidated statement of income, stockholders' equity and cash
flow of the Seller and its Consolidated Subsidiaries for the fiscal year ended
on said date, with the opinion thereon of Price Waterhouse, heretofore furnished
to the Purchasers and the unaudited consolidated balance sheet of the Seller and
its Consolidated Subsidiaries as at June 30, 1998, and their related
consolidated statements of income, stockholders' equity and cash flow of the
Seller and its Consolidated Subsidiaries for the six-month period ended on such
date heretofore furnished to the Purchasers, are complete and correct and fairly
present the consolidated financial condition of the Seller and its Consolidated
Subsidiaries as at said dates and the results of its operations for the fiscal
year and the six-month period on said dates, all in accordance with GAAP, as
applied on a consistent basis (subject, in the case of the interim financial
statements, to normal year-end adjustments).  Neither the Seller nor any
Consolidated Subsidiary has on the Closing Date any material Debt, Trade
Payables, contingent liabilities, liabilities for taxes, unusual forward or
long-term commitments or unrealized or anticipated losses from any unfavorable
commitments, except as referred to or reflected or provided for in the Financial
Statements or in Schedule 4.02.  Since June 30, 1998, there has been no change
or event having a Material Adverse Effect.  Since the date of the Financial
Statements, neither the business nor the Properties of the Seller or any of the
Consolidated Subsidiaries, taken as a whole, have been materially and adversely
affected as a result of any fire, explosion, earthquake, flood, drought,
windstorm, accident, strike or other labor disturbance, embargo, requisition or
taking of Property or cancellation of contracts, permits or concessions by any
Governmental Authority, riot, activities of armed forces or acts of God or of
any public enemy.

     Section 4.03  LITIGATION.  Except as disclosed to the Purchasers in
Schedule 4.03, at the Closing Date there is no litigation, legal, administrative
or arbitral proceeding, investigation or other action of any nature pending or,
to the knowledge of the Seller, threatened against or affecting the Seller or
any Subsidiary which both (a) involves the possibility of any judgment or
liability against the Seller or any Subsidiary not fully covered by insurance
(except for normal deductibles), and (b) would be more likely than not to have a
Material Adverse Effect.

     Section 4.04  NO BREACH.  Neither the execution and delivery of the Basic
Documents, nor compliance with the terms and provisions thereof will conflict
with or result in a breach of, or require any consent which has not been
obtained as of the Closing Date under, the Articles of Incorporation or by-laws
of the Seller, the respective charter, by-laws, partnership agreements or
regulations of any Subsidiary or any Governmental Requirement or any material
agreement or instrument to which the Seller or any Subsidiary is a party or by
which it is bound or to which it or its Properties are subject, 

                                      -13-
<PAGE>   18
 
or constitute a default under any such agreement or instrument, or result in the
creation or imposition of any Lien upon any of the material revenues or assets
of the Seller or any Subsidiary pursuant to the terms of any such agreement or
instrument other than the Liens created by the Loan Documents and the
restrictions contained in the Senior Loan Documents (as amended concurrently
herewith) which limit the circumstances in which BOG can make dividends or
distributions to the Seller and in which the Seller can make cash payments of
interest on the Notes.

     Section 4.05  AUTHORITY.  The Seller and each Subsidiary has all
necessary power and authority to execute, deliver and perform its obligations
under the Basic Documents to which it is a party; and the execution, delivery
and performance by the Seller and each Subsidiary of the Basic Documents to
which it is a party, have been duly authorized by all necessary action on its
part; and the Basic Documents constitute the legal, valid and binding
obligations of the Seller and each Subsidiary, enforceable in accordance with
their terms, except as such enforceability may be limited by bankruptcy,
insolvency, fraudulent transfer and similar laws affecting creditors' rights
generally or by general principles of equity.

     Section 4.06  APPROVALS.  Except for registration of the Securities under
the Securities Act, no authorizations, approvals or consents of, and no filings
or registrations with, any Governmental Authority are necessary for the
execution, delivery or performance by the Seller or any Subsidiary of the Basic
Documents or for the validity or enforceability thereof.

     Section   4.07  USE OF LOANS.  The purchase price of the Notes, the
Warrants and the Acquired Shares shall be used solely to pay principal and
interest outstanding on the Senior Loan.  In no event shall the purchase price
of the Notes, the Warrants or the Acquired Shares be used to finance in whole or
in part any hostile acquisition.  The Seller is not engaged principally, or as
one of its important activities, in the business of extending credit for the
purpose, whether immediate, incidental or ultimate, or buying or carrying margin
stock (within the meaning of Regulation G, U or X of the Board of Governors of
the Federal Reserve System) and no part of the purchase price of the Notes, the
Warrants or the Acquired Shares will be used to buy or carry any margin stock.

     Section 4.08  ERISA.

          (a)  The Seller and each ERISA Affiliate have complied in all material
respects with ERISA and, where applicable, the Code regarding such Plan.

          (b)  Each Plan is, and has been, maintained in substantial compliance
with ERISA and, where applicable, the Code.

          (c)  No act, omission or transaction has occurred which could  result
in imposition on the Seller or any ERISA Affiliate (whether directly or
indirectly) of an amount of $100,000 or more as (i) either a civil penalty
assessed pursuant to section 502(c), (i) or (1) of ERISA or a tax imposed
pursuant to Chapter 43 of Subtitle D of the Code or (ii) breach of fiduciary
duty liability damages under section 409 of ERISA.

          (d)  No Plan (other than a defined contribution plan) or any trust
created under any such Plan has been terminated since September 2, 1974.  No
liability to the PBGC in excess of $100,000 (other than for the payment of
current premiums which are not past due) by the Seller or any ERISA Affiliate
has been or is expected by the Seller or 

                                      -14-
<PAGE>   19
 
any ERISA Affiliate to be incurred with respect to any Plan. No ERISA Event with
respect to any Plan has occurred which could reasonably expected to result in
liabilities of $100,000 or more.

          (e)  Full payment when due has been made of all amounts which the
Seller or any ERISA Affiliate is required under the terms of each Plan or
applicable law to have paid as contributions to such Plan, and no accumulated
funding deficiency in an amount of $100,000 or more (as defined in section 302
of ERISA and section 412 of the Code), whether or not waived, exists with
respect to any Plan.

          (f)  The actuarial present value of the benefit liabilities under each
Plan which is subject to Title IV of ERISA does not, as of the end of the
Seller's most recently ended fiscal year, exceed the current value of the assets
(computed on a plan termination basis in accordance with Title IV of ERISA) of
such Plan allocable to such benefit liabilities by $100,000 or more.  The term
"actuarial present value of the benefit liabilities" shall have the meaning
specified in section 4041 of ERISA.

          (g)  None of the Seller or any ERISA Affiliate sponsors, maintains, or
contributes to an employee welfare benefit plan, as defined in section 3(1) of
ERISA, including, without limitation, any such plan maintained to provide
benefits to former employees of such entities, that may not be terminated by the
Seller or any ERISA Affiliate in its sole discretion at any time without any
material liability.

          (h)  None of the Seller or any ERISA Affiliate sponsors, maintains or
contributes to, or has at any time in the preceding six calendar years,
sponsored, maintained or contributed to, any Multiemployer Plan.

          (i)  None of the Seller or any ERISA Affiliate is required to provide
security under section 401(a)(29) of the Code due to a Plan amendment that
results in an increase in current liability for the Plan.

     Section 4.09  TAXES.   Except as set out in Schedule 4.09, the Seller and
each Subsidiary has filed all United States Federal income tax returns and all
other tax returns which are required to be filed by it and has paid all material
taxes due pursuant to such returns or pursuant to any assessment received by the
Seller or any such Subsidiary, except for any taxes which are being contested in
good faith and by proper proceedings and against which adequate reserves are
being maintained.  The charges, accruals and reserves on the books of the Seller
and its Subsidiaries in respect of taxes and other governmental charges are, in
the opinion of the Seller, adequate.  No tax lien has been filed and, to the
knowledge of the Seller, no claim is being asserted with respect to any such
tax, fee or other charge, except for any taxes, fees or other charges which are
being contested in good faith and by proper proceedings and against which
adequate reserves are being maintained.


                                      -15-
<PAGE>   20

     Section 4.10  TITLES, ETC.
 
          (a)  Subject to the matters set out in Schedule 4.10, each of the
Seller and the Subsidiaries has good and defensible title to (i) the Oil and Gas
Properties that are both (A) evaluated in the most recently delivered Reserve
Report and (B) described in Part One of Exhibit A to the Mortgage, free and
clear of all Liens except Liens permitted by Section 8.02 of the Indenture, and
(ii) to the best of Seller's knowledge, the balance of Seller's material
(individually or in the aggregate) Oil and Gas Properties (and/or those of the
Subsidiaries) that are described in the Mortgage or that are otherwise evaluated
in the most recently delivered Reserve Report, are free and clear (to the best
of Seller's knowledge) of all Liens except Liens permitted by Section 8.02 of
the Indenture.  Except for immaterial divergences, after giving full effect to
the Excepted Liens and the matters set forth in Schedule 4.10, the Seller or its
Subsidiaries own the net interests in production attributable to the Hydrocarbon
Interests that are both (A) evaluated in the most recently delivered Reserve
Report and (B) reflected in the Mortgage, and the ownership of such Hydrocarbon
Interests shall not in any material respect obligate the Seller or its
Subsidiaries to bear the costs and expenses relating to the maintenance,
development and operations of each such Hydrocarbon Interest in an amount in
excess of the working interest of such Hydrocarbon Interest set forth in the
Mortgage (without a corresponding increase in net revenue interest).  The Seller
does not believe, based upon information in its possession, that its most
recently delivered Reserve Report materially overstates its (or any
Subsidiaries) oil and gas reserves, bearing in mind that reserves are evaluated
based upon estimates and assumptions with respect to which reasonable minds of
competent reserve engineers may differ and that reserve estimates are affected
by the oil and gas prices used in the preparation thereof.

          (b)  All leases and agreements necessary for the conduct of the
business of the Seller and the Subsidiaries are valid and subsisting, in full
force and effect and there exists no default or event or circumstance which with
the giving of notice or the passage of time or both would give rise to a default
under any such lease or leases, which would affect in any material respect the
conduct of the business of the Seller and the Subsidiaries.

          (c)  The Properties presently owned, leased or licensed by the Seller
and the Subsidiaries, including, without limitation, all easements and rights of
way, include all Properties necessary to permit the Seller and the Subsidiaries
to conduct their business in all material respects in the same manner as its
business has been conducted prior to the Closing Date.

          (d)  All of the Properties of the Seller and the Subsidiaries which
are reasonably necessary for the operation of their business are in good working
condition in all material respects and are maintained in accordance with prudent
business standards.

     Section 4.11  NO MATERIAL MISSTATEMENTS.  Taken as a whole, the written
information, statements, exhibits, certificates, documents and reports furnished
to the Purchasers by the Seller or any Guarantor in connection with the
negotiation of this Agreement do not contain any material misstatement of fact
or omit to state a material fact or any fact necessary to make the statements
contained therein not materially misleading in the light of the circumstances in
which made and with respect to the Seller or any Guarantor.  As of the Closing
Date, there is no fact peculiar to the Seller or any Guarantor which has a
Material Adverse Effect or in the future is reasonably likely to have 

                                      -16-
<PAGE>   21
 
(so far as the Seller can now foresee) a Material Adverse Effect and which has
not been set forth in this Agreement or the other documents, certificates and
statements furnished to the Purchasers by or on behalf of the Seller or any
Guarantor prior to, or on, the Closing Date in connection with the transactions
contemplated hereby.

     Section 4.12  INVESTMENT COMPANY ACT.  Neither the Seller nor any
Subsidiary is an "investment company" or a company "controlled" by an
"investment company," within the meaning of the Investment Company Act of 1940,
as amended.

     Section 4.13  PUBLIC UTILITY HOLDING COMPANY ACT.  Neither the Seller
nor any Subsidiary is a "holding company," or a "subsidiary company" of a
"holding company," or an "affiliate" of a "holding company" or of a "subsidiary
company" of a "holding company," or a "public utility" within the meaning of the
Public Utility Holding Company Act of 1935, as amended.

     Section 4.14  SUBSIDIARIES.  Except as set forth on Schedule 4.14, the
Seller has no Subsidiaries or any direct or indirect ownership interest in any
other Persons.  Schedule 4.14 sets forth the ownership interest of the Seller
(direct or indirect) in and to all such Persons.

     Section 4.15  LOCATION OF BUSINESS AND OFFICES.  As of the Closing Date,
the Seller's principal place of business and chief executive offices are located
at the address stated in Section 12.06.  The principal place of business and
chief executive office of each Subsidiary are located at the addresses stated on
Schedule 4.14.

     Section 4.16  DEFAULTS.  Neither the Seller nor any Subsidiary is in
default nor has any event or circumstance occurred which, but for the expiration
of any applicable grace period or the giving of notice, or both, would
constitute a default under any material agreement or instrument to which the
Seller or any Subsidiary is a party or by which the Seller or any Subsidiary is
bound which default would have a Material Adverse Effect.  No Default hereunder
has occurred and is continuing.  No "Event of Default" under the Senior Loan
Documents has occurred and is continuing nor has Seller or any of its
Subsidiaries received any notice of a "Default" under the Senior Loan Documents
that has triggered a cure period.

     Section 4.17  ENVIRONMENTAL MATTERS.  Except as provided in Schedule
4.17 or  for matters which are more likely than not to not to have a Material
Adverse Effect (or with respect to (c), (d) and (e) below, where the failure to
take such actions is more likely than not to not have a Material Adverse
Effect):

          (a)  Neither any Property of the Seller or any of its Subsidiaries nor
the operations conducted thereon violate any order or requirement of any court
or Governmental Authority or any Environmental Laws;

          (b)  Without limitation of clause (a) above, no Property of the Seller
or any of its Subsidiaries nor the operations currently conducted thereon or, to
the best knowledge of the Seller, by any prior owner or operator of such
Property or operation, are in violation of or subject to any 

                                      -17-
<PAGE>   22
 
existing, pending or threatened action, suit, investigation, inquiry or
proceeding by or before any court or Governmental Authority or to any remedial
obligations under Environmental Laws;

          (c)  All notices, permits, licenses or similar authorizations, if any,
required to be obtained or filed by the Seller or any of its Subsidiaries in
connection with the operation or use of any and all Property of the Seller and
each of its Subsidiaries, including without limitation present, or to the best
of Seller's knowledge, past treatment, storage, disposal or release of a
hazardous substance or solid waste into the environment, have been duly obtained
or filed, and the Seller and each Subsidiary thereof are in compliance with the
terms and conditions of all such notices, permits, licenses and similar
authorizations;

          (d)  All hazardous substances, solid waste, and oil and gas
exploration and production wastes, if any, generated at any and all Property of
the Seller and each of its Subsidiaries have in the past, during Seller's or its
Subsidiaries' tenure of ownership and to the best of Seller's knowledge, prior
thereto, been transported, treated and disposed of in accordance with
Environmental Laws and so as not to pose an imminent and substantial
endangerment to public health or welfare or the environment, and, to the best
knowledge of the Seller, all such transport carriers and treatment and disposal
facilities have been and are operating in compliance with Environmental Laws and
so as not to pose an imminent and substantial endangerment to public health or
welfare or the environment, and are not the subject of any existing, pending or
threatened action, investigation or inquiry by any Governmental Authority in
connection with any Environmental Laws;

          (e)  The Seller has taken all steps reasonably necessary to determine
and has determined that no hazardous substances, solid waste, or oil and gas
exploration and production wastes, have been disposed of or otherwise released
and there has been no threatened release of any hazardous substances on or to
any Property of the Seller or any of its Subsidiaries except in compliance with
Environmental Laws and so as not to pose an imminent and substantial
endangerment to public health or welfare or the environment;

          (f)  To the extent applicable, all Property of the Seller and each of
its Subsidiaries currently satisfies all design, operation, and equipment
requirements imposed by the OPA or scheduled as of the Closing Date to be
imposed by OPA during the term of this Agreement, and the Seller does not have
any reason to believe that such Property, to the extent subject to OPA, will not
be able to maintain compliance with the OPA requirements during the term of this
Agreement; and

          (g)  Neither the Seller nor any of its Subsidiaries has any known
contingent liability in connection with any release or threatened release of any
oil, hazardous substance or solid waste into the environment.

     Section 4.18  COMPLIANCE WITH THE LAW.  Neither the Seller nor any
Subsidiary has violated any Governmental Requirement or failed to obtain any
license, permit, franchise or other governmental authorization necessary for the
ownership of any of its Properties or the conduct of its business, which
violation or failure would have (in the event such violation or failure were

                                      -18-
<PAGE>   23
 
asserted by any Person through appropriate action) a Material Adverse Effect.
Except for such acts or failures to act as would not have a Material Adverse
Effect, the Oil and Gas Properties (and properties unitized therewith) of the
Seller and its subsidiaries have been maintained, operated and developed in a
good and workmanlike manner and in conformity with all applicable laws and all
rules, regulations and orders of all duly constituted authorities having
jurisdiction and in conformity with the provisions of all leases, subleases or
other contracts comprising a part of the Hydrocarbon Interests and other
contracts and agreements forming a part of such Oil and Gas Properties;
specifically in this connection, but subject to the Material Adverse Effect
qualification set forth above, (i) after the Closing Date, no such Oil and Gas
Property is subject to having allowable production reduced below the full and
regular allowable (including the maximum permissible tolerance) because of any
overproduction (whether or not the same was permissible at the time) prior to
the Closing Date and (ii) none of the wells comprising a part of such Oil and
Gas Properties (or properties unitized therewith) are deviated from the vertical
more than the maximum permitted by applicable laws, regulations, rules and
orders, and such wells are, in fact, bottomed under and are producing from, and
the well bores are wholly within, such Oil and Gas Properties (or in the case of
wells located on properties unitized therewith, such unitized properties).

     Section 4.19  INSURANCE.  Schedule 4.19 attached hereto contains an
accurate and complete description of all material policies of fire, liability,
workmen's compensation and other forms of insurance owned or held by the Seller
and each Subsidiary as of the Closing Date.  All such policies are in full force
and effect, all premiums with respect thereto covering all periods up to and
including the Closing Date have been paid, and no notice of cancellation or
termination has been received with respect to any such policy.  Such policies
are sufficient for compliance with all requirements of law and of all agreements
to which the Seller or any Subsidiary is a party; are valid, outstanding and
enforceable policies; provide adequate insurance coverage in at lease such
amounts and against at least such risks (but including in any event public
liability) as are usually insured against in the same general area by companies
engaged in the same or a similar business for the assets and operations of the
Seller and each Subsidiary; will remain in full force and effect through the
respective dates set forth on Schedule 4.19 without the payment of additional
premiums; and will not in any way be affected by, or terminate or lapse by
reason of, the transactions contemplated by this Agreement.  Schedule 4.19
identifies all material risks, if any, which the Seller, the Subsidiaries and
their respective board of directors or officers have designated as being self
insured.  Neither the Seller nor any Subsidiary has been refused any insurance
with respect to its assets or operations, nor has its coverage been limited
below usual and customary policy limits, by an insurance carrier to which it has
applied for any such insurance or with which is has carried insurance during the
last three years.

     Section 4.20  HEDGING AGREEMENTS.   Schedule 4.20 sets forth, as of the
Closing Date, a true and complete list of all Hedging Agreements (including
commodity price swap agreements, forward agreements or contracts of sale which
provide for prepayment for deferred shipment or delivery of oil, gas or other
commodities) of the Seller and each Subsidiary, the material terms thereof
(including the type, term, effective date, termination date and notional amounts
of volumes), the net mark to market value thereof, all credit support agreements
relating thereto (including any margin required or supplied), and the
counterparty to each such agreement.

                                      -19-
<PAGE>   24
 
     Section 4.21  RESTRICTION ON LIENS.  Neither the Seller nor any
Subsidiary is a party to any agreement or arrangement (other than the Loan
Documents and the Senior Loan Documents), or subject to any order, judgment,
writ or decree, which either restricts or purports to restrict ability to grant
Liens to other Persons on or in respect of their respective assets or
Properties.

     Section 4.22  MATERIAL AGREEMENTS.  Set forth on Schedule 4.22 hereto is
a complete and correct list of all material agreements, leases, indentures,
purchase agreements, obligations in respect of letters of credit, guarantees,
joint venture agreements, and other instruments in effect or to be in effect as
of the Closing Date (other than the Senior Loan Documents and Hedging
Agreements) providing for, evidencing, securing or otherwise relating to any
material Debt of the Seller or any Subsidiary, and all obligations of the Seller
or any Subsidiary to issuers of surety or appeal bonds (excluding operator's
bonds, plugging and abandonment bonds, and similar surety obligations obtained
in the ordinary course of business) issued for account of the Seller or any such
Subsidiary, and such list correctly set forth the names of the debtor or lessee
and creditor or lessor with respect to the Debt or lease obligations outstanding
or to be outstanding and the property subject to any Lien securing such Debt or
lease obligations.

     Section 4.23  GAS IMBALANCES.  As of the Closing Date, except as set
forth in the most recent Reserve Report furnished to the Purchasers or on
Schedule 4.23, on a net basis there are no gas imbalances, take or pay or other
prepayments with respect to the Seller's or any Subsidiary's Hydrocarbon
Interests which would require the Seller or such Subsidiary to deliver five
percent (5%) or more of the monthly production from the Seller's and its
Subsidiaries' Hydrocarbons produced on a monthly basis from the Hydrocarbon
Interests, at some future time without then or thereafter receiving full payment
therefor.

     Section 4.24  CAPITALIZATION.  The authorized Capital Stock of the
Seller consists of: (a) 30,000,000 shares of Common Stock, par value $.01 per
share and (b) 10,000,000 shares of Preferred Stock, par value $.01 per share, of
which there are issued and outstanding 12,253,574 shares of Common Stock and no
other shares of Capital Stock.  All outstanding shares of Common Stock are
validly issued, fully paid and nonassessable and were issued free of preemptive
rights.  Except as set forth on Schedule 4.24, the Seller is not a party to any
voting trust or other agreement with respect to the voting of its Capital Stock.
Except for the Warrants, there are no (i) outstanding securities convertible or
exchangeable into Capital Stock of the Seller or (ii) warrants, contracts,
commitments, agreements, understandings, or arrangements of any kind to which
the Seller is a party relating to the repurchase or issuance of any Capital
Stock.  Except as set forth on Schedule 4.24 and except as contemplated in the
Equity Documents, the Seller is not a party to or bound by any agreement with
respect to any of its securities which grants registration rights to any Person.

     Section 4.25  ACQUIRED SHARES.  When issued and delivered against
payment therefor in accordance with the terms of this Agreement, the Acquired
Shares will be duly and validly issued, fully paid, nonassessable, free of
preemptive rights and free from all taxes payable by the Seller and Liens
(except any Liens created or suffered to be created by the Purchasers) and will
not be subject to any restriction on the voting or transfer thereof created by
the Seller other than in the Equity Documents and the applicable provisions of
federal and state securities laws.

                                      -20-
<PAGE>   25
 
     Section 4.26  WARRANT SHARES.  When issued and delivered against
payment therefor in accordance with the terms of the Warrants, the Warrant
Shares issuable upon exercise of the Warrants will be duly and validly issued,
fully paid, nonassessable, free of preemptive rights and free from all taxes
payable by the Seller and Liens (except any Liens created or suffered to be
created by the Purchasers) and will not be subject to any restriction on the
voting or transfer thereof created by the Seller other than in the Equity
Documents and the applicable provisions of federal and state securities laws.
The Seller has duly and validly reserved the Warrant Shares, as of the Closing
Date, for issuance upon conversion of the Warrants.

     Section 4.27  NO RESTRICTIONS.  The Seller currently is not, and in the
future will not, be subject to any agreements that purport to impose
restrictions or limitations on the Purchasers, as affiliates of the Seller or
otherwise, without the prior written consent and authorization of each of the
Purchasers.

     Section 4.28  CERTAIN FEES.  Except for the fees payable to ECT
Securities Corp. and JEDI-II pursuant to the Structuring Fee Agreement, no fees
or commissions will be payable by the Seller to brokers, finders, investment
bankers, or Purchasers with respect to the issuance and sale of any of the
Securities or the consummation of the transaction contemplated by this
Agreement.  The Seller agrees that it will indemnify and hold harmless the
Purchasers from and against any and all claims, demands, or liabilities for
broker's, finders, placement, or other similar fees or commissions incurred by
the Seller or alleged to have been incurred by the Seller in connection with the
issuance or sale of the Securities or the consummation of the transaction
contemplated by this Agreement.

                                   ARTICLE V
               REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS

     The Purchasers each represent and warrant to the Seller, which
representations and warranties shall survive the execution of any Basic
Document, that as of the date of this Agreement:

     Section 5.01  INVESTMENT.  Each Purchaser represents and warrants to, and
covenants and agrees with, the Seller that the Securities are being acquired for
its own account and with no intention of distributing or reselling the Notes,
the Warrants, the Warrant Shares or the Acquired Shares in any transaction which
would be in violation of the securities laws of the United States of America or
any State, without prejudice, however, to Purchaser's right at all times to sell
or otherwise dispose of all or any part of the Notes, the Warrants, the Warrant
Shares or the Acquired Shares under a registration statement under the
Securities Act and applicable state securities laws or under an exemption from
such registration available thereunder (including, without limitation, if
available, Rule 144A promulgated thereunder).  If either Purchaser should in the
future decide to dispose of any of the Notes, the Warrants, the Warrant Shares
or the Acquired Shares, the Purchasers understand and agree (i) that it may do
so only (A) in compliance with the Securities Act and applicable state
securities law, as then in effect, and (B) in the manner contemplated by any
registration statement pursuant to which such securities are being offered, and
(ii) that stop-transfer instructions to that effect will be in effect with
respect to such securities.  The Purchasers agree to 

                                      -21-
<PAGE>   26
 
the imprinting, so long as appropriate, of a legend on each Note and on each
certificate representing Warrants, Warrant Shares or the Acquired Shares, to the
effect as set forth above.

     Section 5.02  NATURE OF PURCHASERS.  Each Purchaser represents and
warrants to, and covenants and agrees with, the Seller that, (i) it is an
"accredited investor" within the meaning of paragraphs (a)(3) or (8) of Rule 501
under the Securities Act and (ii) by reason of its business and financial
experience it has such knowledge, sophistication and experience in business and
financial matters so as to be capable of evaluating the merits and risks of the
prospective investment in the Securities, is able to bear the economic risk of
such investment and, at the present time, would be able to afford a complete
loss of such investment.

     Section 5.03  RECEIPT OF INFORMATION; AUTHORIZATION.  Each Purchaser
acknowledges that it has been furnished all information that it deems necessary
or desirable to the making of an informed investment decision concerning the
Securities.  Each Purchaser acknowledges that it has had an opportunity to ask
questions of and receive satisfactory answers from designated representatives of
the Seller concerning the terms and conditions pursuant to which the purchase of
the Securities are made.  Each Purchaser acknowledges that it has been afforded
an opportunity to examine such documents and other information which it has
requested for the purpose of verifying the information provided to it and for
the purpose of answering any questions it may have concerning the business
affairs and financial condition of the Seller.  Each Purchaser represents that
it alone or with its advisors has knowledge and experience in the business of
the Seller and the Seller so as to be capable of evaluating the merits and risks
of an investment in the Seller based upon the information furnished to it, its
knowledge of the business and affairs of the Seller, the records, files, and
plans of the Seller (which have been made available to it), such additional
information as it has requested and has received from the Seller, and the
independent inquiries and investigations undertaken by it.  Each Purchaser
represents and warrants that the purchase of the Securities by it has been duly
and properly authorized and this Agreement and each Basic Document to which the
Purchasers are a signatory has been duly executed and delivered by it or on its
behalf.

                                  ARTICLE VI
                        CONDITIONS PRECEDENT TO FUNDING

     Section 6.01  CONDITIONS PRECEDENT TO OBLIGATIONS OF THE PURCHASERS.  The
obligation of the Purchasers to acquire the Securities on the Funding Date is
subject to each of the following:

          (a)  The accuracy as of the Closing Date of each and every
representation and warranty of the Seller, each Guarantor, and the Senior Loan
Agent made in this Agreement or any other Basic Document, or in any certificate
delivered to the Purchasers pursuant to or in connection with this Agreement,
and receipt by the Purchasers of a Certificate executed by a duly Responsible
Officer, dated as of the Funding Date, certifying that each of the
representations and warranties of the Seller and each Guarantor made in this
Agreement or any other Basic Document are true and correct as of the Funding
Date, and that the Seller and each Guarantor has performed to date all of its
respective covenants and agreements under the Basic Documents.

                                      -22-
<PAGE>   27
 
          (b)  The absence as of the Closing Date and the Funding Date of a
Default or Event of Default hereunder or an "Event of Default" under the Senior
Credit Agreement or any Default hereunder the Senior Loan Documents that has
triggered a cure period.

          (c)  The performance by the Seller of its respective obligations to be
performed hereunder on or before the Funding Date.

          (d)  The satisfaction of each of the following conditions as of or
prior to the Closing Date:

               (i)   The Purchasers (or the Trustee, where appropriate) shall
     have received the following, each in form and substance satisfactory to the
     Purchasers and in sufficient counterparts:

                     (A)   Duly executed counterparts of this Agreement and the
          Indenture signed by all the parties hereto and thereto.

                     (B)   The duly executed Financing Agreement, Structuring
          Fee Agreement, Guaranty Agreements, Subordination Agreement and
          Registration Rights Agreement, dated as of the Closing Date in form
          and substance satisfactory to Purchasers.

                     (C)   Duly executed counterparts of the Collateral
          Documents (including without limitation UCC-1 Financing Statements).

                     (D)   Certificates of good standing as to the Seller and
          each Guarantor issued by the Secretary of State of their respective
          states of incorporation or formation.

                     (E)   The duly executed certificate of the Secretary of the
          Seller setting forth (i) resolutions of its directors in form and
          substance satisfactory to the Purchasers with respect to the
          authorization of this Agreement and the other Basic Documents to which
          it is a party and the transactions contemplated hereby and thereby;
          (ii) the names and true signatures of the officers authorized to sign
          such instruments; and (iii) copies of the articles or certificate of
          incorporation and the bylaws of the Seller.

                     (F)   The duly executed certificate of the Secretary of
          each Guarantor which is a corporation setting forth (i) resolutions of
          its directors in form and substance satisfactory to the Purchasers
          with respect to the authorization of the Guaranty Agreements executed
          by such Guarantors and the transactions contemplated hereby and
          thereby; (ii) the names and true signatures of the officers authorized
          to sign such instruments; and (iii) copies of the articles or
          certificate of incorporation and the bylaws of each Guarantor.

                                      -23-
<PAGE>   28
 
                     (G)   The duly executed certificate of all the partners of
          each Guarantor that is a Partnership and each member of each Guarantor
          that is a limited liability company, setting forth (i) the
          authorization of the Guaranty Agreements and the transactions
          contemplated hereby and thereby; (ii) the names and title of all
          persons authorized to sign such instruments; and (iii) copies of the
          applicable partnership agreement or other regulating documents of each
          such Guarantor.

                     (H)   Evidence that the insurance required hereunder and
          under the other Basic Documents has been obtained and is in full force
          and effect.

                     (I)   Copies of the Senior Loan Documents.

                     (J)   Any other document which the Purchasers may
          reasonably request, including opinions addressed to Purchasers, dated
          as of the Closing Date, from the counsel for the Seller and each of
          the Guarantors acceptable to each of the Purchasers addressing the
          existence and good standing of the Seller, the authorization of the
          Basic Documents, the enforceability of the Basic Documents, the
          absence of conflicts with law, other material agreements, and court
          orders, the absence of litigation, and such other matters as the
          Purchasers may reasonably request.

               (ii)  The Seller shall have executed (but not delivered) the
     Notes, Warrants and Acquired Shares, each in form and substance
     satisfactory to the Purchasers.

               (iii) The Seller shall have received consents to the Basic
     Documents by the Senior Lenders; and the Senior Loan Documents shall have
     been amended in form and substance reasonably satisfactory to Purchasers to
     permit the transactions contemplated by the Loan Documents, including the
     payment of dividends or other distributions by Subsidiaries to the Seller
     in order for the Seller to meet its debt service obligations to the
     Purchasers under the Notes.

               (iv)  The Purchasers shall have completed a due diligence review
     of the Seller and the Subsidiaries to the satisfaction of the Purchasers in
     their sole discretion.

               (v)   The Purchasers shall have received the latest internally
     prepared consolidated financial statements of the Seller and its
     Subsidiaries which shall be at least through June 30, 1998.  Since June 30,
     1998, there shall have occurred no event which could have a Material
     Adverse Effect.

               (vi)  The Board of Directors of each of the Seller, the
     Guarantors, the Purchasers and Enron Corp. must have approved the
     transactions contemplated under this Agreement and the other Basic
     Documents.

               (vii) All other consents, including without limitation any
     required shareholder approval, and waivers necessary to complete the
     transactions under this 

                                      -24-
<PAGE>   29
 
     Agreement and the other Basic Documents shall have been obtained by the
     Seller, the Guarantors and the Purchasers.

          (e)  The Warrants Shares and the Acquired Shares shall have been
approved for listing on NASDAQ and the registration statement on Form S-1
registering the Notes, the Warrants, and the Acquired Shares shall have been
declared effective by the Commission and no stop order with respect thereto
shall have been issued.

          (f)  The Seller shall have delivered to the Purchasers the executed
Notes, Warrants and Acquired Shares.

          (g)  The Mortgages shall have been filed in two counties of 
Purchasers's choice.

          (h)  The Seller shall have paid to ECT Securities Corp. and JEDI-II
all payments required under the terms of the Structuring Fee Agreement.

          (i)  If requested in writing by either of the Purchasers, a Designee
of the Purchasers shall have been appointed to the Board of Directors of the
Seller pursuant to Section 7.03.

          (j)  The Seller shall have duly and validly reserved the Warrant
Shares for issuance upon conversion of the Warrants.

          (k)  The issuance of the Securities by the Seller shall not as of the
Funding Date be enjoined (temporarily or permanently) under the laws of any
jurisdiction to which the Seller is subject.

          (l)  Each of the Basic Documents shall have been executed and
delivered by all the respective parties thereto and shall be in full force and
effect.

     Section 6.02  CONDITIONS PRECEDENT TO OBLIGATIONS OF THE SELLER.  The
obligations of the Seller to issue and sell Securities hereunder is subject, on
the Funding Date, to the prior or simultaneous satisfaction or waiver of the
following conditions:

          (a)  The representations and warranties made by the Purchasers herein
shall be true and correct in all respects on and as of the Funding Date with the
same effect as though such representations and warranties had been made on and
as of the Funding Date.

          (b)  The Purchasers shall have accepted delivery of and made payment
for the Securities.

          (c)  The issuance of the Securities by the Seller shall not as of the
Funding Date be enjoined (temporarily or permanently) under the laws of any
jurisdiction to which the Seller is subject.

                                      -25-
<PAGE>   30
 
          (d)  Each of the Basic Documents shall have been executed and
delivered by all the respective parties thereto and shall be in full force and
effect.

     Section 6.03  CONDITIONS PRECEDENT TO THE OBLIGATIONS OF PURCHASERS AND 
SELLER.  The obligations of the Purchasers and Seller hereunder are contingent
upon the Funding Date  occurring on or before 5:00 p.m., Houston, Texas time on
September 1, 1998.

                                  ARTICLE VII
                             AFFIRMATIVE COVENANTS

     Unless the prior written consent to the contrary is obtained from (i) the
holders of the majority of the Warrants (as to Sections 7.01 and 7.02) and (ii)
ECT (as to Sections 7.03 and 7.04) the Seller will, for the benefit of each of
the holders of the Warrants or Warrant Shares and the holders of the Acquired
Shares, comply with the covenants contained in this Article VII (or cause each
Subsidiary's compliance with the applicable covenants).

     Section 7.01  WARRANTS.  Seller shall at all times during the term of
the Warrants maintain a sufficient number of shares of Common Stock of the
Seller to be issued as Warrant Shares upon the exercise of all or part of the
Warrants.  Seller shall (i) notify the holders of the Warrants promptly after
the exercise of any of the Warrants by a holder or holders thereof, of the
exercise thereof, (ii) provide to the holders of the Warrants such information
or materials in connection therewith as may be reasonably requested by the
holders of the Warrants, and (iii) otherwise provide to all the holders of the
Warrants copies of all notices provided to or from the Seller in connection with
the Warrants.  Seller's obligations under this Section 7.01 shall expire upon
expiration of the term of the Warrants.

     Section 7.02  HART-SCOTT-RODINO COMPLIANCE.  As soon as practicable
after the receipt from any holder of the Warrants or any Seller (the "Notice
Giver") of notice of the exercise of a number of Warrants sufficient to require
a filing under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 and the
rules, regulations and formal interpretations thereunder, as amended from time
to time (the "HSR Act"), but in any event no later than the 10th Business Day
after receipt of such notice, the Seller will (i) prepare and file with the
Antitrust Division of the Department of Justice (the "DOJ") and the Federal
Trade Commission (the "FTC") the Notification and Report Form (accompanied by
all documentary attachments contemplated thereby) required by the HSR Act, (ii)
upon the request of any holder of the Warrants (the "Notice Giver"), request
early termination of the waiting period imposed by the HSR Act, (iii) coordinate
and cooperate with the Notice Giver in responding to formal and informal
requests for additional information and documentary material from the DOJ and
the FTC in connection with such filing, and (iv) use its best efforts to take,
or cause to be taken, all reasonable action and to do, or cause to be done, all
things reasonably necessary and appropriate to permit the issuance to the Notice
Giver of the shares of common stock issuance upon the exercise of the warrants
with respect to which any filing is required under the HSR Act, and (v)
reimburse the holders of the Warrants for the entire amount of any filing fee or
any other costs and expenses incurred by holders of the Warrants in connection
therewith (including legal fees), or as required to be paid under the HSR Act.
Seller's obligations under this Section 7.02 shall expire one (1) year following
the expiration of the term of the Warrants.

                                      -26-
<PAGE>   31
 
     Section 7.03  BOARD REPRESENTATION.  ECT or its designated Affiliate
(the "Acting Party") shall have the right (a) to designate one member of the
Board of Directors of the Seller or (b) (i) to receive (and Seller covenants and
agrees to deliver to the Acting Party) prior notice of any proposed board action
and to receive (and Seller covenants and agrees to deliver to the Acting Party)
reasonable notice of and a right to attend any meeting of the Seller's Board of
Directors, (ii) to receive (and Seller covenants and agrees to deliver to the
Acting Party), promptly after they are produced, all management reports and
accounts relating to the Seller that are provided to Seller's Board of Directors
or any committee of the Board of Directors and (iii) upon reasonable notice, to
have reasonable access to the books and records of the Seller, including
statutory books, minute books and customer lists.  In the event the Acting Party
elects to designate a person to serve as a member of the Board of Directors of
the Seller (the "Designee"), the Seller shall (x) expand as required the number
of directors constituting the entire board, (y) fill the vacancy created by such
expansion with such Designee and (z) submit the name of such Designee to the
stockholders of the Seller (together with a recommendation of his or her
election) at each meeting of stockholders at which directors are elected, until
requested otherwise by the Acting Party. The obligations of the Seller pursuant
to this Section 7.03 shall continue in full force and effect for so long as the
ECT and JEDI-II and/or their respective Affiliates beneficially own 5% or more
of the outstanding Common Stock of the Seller (including the Warrant Shares
represented by the Warrants, whether exercised or not).  Any Designee shall
agree to resign at the request of the Seller, at any time after the expiration
of the rights of the ECT and any Acting Party pursuant to this Section 7.03.
The rights of ECT under this Section 7.03 shall not be assignable other than to
an Affiliate of ECT.

     Section 7.04  COMMON STOCK; DIVIDENDS; VOTING RIGHTS.  The declaration
of dividends by the Seller shall be solely at the discretion of the Board of
Directors of the Seller.  Except for holders of Common Stock, no other class of
Capital Stock of the Seller shall have any voting rights whatsoever, either
separately or in conjunction with the Common Stock.  Seller's obligations under
this Section 7.04 shall expire upon payment of the Notes in full.


                                 ARTICLE VIII
                        [OMITTED BY THE PARTIES HERETO]


                                  ARTICLE IX
                        [OMITTED BY THE PARTIES HERETO]


                                   ARTICLE X
                        [OMITTED BY THE PARTIES HERETO]


                                  ARTICLE XI
                        [OMITTED BY THE PARTIES HERETO]

                                      -27-
<PAGE>   32
 
                                  ARTICLE XII
                                 MISCELLANEOUS

     Section 12.01.  INTERPRETATION AND SURVIVAL OF PROVISIONS.  Article,
Section, Schedule, and Exhibit references are to this Agreement, unless
otherwise specified.  All references to instruments, documents, contracts, and
agreements are references to such instruments, documents, contracts, and
agreements as the same may be amended, supplemented, and otherwise modified from
time to time, unless otherwise specified.  The word "including" shall mean
"including but not limited to."  Whenever the Seller has an obligation under the
Basic Documents, the expense of complying with that obligation shall be an
expense of the Seller unless otherwise specified.  Whenever any determination,
consent, or approval is to be made or given by the Purchasers, any holder of the
Warrants or the Acquired Shares, such action shall be in such Person's sole
discretion unless otherwise specified in this Agreement.  If any provision in
the Basic Documents is held to be illegal, invalid, not binding, or
unenforceable, such provision shall be fully severable and the Basic Documents
shall be construed and enforced as if such illegal, invalid, not binding, or
unenforceable provision had never comprised a part of the Basic Documents, and
the remaining provisions shall remain in full force and effect.  The Basic
Documents have been reviewed and negotiated by sophisticated parties with access
to legal counsel and shall not be construed against the drafter.  The
representations, warranties, and covenants made in this Agreement, the Notes or
any other Basic Document shall remain operative and in full force and effect
regardless of (a) any investigation made by or on behalf of the Seller or the
Purchasers or (b) acceptance of any of the Securities and payment therefor and
repayment or repurchase thereof.  All indemnification obligations of the Seller
and the provisions of Section 12.02 shall remain operative and in full force and
effect unless such obligations are expressly terminated in a writing referencing
those individual Sections, regardless of any purported general termination of
this Agreement.

     Section 12.02  COSTS, EXPENSES AND TAXES. 

          (a)   Intentionally Deleted.

          (b)   The Seller agrees to indemnify the Purchasers, and their
respective officers, directors, employees, representatives, agents, attorneys,
and Affiliates (collectively, "Related Parties") from, hold each of them
harmless against and promptly upon demand pay or reimburse each of them for, any
and all actions, suits, proceedings (including any investigations, litigation,
or inquiries), claims, demands, and causes of action by third parties, and, in
connection therewith, all reasonable costs, losses, liabilities, damages, or
expenses of any kind or nature whatsoever (collectively the "INDEMNITY MATTERS")
which may be incurred by or asserted against or involve any of them (whether or
not any of them is designated a party thereto) as a result of, arising out of,
or in any way related to (i) any actual or proposed use by the Seller of the
proceeds of any sale of the Securities, (ii) the operations of the business of
the Seller or any Subsidiary, (iii) any bodily injury or death or property
damage occurring in or upon or in the vicinity of any Collateral, (iv) any claim
by any third Person against any Collateral assigned to or paid to any Noteholder
pursuant to any Collateral Document, (v) the failure of the Seller or any
Subsidiary to comply with any Governmental Requirement, or (vi) any other aspect
of this Agreement and the other Basic 

                                      -28-
<PAGE>   33
 
Documents, including, without limitation, the reasonable fees and disbursements
of counsel and all other reasonable expenses incurred in connection with
investigating, defending or preparing to defend any such action, suit,
proceeding (including any investigations, litigation, or inquiries), or claim
and INCLUDING ALL INDEMNITY MATTERS ARISING BY REASON OF THE ORDINARY NEGLIGENCE
OF ANY INDEMNITEE (but excluding all Indemnity Matters arising solely by reason
of claims between the Purchasers or any Purchaser's shareholders against any
Purchaser or by reason of the gross negligence or wilful misconduct of any
Indemnitee).

          (c)  The Seller agrees to pay and hold the Purchasers harmless from
and against any and all present and future stamp and other similar taxes with
respect to this Agreement and the  Equity Documents and save the Purchasers
harmless from and against any and all liabilities with respect to or resulting
from any delay or omission to pay such taxes, and will indemnify the Purchasers
for the full amount of taxes paid by the Purchasers in respect of payments made
or to be made under this Agreement, any other Equity Document and any liability
(including penalties, interest, and expenses) arising therefrom or with respect
thereto, whether or not such taxes were correctly or legally asserted.

          (d)  In the case of any indemnification hereunder, the Purchaser or
other Person indemnified hereunder shall give notice to the Seller within a
reasonable period of time of any such claim or demand being made against the
Purchaser or other indemnified Person and the Seller, at its sole cost and
expense, shall provide a defense of such claim, provided, however, that, (i) if
the Seller has failed to assume the defense and employ counsel or (ii) if the
defendants in any such action include both the indemnified party and the Seller
or any Subsidiary and counsel to the indemnified party shall have concluded that
there may be reasonable defenses available to the indemnified party that are
different from or additional to those available to the Seller or such Subsidiary
or if the interests of the indemnified party reasonably may be deemed to
conflict with the interest of the Seller or such Subsidiary, then the
indemnified party shall have the right to select a separate counsel and to
assume such legal defense and otherwise to participate in the defense of such
action, with the expenses and fees of such separate counsel and other expenses
related to such participation to be reimbursed by the Seller as incurred.

          (e)  No indemnitee may settle any claim to be indemnified without the
consent of the indemnitor, such consent not to be unreasonably withheld;
provided, that the indemnitor may not reasonably withhold consent to any
settlement that an indemnitee proposes if the indemnitor does not have the
financial ability to pay all its obligations outstanding and asserted against
the indemnitee at that time, including the maximum potential claims against the
indemnitee to be indemnified pursuant to this Section 12.02.

          (f)  This Section 12.02 shall not apply to actions, suits,
proceedings, investigations, demands, losses, liabilities, claims, damages,
deficiencies, interest, judgements, costs, or expenses relating to any Property
to the extent arising from the acts or omissions of the Agent or any Noteholder
during the period after which such Person, its successors or assigns shall have
acquired possession of such Property (whether through foreclosure or deed in
lieu of foreclosure, as mortgagee in possession or otherwise).

                                      -29-
<PAGE>   34
 
          (g)  The Seller's obligations under this Section 12.02 shall survive
any termination of this Agreement and the payment of the Obligations.

     Section 12.03  NO WAIVER; MODIFICATIONS IN WRITING. 

          (a)  No failure or delay on the part of the Seller or the Purchasers
in exercising any right, power, or remedy hereunder shall operate as a waiver
thereof, nor shall any single or partial exercise of any such right, power, or
remedy preclude any other or further exercise thereof or the exercise of any
right, power, or remedy.  The remedies provided for herein are cumulative and
are not exclusive of any remedies that may be available to the Seller or the
Purchasers at law or in equity or otherwise.

          (b)  Except as otherwise provided herein, no amendment, waiver,
consent, modification, or termination of any provision of this Agreement, shall
be effective unless signed by the Seller and the holders of more than 50% of the
outstanding principal balance of the Notes and the holders of more than 50% of
the Warrants.  Any amendment, supplement or modification of or to any provision
of this Agreement or any other Equity Document, any waiver of any provision of
this Agreement or any other Equity Document, and any consent to any departure by
the Seller from the terms of any provision of this Agreement or any other Equity
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 this Agreement, no notice to or demand on the Seller in any case shall
entitle the Seller to any other or further notice or demand in similar or other
circumstances.

     Section 12.04  BINDING EFFECT; ASSIGNMENT.  This Agreement shall be
binding upon the Seller and the Purchasers, and their respective successors and
permitted assigns. Except as expressly provided in this Agreement, this
Agreement shall not be construed so as to confer any right or benefit upon any
Person other than the parties to this Agreement, and their respective successors
and permitted assigns.  Subject to applicable federal and state securities laws
the rights and obligations of the Purchasers under this Agreement with respect
to the Warrants and the Equity Documents may be sold, assigned or pledged by any
Purchaser, in whole or in part, in accordance with the provisions of the
Warrants, and upon any such assignment, the holders of the Warrants shall
succeed to all of the selling Purchaser's rights and obligations under this
Agreement with respect to the Warrants and the Equity Documents to the extent
assigned and the selling Purchaser shall be automatically released from any
obligations thereunder with respect to the Warrants and the Equity Documents to
the extent assigned.  Subject to applicable federal and state securities laws
the Acquired Shares may be sold, assigned or pledged subject only to the
Registration Rights Agreement and upon any such assignment the holders of the
Acquired Shares shall succeed to the Purchaser's rights and obligations under
the Registration Rights Agreement.  Upon request of any Purchaser in connection
with any transfer of the Warrants or Acquired Shares, the Seller shall execute
and deliver any amendment to this Agreement, the Warrants, and the other Equity
Documents reasonably requested by the Purchaser to reflect the transfer and
delineate the rights of the transferor and the transferee.

     Section 12.05  REPLACEMENT SECURITIES.  Upon receipt of evidence
satisfactory to the Seller of the loss, theft, destruction, or mutilation of any
Warrants, Warrant Shares or Acquired Shares and, 

                                      -30-
<PAGE>   35
 
in the case of any such loss, theft, or destruction, upon delivery of any
unsecured letter of indemnity reasonably satisfactory to the Seller or, in the
case of any such mutilation, upon surrender or cancellation thereof, the Seller
will issue a new Warrants, Warrant Shares or Acquired Shares, as applicable.

     Section 12.06  COMMUNICATIONS.  All notices and demands provided for
hereunder shall be in writing and shall be given by registered or certified
mail, return receipt requested, telecopy, air courier guaranteeing overnight
delivery or personal delivery to the following addresses:

     If to the Purchasers:

     Enron Capital Management II Limited Partnership
     c/o Enron Capital II Corp.
     1400 Smith Street
     Houston, Texas 77002
     Attention: Shirley Hudler
     Telecopier: (713) 646-8008

     and

     Enron Capital & Trade Resources Corp.
     1400 Smith Street
     Houston, Texas 77002
     Attention: Donna Lowry
     Telecopier: (713) 646-4039

     If to the Seller:

     6300 Bridge Point Parkway
     Building 2, Suite 500
     Austin, Texas 78730
     Attention: Craig M. Fleming
     Telecopier: (512) 472-3400

or to such other address as the Seller or any Purchaser may designate in
writing.  All other communications may be by regular mail.  All notices and
communications shall be deemed to have been duly given:  at the time delivered
by hand, if personally delivered; four days after being sent by certified mail,
return receipt requested, if mailed; when receipt acknowledged, if telecopied;
and on the next Business Day if timely delivered to an air courier guaranteeing
overnight delivery.

     Section 12.07  GOVERNING LAW.  This Agreement will be construed in
accordance with and governed by the laws of the State of Texas without regard to
principles of conflicts of laws.


                                      -31-
<PAGE>   36

     Section 12.08  ARBITRATION.
 
          (a)  BINDING ARBITRATION.  Subject to the provisions of subparagraph
(e), on the request of either the Seller or any Purchaser, whether made before
or after the institution of any legal proceeding, any action, dispute, claim or
controversy of any kind now existing or hereafter arising between any of the
parties hereto in any way arising out of, pertaining to or in connection with
this Agreement (a "Dispute") shall be resolved by binding arbitration in
accordance with the terms hereof.  Either the Seller or any Purchaser may, by
summary proceedings, bring an action in court to compel arbitration of any
Dispute.

          (b)  GOVERNING RULES.  Any arbitration shall be administered by the
American Arbitration Association (the "AAA") in accordance with the terms of
this Section, the Commercial Arbitration Rules of the AAA, and, to the maximum
extent applicable, the Federal Arbitration Act.  Judgment on any award rendered
by an arbitrator may be entered in any court having jurisdiction.

          (c)  ARBITRATORS.  Any arbitration shall be conducted before a three
person panel of neutral arbitrators. Such panel shall consist of one person from
each of the following categories: (1) an attorney who has practiced in the area
of commercial law for at least 10 years or a retired judge at the Texas or
United States District Court or an appellate court level; (2) a person with at
least 10 years experience in commercial lending; and (3) a person with at least
10 years experience in the energy service industry. The AAA shall submit a list
of persons meeting the criteria outlined above for each category of arbitrator,
and the parties shall select one person from each category in the manner
established by the AAA. If the parties cannot agree on an arbitrator within 30
days after the request for an arbitration, then any party may request the AAA to
select an arbitrator. The arbitrator may engage engineers, accountants or other
consultants that the arbitrator deems necessary to render a conclusion in the
arbitration proceeding.

          (d)  CONDUCT OF ARBITRATION.  To the maximum extent practicable, an
arbitration proceeding hereunder shall be concluded within 180 days of the
filing of the Dispute with the AAA.  Arbitration proceedings shall be conducted
in Houston, Texas.  At the conclusion of any arbitration proceeding, the
arbitrator shall make specific written findings of fact and conclusions of law.
The arbitrator shall have the power to award recovery of all costs and fees to
the prevailing party.  The Seller and the Purchasers each agree to keep all
Disputes and arbitration proceedings strictly confidential except for disclosure
of information required by applicable law.

          (e)  COSTS OF ARBITRATION.  All fees of the arbitrator and any
engineer, accountant or other consultant engaged by the arbitrator, shall be
paid by the Seller (as to 50%) and the Purchasers (as to 50%) unless otherwise
awarded by the arbitrator.

     Section 12.09  EXECUTION IN COUNTERPARTS.  This Agreement may be executed
in any number of counterparts and by different parties hereto in separate
counterparts, each of which counterparts, when so executed and delivered, shall
be deemed to be an original and all of which counterparts, taken together, shall
constitute but one and the same Agreement.

                                      -32-
<PAGE>   37
 
          IN WITNESS WHEREOF, the parties hereto execute this Agreement,
effective as of the date first above written.

                              BRIGHAM EXPLORATION COMPANY,
                              a Delaware corporation



                              By:  /s/ CRAIG M. FLEMING
                                  ---------------------------------------------
                                    Craig M. Fleming
                                    Chief Financial Officer

                                      -33-
<PAGE>   38
 
                              JOINT ENERGY DEVELOPMENT
                              INVESTMENTS II LIMITED PARTNERSHIP,
                              a Delaware limited partnership, as Purchaser


                              By:  Enron Capital Management II Limited
                                   Partnership, its General Partner

                                  By:  Enron Capital II Corp., its
                                       General Partner


                                         By: /s/ MARK J. WARNER
                                             ----------------------------------
                                         Name:   Mark J. Warner
                                               --------------------------------
                                         Title:  Agent and Attorney-in-Fact
                                                -------------------------------


                              ENRON CAPITAL & TRADE RESOURCES
                              CORP., a Delaware corporation



                              By: /s/ MARK J. WARNER
                                  --------------------------------------------
                              Name:   Mark J. Warner
                                    ------------------------------------------
                              Title:  Agent and Attorney-in-Fact
                                     -----------------------------------------

                                      -34-