Document:

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                                                                   EXHIBIT 10.10

                                                                  EXECUTION COPY

                               SECOND AMENDMENT TO
                    INTERCREDITOR AND SUBORDINATION AGREEMENT

                  This Second Amendment to Intercreditor and Subordination
Agreement (this "Amendment") is dated as of February 17, 2000 by and among ECT
Merchant Investments Corp., a Delaware corporation ("ECT Merchant"), Joint
Energy Development Investments II Limited Partnership, a Delaware limited
partnership ("JEDI-II," and, together with ECT Merchant, the "Subordinated
Lender"), and JEDI-II, as agent for the Subordinated Lender (in such capacity,
the "Subordinated Agent"), and Bank of Montreal, as agent (in such capacity, and
together with any successor in such capacity, the "Senior Agent") for each of
the lenders that is a signatory to, or which becomes a signatory to, the Senior
Credit Agreement (as defined below) and/or the Restated Senior Credit Agreement
(as defined below) (collectively, the "Senior Lender"), for the benefit of the
Senior Agent and the Senior Lender.

                                    RECITALS

                  A. Brigham Oil & Gas, L.P., a Delaware limited partnership
(the "Borrower"), the Senior Agent and the Senior Lender previously entered into
that certain Credit Agreement dated as of January 26, 1998, as amended by First
Amendment to Credit Agreement dated August 20, 1998, Second Amendment to Credit
Agreement dated as of March 26, 1999, Third Amendment to Credit Agreement dated
as of July 19, 1999 and Fourth Amendment to Credit Agreement dated as of October
7, 1999 (as so amended, the "Senior Credit Agreement"), pursuant to which the
Senior Lender agreed to make certain loans and extensions of credit to the
Borrower.

                  B. On even date herewith, Borrower, Senior Agent, and Bank of
Montreal, Societe Generale, Southwest Agency ("Soc-Gen") and Shell Capital Inc.
("SCI"), each a Senior Lender are executing that certain Amended and Restated
Credit Agreement (such agreement as may from time to time be amended or
modified, called the "Restated Senior Credit Agreement"), which amends and
restates the Senior Credit Agreement in its entirety.

                  C. Brigham Exploration Company, a Delaware corporation (the
"Parent") has executed an Indenture dated August 20, 1998, with Chase Bank of
Texas, National Association, Trustee, as amended by First Amendment to Indenture
dated March 26, 1999 and by Second Amendment to Indenture dated as of February
17, 2000 (as so amended, the "Indenture"), pursuant to which the Parent has
issued its Senior Subordinated Secured Notes due 2003, in the aggregate
principal amount of $50,000,000 (the "Subordinated Notes").

                  D. JEDI-II and ECT Merchant, as the Subordinated Lender, own
100% of the Subordinated Notes currently outstanding under the Indenture.

<PAGE>   2

                  E. The Parent owns indirectly 100% of the general and limited
partnership interests in the Borrower, and the Parent and Borrower are members
of the same consolidated group of companies and are engaged in related
businesses, and the Parent has derived and will derive direct and indirect
economic benefit from the Restated Senior Credit Agreement.

                  F. Pursuant to the terms and conditions stated in the
Indenture, the Senior Credit Agreement and the Restated Senior Credit Agreement,
the Subordinated Lender, the Subordinated Agent, the Senior Agent, the Borrower,
the Parent and certain of the Parent's Subsidiaries entered into the
Intercreditor and Subordination Agreement (the "Subordination Agreement") dated
as of August 20, 1998.

                  G. The Subordinated Lender, the Subordinated Agent and the
Senior Agent now desire to amend certain provisions of the Subordination
Agreement.

                  NOW, THEREFORE, in consideration of the mutual covenants and
agreements herein contained, the Subordinated Lender, the Subordinated Agent and
the Senior Agent hereby agree that the Subordination Agreement shall be amended
as follows:

Section 1. Certain Definitions. As used in this Amendment, the terms "Senior
Agent", "Amendment", "Subordinated Agent", "Borrower", "SCI", "Soc-Gen",
"Subordination Agreement", "Senior Credit Agreement", "Restated Senior Credit
Agreement", "Parent", "Senior Lender," "Subordinated Notes", "ECT Merchant",
"JEDI-II", and "Subordinated Lender" shall have the meanings indicated above;
and unless otherwise defined herein, all terms beginning with a capital letter
which are defined in the Subordination Agreement shall have the same meanings
herein as therein unless the context hereof otherwise requires.

                  Section 2. Amendments to Subordination Agreement.

                  2.1 Section 1.2 of the Subordination Agreement is amended
hereby:

                      (i)    by inserting the following definitions where
                             alphabetically appropriate:

                           "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 owns directly or

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                      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.

                           "Term ORRI" shall heave the meaning attributed to
                      such term under the Indenture.

                           "Term ORRI Conveyance" shall have the meaning
                      attributed to such term under the Indenture.

                      (ii) by deleting the definition of the term "Hedging
                           Agreement" in its entirety and substituting the
                           following therefor:

                           "Hedging Agreement" shall mean 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 in existence as of the date hereof or
                      hereafter arising between (i) Borrower and Bank of
                      Montreal and its successors or assigns (a "BMO Hedge
                      Party") and Soc-Gen and its successors or assigns (a
                      "Soc-Gen Hedge Party") entered into while such BMO Hedge
                      Party or such Soc-Gen Hedge Party is a Lender; and (ii)
                      Borrower and SCI and its successors or assigns (with Loans
                      or Commitments of $20 million or more) or any Affiliate of
                      SCI (SCI and any Affiliate of SCI a "SCI Hedge Party")
                      entered into while such SCI Hedge Party or Fathom Energy
                      Capital I, L.L.C, is a Lender.

                      (iii) by deleting the reference "Hedging Agreement" in the
                            definition of "Senior Indebtedness" and substituting
                            therefor the reference "Hedging Agreements."

                      (iv) by amending the Recital H of the Subordination
                            Agreement by inserting the words "as any of such
                            documents or instruments may be amended,
                            supplemented or replaced from time to time" after
                            the words "attached hereto" in the last line
                            thereof.

                  2.2 Section 2.6(a)(i) of the Subordination Agreement is
amended by inserting, after the phrase "modify the interest payment schedule"
the additional phrase: "so as to require earlier payments of interest".

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                  2.3 Section 2.6 of the Subordination Agreement is amended by
inserting the following phrase at the beginning of subsections (b) and (d):

                  "Subject to the Term ORRI Conveyances,"

                  2.4 The following new Section 2.9 to the Subordination
Agreement is inserted after Section 2.8:

                  "Section 2.9. Notwithstanding anything in this Agreement or
                  any other Senior Loan Document to the contrary, (a) no Term
                  ORRI Conveyance shall be considered a Subordinated Loan
                  Document for the purposes of this Agreement, (b) no
                  obligations or liabilities under any Term ORRI Conveyance
                  shall be Subordinated Indebtedness, and (c) reductions of the
                  Subordinated Indebtedness pursuant to the terms of the Term
                  ORRI Conveyances shall not be prohibited under the terms of
                  this Agreement and any other Senior Indebtedness Document.
                  Upon any payment or distribution of property or securities to
                  the creditors of the Parent, BOG, or any other grantor under
                  any Term ORRI Conveyance in a liquidation, dissolution,
                  insolvency or reorganization of such person or property or in
                  an assignment for the benefit of creditors or any marshaling
                  of its assets and liabilities, the grantee under any Term ORRI
                  Conveyance shall be entitled to receive payment in full of all
                  amounts not paid when due pursuant to Section 4.2 of the Term
                  ORRI Conveyances without any limitation under this Agreement
                  or any Senior Loan Document. In the event the Senior Agent or
                  any Senior Lender shall receive any amounts owed to the
                  grantee under any Term ORRI Conveyance (but only such amounts
                  owed pursuant to such Term ORRI Conveyance), the Senior Agent
                  or such Senior Lender will hold any amount so received in
                  trust for such grantee and will forthwith turn over such
                  payment to grantee in the form received by it (together with
                  any necessary endorsement)."

                  2.5 Section 3.3(d) of the Subordination Agreement is amended
to hereafter read in its entirety as follows:

                  "(c) not amend, supplement or otherwise modify the terms of
                  the Subordinated Indebtedness (including, without limitation,
                  the Subordinated Loan Documents) without the express written
                  consent of the Senior Agent, which consent will not be
                  unreasonably withheld, which has the effect of (i) increasing
                  the principal amount of the Subordinated Indebtedness,
                  provided that the foregoing shall not affect the Parent's
                  right to make payment in kind of accrued interest or the
                  Subordinated Lender's ability to accept payment in kind as
                  provided in the Subordinated Loan Documents, thereby
                  increasing the principal amount of the Subordinated
                  Indebtedness, (ii) increasing the rate of interest or any fees
                  charged on the Subordinated Indebtedness (provided that the
                  foregoing shall not prohibit any fees or changes in the rate
                  of interest contemplated by the terms of the

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                  Securities Purchase Agreement), (iii) amending or modifying
                  the terms of the Term ORRI Conveyance or (iv) amending or
                  modifying the terms of the Indenture which relate to the Term
                  ORRI."

                  2.6 All references to the "Senior Credit Agreement" in the
Subordination Agreement shall henceforth refer to the Restated Senior Credit
Agreement as defined in this Amendment, as such Restated Senior Credit Agreement
is from time to time further amended, supplemented or restated.

                  Section 3. Representations and Warranties. The Subordinated
Lender and the Subordinated Agent hereby reaffirm that as of the effective date
of this Amendment, the representations and warranties made by the Subordinated
Lender and the Subordinated Agent in Article III of the Subordination Agreement
will be true and correct as though made on and as of the effective date of this
Amendment. The Senior Agent hereby reaffirms that as of the effective date of
this Amendment, the representations and warranties made by the Senior Agent in
Article III of the Subordination Agreement will be true and correct as though
made on and as of the effective date of this Amendment.

                  Section 4. Consents.

                  (a) Notwithstanding any provisions of Section 2.6 of the
Subordination Agreement, the Subordinated Lender and the Subordinated Agent of
their own free will hereby consent in all respects to and acknowledge the Senior
Credit Agreement, as amended as provided in Recital A above (a copy of which is
attached hereto as Schedule I), and the Restated Senior Credit Agreement, as
restated and amended as provided in Recital B above (a copy of which is attached
hereto as Schedule II) and to the transactions contemplated thereby and confirm
that they remain bound by the subordination provisions of Article II of the
Subordination Agreement. The Senior Lenders and the Senior Agent hereby consent
to the amendment of the Indenture pursuant to the Second Amendment to Indenture
and to the transactions contemplated therein, including the execution of the
Term ORRI Conveyances.

                  (b) The Senior Agent and the Senior Lender covenant and agree
not to contest or dispute, whether in any proceeding or otherwise, the validity,
enforceability, attachment, priority or perfected status of (i) any Lien granted
in favor of the Subordinate Agent or any Subordinate Lender or (ii) any Term
ORRI Conveyance or, with respect to the Term ORRI Conveyance, take any steps or
actions, including the institution of any proceedings, to enjoin or restrain the
grantee under any Term ORRI Conveyance from the exercise of the remedies
afforded them under any Term ORRI Conveyance.

                  Section 5. Ratification. The Subordinated Lender, the
Subordinated Agent and the Senior Agent hereby expressly ratify and affirm their
respective obligations under the Subordination Agreement (as amended hereby) and
agree that the Subordination Agreement remains in full force and effect.

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<PAGE>   6

                  Section 6. Descriptive Headings, etc. The headings,
descriptive or otherwise, of this Amendment and the several Sections of this
Amendment are inserted for convenience only and shall not be deemed to affect
the meaning or construction of any of the provisions hereof.

                  Section 7. Counterparts. This Amendment may be executed in any
number of counterparts and by different parties on separate counterparts and all
of such counterparts shall together constitute one and the same instrument.

                           [SIGNATURES ON NEXT PAGE.]

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                  IN WITNESS WHEREOF, the parties hereto have caused this
Amendment to be duly executed and delivered and effective as of the date first
above written.

                                       SENIOR AGENT:

                                       BANK OF MONTREAL

                                       By:
                                            ---------------------------------
                                       Name:  Thomas McGraw
                                       Title:    Director

                                       SUBORDINATED LENDER:

                                       ECT MERCHANT INVESTMENTS CORP.

                                       By:
                                            ---------------------------------
                                       Name:
                                             --------------------------------
                                       Title:
                                              -------------------------------

                                       JOINT ENERGY DEVELOPMENT INVESTMENTS II
                                       LIMITED PARTNERSHIP

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

                                       By: Enron Capital II Corp., its General
                                       Partner

                                       By:
                                            ---------------------------------
                                       Name:
                                             --------------------------------
                                       Title:
                                              -------------------------------

                                       S
<PAGE>   8

                                       SUBORDINATED AGENT:

                                       JOINT ENERGY DEVELOPMENT INVESTMENTS II
                                       LIMITED PARTNERSHIP, as a Subordinated
                                       Lender and Subordinated Agent

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

                                       By: Enron Capital II Corp., its General
                                       Partner

                                       By:
                                            ---------------------------------
                                       Name:
                                             --------------------------------
                                       Title:
                                              -------------------------------

                                       S

<PAGE>   9

ACKNOWLEDGED AND CONSENTED TO:

Brigham Exploration Company

By:
    ---------------------------
         Karen E. Lynch
         Vice President

Brigham Oil & Gas, L.P.

By:      Brigham, Inc., its
         General Partner

By:
    ---------------------------
         Karen E. Lynch
         Vice President

Brigham, Inc.

By:
    ---------------------------
         Karen E. Lynch
         Vice President

Brigham Holdings I, LLC,
a Nevada limited liability company

By:
    ---------------------------
Name:
      -------------------------
Title:
      -------------------------

Brigham Holdings II LLC,
a Nevada limited liability company

By:
    ---------------------------
Name:
      -------------------------
Title:
      -------------------------

                                        S<PAGE>   1
                                                                   EXHIBIT 10.11

                          SECOND AMENDMENT TO INDENTURE

         This SECOND AMENDMENT TO INDENTURE, dated as of February 17, 2000
("this Amendment"), is among BRIGHAM EXPLORATION COMPANY, a corporation duly
organized and existing under the laws of the State of Delaware (the "Borrower"),
and CHASE BANK OF TEXAS, NATIONAL ASSOCIATION, a national banking association
existing under the laws of the United States, as trustee (the "Trustee").

                              PRELIMINARY STATEMENT

         All covenants and agreement made by the Borrower herein are for the
benefit and security of the holders of the Borrower's Senior Subordinated
Secured Notes due 2003.

                                    RECITALS

         The Borrower and the Trustee are parties to that certain Indenture
dated as of August 20, 1998, as amended by the First Amendment to Indenture
dated as of March 26, 1999 (as amended, the "Indenture"). Capitalized terms used
and not otherwise defined herein are used with the meanings ascribed thereto in
the Indenture.

         The Borrower has advised the Noteholders and the Trustee that it
desires to amend certain provisions of the Indenture, and the Borrower has
requested that the Trustee and the Noteholders agree to various amendments to
certain provisions of the Indenture.

         The Trustee, upon the consent and authorization of the Noteholders, has
agreed to so amend certain provisions of the Indenture upon the terms and
subject to the conditions and limitations of this Amendment.

         NOW, THEREFORE, in consideration of the premises, covenants and
agreements contained herein, the parties hereto agrees as follows:

         Section 1. Definitions. The following capitalized terms shall have the
following respective meanings when used herein:

               1.1 "RELEASED CLAIMS" SHALL MEAN ANY AND ALL CLAIMS (INCLUDING
         WITHOUT LIMITATION ANY LIABILITIES, DAMAGES, DEMANDS AND CAUSES OF
         ACTION ARISING THEREFROM), WHETHER (A) AT LAW OR IN EQUITY, (B) ON THE
         ALLEGED COMMISSION OF A TORT, (C) ON THE ALLEGED BREACH (OR
         ANTICIPATORY BREACH OR REPUDIATION) OF ANY CONTRACT, DUTY, OR WARRANTY
         (WHETHER

<PAGE>   2

         ORAL OR WRITTEN, EXPRESS OR IMPLIED), (D) ON THE ALLEGED VIOLATION OF
         ANY STATUTE, TARIFF, OR REGULATION (WHETHER PROMULGATED BY THE UNITED
         STATES, ANY STATE THEREOF, ANY FOREIGN STATE OR COUNTRY, OR ANY OTHER
         GOVERNMENTAL AGENCY OR ENTITY, WHEREVER LOCATED), OR (E) ON ANY OTHER
         FACTUAL, LEGAL OR EQUITABLE THEORY, INCLUDING, WITHOUT LIMITATION, ANY
         CLAIM FOR DAMAGES OF ANY TYPE OR NATURE, FOR INJUNCTIVE OR OTHER
         RELIEF, FOR ATTORNEYS' FEES, INTEREST OR ANY OTHER LIABILITY WHATSOEVER
         ON ANY THEORY, INCLUDING WITHOUT LIMITATION ANY LOSS, COST OR DAMAGE IN
         CONNECTION WITH OR BASED UPON "LENDER LIABILITY", UNFAIR DEALING,
         DURESS, COERCION, CONTROL OR UNDUE INFLUENCE, EXTORTION OR COMMERCIAL
         BRIBERY, BREACH OF AN IMPLIED COVENANT OR DUTY OF GOOD FAITH AND FAIR
         DEALING, MATERIAL MISREPRESENTATION OR OMISSION, OVERREACHING,
         UNCONSCIONABILITY, CONFLICT OF INTEREST, BAD FAITH, MALPRACTICE,
         DISPARATE BARGAINING POSITION, DETRIMENTAL RELIANCE, PROMISSORY
         ESTOPPEL, ESTOPPEL BY DEED, WAIVER, LACHES, OR ANY OTHER EQUITABLE
         THEORY, EQUITABLE SUBORDINATION, BREACH OF FIDUCIARY DUTY OR ANY OTHER
         DUTY, OR TORTIOUS INDUCEMENT TO COMMIT SUCH BREACH, TORTIOUS
         INTERFERENCE WITH CONTRACT OR PROSPECTIVE BUSINESS RELATIONS, NEGLIGENT
         PERFORMANCE OF CONTRACTUAL OBLIGATIONS, OR OTHER THEORIES OF
         NEGLIGENCE, NEGLIGENT OR INTENTIONAL INFLICTION OF EMOTIONAL DISTRESS,
         SLANDER, LIBEL, OTHER DEFAMATION, FRAUDULENT TRANSFER, CONVERSION,
         TRESPASS TO (OR CLOUDING THE TITLE OF) PROPERTY, USURY, VIOLATIONS OF
         THE RACKETEER INFLUENCED AND CORRUPT ORGANIZATIONS ACT, DECEPTIVE TRADE
         PRACTICES, CONSPIRACY, OR ANY THEORY OF LIABILITY AS PARTNERS OR JOINT
         VENTURERS, THAT ANY RELEASING PARTY MAY HAVE AS OF THE DATE HEREOF
         AGAINST ANY RELEASED PARTY WITH RESPECT TO THE LENDING RELATIONSHIP.

               1.2 "Released Party" shall mean each of the Trustee, the
         Noteholders and their respective predecessors, successors, assigns,
         directors, officers, partners, employees, agents, attorneys, principals
         and Affiliates and all other Persons liable or who might be claimed to
         be liable on their behalf (collectively, the "Released Parties").

               1.3 "Releasing Party" shall mean each of the Borrower and the
         Guarantors and their respective predecessors, successors, assigns,
         directors, officers, partners, employees, agents, attorneys,
         principals, Affiliates and all other Persons who might have a claim
         against any Released Party (collectively, the "Releasing Parties").

                                      -2-
<PAGE>   3

         Section 2. Amendments to Indenture. The Indenture is amended as
follows:

               2.1     Section 1.01. Section 1.01 is amended as follows:

               2.1.1   The definition of "Consolidated Net Income" is amended as
         follows:

               2.1.1.1 By deleting all of subsection (iv) and replacing with the
         following:

                       "(iv) any extraordinary gains or losses;"

               2.1.1.2 By inserting after the end of subsection (iv) a new
         subsection (v) as follows:

                       "(v) any gains or losses attributable to Property sales
                       not in the ordinary course of business or attributable to
                       sales of Hydrocarbon Interests other than sales of
                       Hydrocarbon production in the ordinary course of
                       business: and"

               2.1.1.3 By relettering the existing subsection (v) as subsection
         (vi).

               2.1.1.4 By adding to the end of such definition the following:

                       "Any amounts paid on account of the Term ORRI shall be
                       added to Consolidated Net Income, regardless of the
                       accounting treatment afforded the Term ORRI."

               2.1.2   By adding to the end of the definition of "ECT", the
         words "and its successors and assigns".

               2.1.3   By deleting the definition of the term "First Borrowing
         Base Determination Date" in its entirety and substituting the following
         therefor:

                       "First Borrowing Base Determination Date" shall have the
                       meaning assigned to it in the Senior Credit Agreement."

               2.1.4   By deleting the definition of the term "Interest Expense"
         in its entirety and substituting the following therefor:

                       "Interest Expense" means, for each applicable period for
                       which EBITDA is to be calculated, the sum of all required
                       payments of interest (whether paid in cash or in kind,
                       but excluding any payments made on account of the Term
                       ORRI) during such period on borrowed money."

                                      -3-
<PAGE>   4

               2.1.5   By deleting the definition of the term "Adjusted
         Consolidated Net Tangible Assets" in its entirety.

               2.1.6   By deleting subsection (a) of the definition of the term
         "Permitted Debt" in its entirety and substituting the following
         therefor:

                       "(a) The Senior Loan, up to the lesser of (i) $75,000,000
                       or (ii) the Borrowing Base; provided that upon the
                       payment of any portion of the principal of the Senior
                       Loan, the maximum principal balance permitted under the
                       Senior Loan Documents shall be reduced by the amount of
                       the payment unless, until and to the extent reborrowing
                       such amount would be supported by an industry standard
                       "borrowing base" as reasonably determined by the Senior
                       Lenders constituting Majority Lenders under the Senior
                       Loan Documents, whether as part of a formal Borrowing
                       Base determination or in determination of the Target
                       Asset Value (as defined in the Senior Credit Agreement)
                       under the Senior Credit Agreement;"

               2.1.7   By adding the phrase "(other than the Senior Loan)"
         following the words "Financial Statements" in subsection (c) of the
         definition of "Permitted Debt".

               2.1.8   By adding to the end of the definition of "Registration
         Rights Agreement", the words ", as it may be amended, supplemented or
         restated from time to time".

               2.1.9   By inserting the following new definitions:

                       "Accrued PIK Amount" means, as of any particular day, the
                       aggregate dollar amount of all accrued interest on the
                       Notes that has been paid in kind (and not in cash) as of
                       such day in accordance with this Indenture, as reduced by
                       any amounts paid on or prior to such day under any Term
                       ORRI Conveyances or otherwise paid in cash as reduced
                       pursuant to Section 9.01. The Accrued PIK Amount as of
                       February 20, 2000 shall be $6,936,456.

                       "Applied Payments" has the meaning assigned to it in
                       Section 2.5.

                       "Non-Proved Reserves" means any reserves, other than
                       Proved Reserves.

                       "PDNP Reserves" shall mean proved, developed,
                       non-producing oil and gas reserves, as determined in
                       conformity with the guidelines in effect from time to
                       time as promulgated by the Society of Petroleum Engineers
                       or its successor association.

                                      -4-
<PAGE>   5

                       "PDP Reserves" shall mean proved, developed, producing
                       oil and gas reserves, as determined in conformity with
                       the guidelines in effect from time to time as promulgated
                       by the Society of Petroleum Engineers or its successor
                       association.

                       "Proved Reserves" means PDP Reserves, PDNP Reserves and
                       PUD Reserves.

                       "PUD Reserves" shall mean proved, undeveloped oil and gas
                       reserves, as determined in conformity with the guidelines
                       in effect from time to time as promulgated by the Society
                       of Petroleum Engineers or its successor association.

                       "Second Amendment" means the Second Amendment to
                       Indenture among the Borrower and the Trustee dated
                       February 17, 2000.

                       "Subject Reserves" means (a) any PDP Reserves and PDNP
                       Reserves identified by BOG or Borrower (or any Subsidiary
                       thereof) as of the date hereof as being produced or
                       producible in paying quantities out of wells now located
                       on the Hydrocarbon Interests owned by any of them as of
                       the date hereof including those listed on the attached
                       Exhibit I or (b) any PDP Reserves and PDNP Reserves
                       identified by BOG or Borrower (or any Subsidiary thereof)
                       following the date hereof and on or before December 31,
                       2000, as being produced or producible in paying
                       quantities out of any well spudded or acquired by BOG or
                       Borrower (or any Subsidiary thereof) on or before
                       December 31, 2000, (c) in the event only that Borrower's
                       Consolidated Interest Coverage Ratio calculated as of
                       September 30, 2000 (in accordance with the Indenture), is
                       less than 1.1 to 1.0, any PDP Reserves and PDNP Reserves
                       identified by BOG or Borrower (or any Subsidiary thereof)
                       following December 31, 2000 and on or before December 31,
                       2001, as being produced or producible in paying
                       quantities out of any well spudded or acquired after
                       December 31, 2000 but on or before December 31, 2001, and
                       (d) in the cases of (a), (b) and (c), above, a sufficient
                       interest in the Hydrocarbon Interests and Oil and Gas
                       Properties to afford BOG or the Borrower as applicable
                       the right, prior to giving effect to any Term ORRI
                       Conveyance, to secure the maximum authorized share of
                       production that is allocable to PDP Reserves and, when
                       applicable, PDNP Reserves found in each Subject Well.
                       Under no circumstances, and notwithstanding any provision
                       hereof to the contrary, shall the term "Subject Reserves"
                       include (1) any PUD Reserves or any Non-Proved Reserves
                       or (2) any PDP Reserves and/or PDNP Reserves beneficially
                       or legally owned

                                      -5-
<PAGE>   6

                       (whether in a vested or contingent manner) by a third
                       party (which is not an Affiliate of the Borrower) under
                       or pursuant to any agreement or other matter disclosed in
                       Exhibit H hereto, or (3) any PDP Reserves or PDNP
                       Reserves identified by Borrower or BOG as a result of the
                       deepening or sidetracking of a Subject Well after
                       December 31, 2000 (in the event item (c) of the
                       definition of Subject Reserves is not triggered) and
                       after December 31, 2001, (in the event item (c) of the
                       definition of Subject Reserves is triggered). Under no
                       circumstances shall the term "Subject Reserves" include
                       reserves that are not either producing or capable of
                       producing (or being made in the case of PDNP Reserves to
                       produce or capable of producing) in "paying quantities,"
                       as such term is defined under the Texas common law
                       (regardless of the jurisdiction in which the subject Oil
                       and Gas Properties are located).

                       "Subject Wells" means wells in which Subject Reserves are
                       now or hereafter identified and which are covered by a
                       Term ORRI Conveyance.

                       "Term ORRI" means any present or future right and
                       interest in the Oil and Gas Properties owned or hereafter
                       acquired by the Borrower, BOG or any other Affiliate of
                       the Borrower, to be conveyed by the Borrower and/or its
                       Subsidiaries, as applicable, to the Noteholders in
                       accordance with this Indenture, entitling the holders
                       thereof to 4% of the net proceeds (reducing to 3% of the
                       net proceeds) received by the Borrower or its Subsidiary
                       on account of production from the Subject Reserves. Each
                       Term ORRI shall be conveyed pursuant to a Term ORRI
                       Conveyance.

                       "Term ORRI Conveyance" means a conveyance of a Term ORRI
                       by the Borrower and/or its Subsidiaries, pursuant to
                       which the Borrower (or the applicable Subsidiary) conveys
                       to the Noteholders, a Term ORRI in the Oil and Gas
                       Properties owned or hereafter acquired by the Borrower,
                       BOG or any other Affiliate of the Borrower, in the form
                       attached hereto as Exhibit I.

               2.2 Section 1.02. Section 1.02 is amended by deleting the phrase
         "(including the ACNTA calculations)".

               2.3 Section 4.01. Section 4.01 is amended by adding the phrase
         "the ORRI and" following the words "subordinate in priority only to",
         in the introductory paragraph.

               2.4 Section 7.01. Section 7.01 of the Indenture is amended as
         follows:

                                      -6-
<PAGE>   7

               2.4.1 By deleting the reference "60" from the first sentence of
         subsection (b) and inserting the reference "45".

               2.4.2 By deleting subparagraph (g) in its entirety and
         substituting the following therefor:

                         "(g) Notices Under Other Loan Agreements. Concurrently
                         with the furnishing thereof to any Senior Lender or the
                         Senior Loan Agent, copies of any statement (including
                         financial statements), report or notice so furnished to
                         any Senior Lender or the Senior Loan Agent pursuant to
                         the terms of the Senior Loan Documents and not
                         previously furnished to the Agent or the Trustee
                         pursuant to any other provision of this Section 7.01."

               2.4.3 By amending subparagraph (j) to add a new sentence to the
         end as follows:

                         "Until the earliest date (i) on which there is a
                         payment in full of the Accrued PIK Amount and all other
                         Obligations, (ii) on or after November 21, 2000, on
                         which there is a payment in full of the Accrued PIK
                         Amount, or (iii) after November 21, 2000, on which the
                         Noteholders have received payment in full of the
                         Accrued PIK Amount through payment of the Term ORRI,
                         each monthly operating report shall identify all Oil
                         and Gas Properties that constitute Subject Reserves,
                         the date at which the well attributable to the Subject
                         Reserves was spudded and any additions to Subject
                         Reserves from the previous month's operating report."

               2.4.4 By deleting the final paragraph of Section 7.01 and
         substituting the following therefor:

                         "The Borrower will furnish to the Agent, at the time it
                         furnishes each set of financial statements pursuant to
                         paragraph (a) or (b) above, a certificate substantially
                         in the form of Exhibit J attached hereto executed by a
                         Responsible Officer (i) certifying as to the matters
                         set forth therein and stating that no Default has
                         occurred and is continuing (or, if any Default has
                         occurred and is continuing, describing the same in
                         reasonable detail), (ii) for the year 2000, setting
                         forth in reasonable detail an aged accounts payable and
                         accounts receivable listing, (iii) setting forth in
                         reasonable detail the computations necessary to
                         determine whether the Borrower is in compliance with
                         the financial covenants in Sections 8.16 and 8.17 as of
                         the end of the applicable reporting period(s) and,
                         together with pro forma calculations for each of such
                         financial covenants as of the end of the next fiscal
                         quarter, and (iv) certifying that said financial
                         statements fairly present the consolidated and
                         consolidating financial

                                      -7-
<PAGE>   8

                         condition and consolidated results of operations in
                         accordance with GAAP, as at the end of, and for, such
                         period (subject to normal year-end audit adjustments)."

               2.5 Section 7.07. Section 7.07 is amended by deleting subsection
         (b) in its entirety and substituting the following therefor:

                         "(b) Not less than 15 days prior to each of the First
                         Borrowing Base Determination Date and any Scheduled
                         Redetermination Date, the Borrower shall furnish to the
                         Agent a Reserve Report. The Reserve Report furnished
                         for the First Asset Valuation Date (as defined in the
                         Senior Credit Agreement) shall be prepared as of July
                         31, 2000, and the Reserve Report furnished for the
                         First Borrowing Base Determination Date shall be
                         prepared as of December 31, 2001. The Reserve Report
                         furnished for the Scheduled Redetermination Date to
                         occur in March of each year shall be prepared as of the
                         preceding December 31, and the Reserve Report furnished
                         for the Scheduled Redetermination Date to occur in
                         September of each year other than such First Asset
                         Valuation Date, shall be prepared as of the preceding
                         June 30. The Reserve Report to be furnished in March of
                         each year shall be prepared by certified independent
                         petroleum engineers or other independent petroleum
                         consultant(s) acceptable to the Agent and the Reserve
                         Reports to be furnished in September of each year shall
                         be prepared by or under the supervision of the chief
                         engineer or Vice President of Operations of the
                         Borrower who shall certify such Reserve Report to have
                         been prepared in accordance with the procedures used in
                         the immediately preceding March Reserve Report. At
                         Borrower's option, the Reserve Report to be furnished
                         in September of each year may instead consist of a
                         report from the independent petroleum engineers
                         referred to above on any new wells and a roll-forward
                         by Borrower on any wells previously reported in the
                         Reserve Report described in the immediately preceding
                         March."

               2.6 Section 7.12. A new Section 7.12 is added to the Indenture as
         follows:

                   "Section 7.12 Term ORRI. (a) Contemporaneously with the
                   execution of the Second Amendment, the Borrower has executed
                   and delivered, or caused its Subsidiaries to execute and
                   deliver, to the Noteholders, in their respective
                   Participations, a Term ORRI Conveyance to the Noteholders
                   covering all Hydrocarbon Interests owned by the Borrower and
                   its Subsidiaries. On the last Business Day of each calendar
                   month following the date of the Second Amendment, beginning
                   March 31, 2000, the Borrower shall execute and deliver, or
                   cause its Subsidiaries to execute and deliver, to the
                   Noteholders, in their respective Participations, (i) a Term
                   ORRI Conveyance covering all Hydrocarbon Interests owned by
                   the Borrower and its Subsidiaries identified

                                      -8-
<PAGE>   9

                   or acquired during the prior calendar month on or before
                   December 31, 2000, and (ii) in the event the Borrower's
                   Consolidated Interest Coverage Ratio calculated as of
                   September 30, 2000, is less than 1.1 to 1.0, a Term ORRI
                   Conveyance covering all Hydrocarbon Interests owned by the
                   Borrower and its Subsidiaries identified or acquired during
                   the prior calendar month on or before December 31, 2001.

                   (b) Any and all payments made on account of any Term ORRI or
                   otherwise pursuant to any Term ORRI Conveyance (the "Applied
                   Payments"), including payments made on account of the sale of
                   ORRI Hydrocarbons and payments made on account of a
                   piggy-back sale, farm-out, exchange or other transfer of a
                   Term ORRI pursuant to Section 3.2(a) of any Term ORRI
                   Conveyance, shall reduce the Accrued PIK Amount by the dollar
                   amount of such payment(s).

                   (c) Notwithstanding any provision hereof to the contrary, an
                   actual payment obligation on account of the Term ORRI shall
                   only be triggered by (i) the actual production, sale and
                   collection of proceeds on account of PDP Reserves from
                   Subject Reserves or (ii) a piggy-back sale, farm-out,
                   exchange or other transfer of any Term ORRI, or any portion
                   thereof, pursuant to Section 3.2 of any Term ORRI Conveyance,
                   and the mere identification by Borrower or BOG of PDP
                   Reserves and/or PDNP Reserves in any particular Subject Well
                   shall not trigger such an actual payment obligation or
                   otherwise constitute a representation, warranty or other
                   assurance that any such reserves (at any level) actually
                   exist and/or are producible in paying quantities.

                   (d) Notwithstanding any provision of this Amendment or any
                   Term ORRI Conveyance to the contrary, Agent shall serve as
                   agent and attorney-in-fact on behalf of the Noteholders for
                   purposes of (A) receiving Applied Payments under the Term
                   ORRI Conveyances, (B) receiving notices and other
                   communications under the Term ORRI Conveyances and (C)
                   executing instruments necessary or appropriate, in the
                   reasonable discretion of Borrower, to give effect to Section
                   2.4 or the last sentence of Section 3.2 of each Term ORRI
                   Conveyance.

                   (e) Notwithstanding any provision of any Term ORRI Conveyance
                   to the contrary, (i) all of the rights and interests of any
                   particular Noteholder under all, but not less than all, of
                   the Term ORRI Conveyances may be assigned by such Noteholder
                   to an Affiliate of such Noteholder, (ii) all or an undivided
                   portion of the rights and interests of any particular
                   Noteholder under all, but not less than all, of the Term ORRI
                   Conveyances may be assigned to a successor or assign of all
                   or a portion of such Noteholder's interest in the Loan
                   Documents, in proportion to the interest so transferred, or
                   (iii) all or an undivided portion of the rights and interests
                   of any particular Noteholder under all, but not less than
                   all, of the Term ORRI Conveyances may be assigned to a
                   successor or assign of all or a portion of such Noteholder's

                                      -9-
<PAGE>   10

                   interest in Accrued PIK Amounts subject to payment by virtue
                   of any Term ORRI. Upon any transfer of a Noteholder's
                   interest in the Term ORRI's and under the Term ORRI
                   Conveyances pursuant to this subsection (e), the Agent shall
                   serve as agent and attorney-in-fact on behalf of the
                   transferee for purposes of (A) receiving Applied Payments
                   under the Term ORRI Conveyances, (B) receiving notices and
                   other communications under the Term ORRI Conveyances and (C)
                   executing instruments necessary or appropriate, in the
                   reasonable discretion of Borrower, to give effect to Section
                   2.4 or the last sentence of Section 3.2 of each Term ORRI
                   Conveyance.

                   (f) The Term ORRI shall not apply to any Subject Reserves as
                   are, as of the date hereof, subject to the rights and
                   interests of third parties that are not Affiliates of the
                   Borrower under any agreement or other matter described in
                   Exhibit H hereto.

                   (g) Unless and until there is an Event of Default that is
                   continuing (and no longer subject to a cure period), BOG
                   under each Term ORRI Conveyance shall, notwithstanding any
                   provision of Section 4.2 of any Term ORRI Conveyance to the
                   contrary, have the absolute right to receive all payments for
                   (or on account of) ORRI Hydrocarbons as defined in the Term
                   ORRI Conveyance, and to net out Permissible Charges as
                   defined in the Term ORRI Conveyance and make distributions to
                   Agent, on behalf of Noteholders. In the event Agent or
                   Noteholders begin to receive payments on account of the Term
                   ORRI after and during the continuance of an Event of Default,
                   on or before the last day of each month, Agent shall provide
                   Borrower with an accounting of payments received (and a copy
                   of any invoices delivered to Agent in connection therewith)
                   during the previous calendar month on account of the Term
                   ORRI.

                   (h) Neither the Borrower nor any Subsidiary shall have any
                   obligation under any Term ORRI Conveyance, express or
                   implied, to maintain any Oil and Gas Property in force and
                   effect (whether by drilling, production, payment of delay
                   rentals, exercise of an option or otherwise), such
                   maintenance and all decisions with respect thereto to be in
                   the sole and absolute discretion of Borrower and BOG.

                   (i) In the event that Borrower's Consolidated Interest
                   Coverage Ratio calculated as of September 30, 2000 (in
                   accordance with the Indenture) is 1.1 to 1.0 or greater, the
                   Noteholders or Agent, on behalf of Noteholders, shall, on or
                   before January 30, 2001, release and reconvey to BOG, under a
                   form reasonably satisfactory to both Borrower and Noteholders
                   and free of all liens, claims and encumbrances created by,
                   through or under Noteholders, all rights, titles and
                   interests described in or covered by any Term ORRI
                   Conveyance, other than those carved out of Oil and Gas
                   Properties constituting Subject Reserves. In the event that
                   Borrower's Consolidated Interest Coverage Ratio calculated as
                   of September 30, 2000 (in accordance with the Indenture) is
                   1.1 to 1.0 or greater, Noteholders or Agent, on behalf of
                   Noteholders, shall, on or before January 30, 2002, release
                   and reconvey to BOG, under a form

                                      -10-
<PAGE>   11

                   reasonably satisfactory to both Borrower and Noteholders and
                   free of all liens, claims and encumbrances created by,
                   through or under Noteholders, all rights, titles and
                   interests described in or covered by any Term ORRI
                   Conveyance, other than those carved out of Oil and Gas
                   Properties constituting Subject Reserves. Upon termination of
                   the Term ORRIs, the Noteholders shall execute such documents
                   as the Borrower may reasonably request to evidence such
                   termination."

               2.7 Section 8.01. Section 8.01 of the Indenture is amended as
         follows:

               2.7.1 By deleting subsection (a) in its entirety and substituting
         the following therefor:

                   "(a) Incur, create or assume any Debt other than Permitted
                   Debt."

               2.7.2 By deleting the last paragraph of Section 8.01 in its
         entirety.

               2.8 Section 8.07. Section 8.07 of the Indenture is amended hereby
         by deleting clause (ii) in its entirety and substituting the following
         therefor:

                   "(ii) after giving effect to such merger or consolidation,
                   the Borrower or the applicable Subsidiary shall be the
                   surviving entity, and"

               2.9 Section 8.16. Section 8.16 of the Indenture is amended by
         deleting the section in its entirety and substituting the following
         therefor:

                   "Section 8.16 Consolidated Interest Coverage Ratio. As of the
                   last day of each fiscal quarter, beginning September 30,
                   2000, the Borrower will not permit the Consolidated Interest
                   Coverage Ratio to be less than (i) 1.05 to 1.0 as of
                   September 30, 2000, (ii) 1.2 to 1.0 as of December 31, 2000,
                   (iii) 1.4 to 1.0 as of March 31, 2001, (iv) 1.6 to 1.0 as of
                   June 30, 2001, (v) 1.8 to 1.0 as of September 30, 2001, and
                   (vi) 2.0 to 1.0 as of December 31, 2001 and the end of each
                   fiscal quarter thereafter."

               2.10 Article VIII. Article VIII of the Indenture is amended by
         inserting the following new Section 8.18 at the end of Article VIII:

                   "Section 8.18 Prepayments. During the continuation of any
                   Default, BOG shall not make any optional prepayment of the
                   Senior Loans pursuant to Section 2.01(i) of the Equity
                   Conversion Agreement (as defined in the Senior Credit
                   Agreement)."

               2.11 Section 9.01. Section 9.01 of the Indenture is amended by
         inserting the following at the end of Section 9.01:

                                      -11-
<PAGE>   12

                   "In addition, any payments received by the Agent or the
                   Noteholders (or otherwise owing to the Noteholders in
                   instances where the Noteholders have elected to be paid
                   directly on account of the Term ORRI pursuant to Section 4.2
                   of any Term ORRI Conveyance) which payments are (a)
                   attributable to any Term ORRI or (b) otherwise received
                   pursuant to Section 3.2(a) of any Term ORRI Conveyance
                   (collectively, the "Applied Payments") shall constitute a
                   prepayment on the Notes of that portion of the principal
                   balance which has been added to the Notes as a result of the
                   Borrower's election to pay accrued interest in kind in
                   accordance with the provisions of Section 9.02(b).
                   Notwithstanding the foregoing, to the extent that any Applied
                   Payment received by any Noteholder due to any Term ORRI is
                   subsequently invalidated, declared to be fraudulent or
                   preferential, set aside or required to be repaid by the Agent
                   or any Noteholder to the Borrower, any Subsidiary, trustee,
                   debtor in possession, receiver or other Person under any
                   bankruptcy law, common law or equitable cause, then to such
                   extent and further only to the extent Agent or Noteholder has
                   actually repaid the affected Applied Payment, the obligations
                   hereunder with respect to the Notes satisfied by payment of
                   the Term ORRI in the form of the affected Applied Payment
                   shall be revived and continue as if such payment or proceeds
                   had not been received and the Agent's and the Noteholder's
                   Liens, interests, rights, powers and remedies under this
                   Indenture and the Loan Documents shall continue in full force
                   and effect."

               2.12 Section 9.02. Section 9.02 of the Indenture is amended as
         follows:

               2.12.1 By deleting the last two sentences of subsection (a)
         beginning with "Notwithstanding".

               2.12.2 By deleting subsection (b) in its entirety and
         substituting the following therefor:

                   "(b) The Borrower shall have the option to pay accrued
                   interest on the Notes in kind on each of the seven (7)
                   consecutive Interest Payment Dates commencing with and
                   following February 20, 1999, as provided in this Section
                   9.02(b). In addition, the Borrower shall have the option to
                   pay accrued interest on the Notes in kind on November 20,
                   2000, in the event one of the following events has occurred
                   following the date of the Second Amendment and on or before
                   August 31, 2000: (i) Borrower sells common or preferred
                   equity securities resulting in net proceeds received by
                   Borrower (after deducting all costs and expenses incurred in
                   such sale) of at least $10,000,000; or (ii) BOG and/or
                   Borrower acquires in exchange for common or preferred equity
                   securities, Oil and Gas Properties containing PDP Reserves
                   and PDNP Reserves with a collective net

                                      -12-
<PAGE>   13

                   present value, discounted at 10% per annum, of at least
                   $10,000,000 (in the reasonable judgement of Majority
                   Noteholders); or (iii) through a combination of (i) and (ii)
                   above, Borrower receives net proceeds and newly acquired Oil
                   and Gas Properties, which (as valued above), total at least
                   $10,000,000 in net present value. In the event Borrower pays
                   interest in kind, at any time, the accrued interest due on
                   the applicable Interest Payment Date shall be calculated at
                   the rates set forth in this Section 9.02(b) and the interest
                   due (calculated at the rates set forth in this Section
                   9.02(b)) shall be deemed an advance of principal on the Notes
                   and, as of the applicable Interest Payment Date, shall be
                   added to the outstanding principal balance of the Notes
                   (notwithstanding the outstanding principal balance may
                   exceed, in the aggregate, the face amount of the Notes). In
                   order to not exercise its option under the first sentence of
                   this Section 9.02(b), the Borrower must, on or before the
                   applicable Interest Payment Date, deliver written notice to
                   the Agent executed by a Responsible Officer notifying Agent
                   of its election to not pay interest in kind. Should Borrower
                   fail to deliver such written notice in a timely fashion,
                   Borrower shall be deemed to have irrevocably elected to make
                   payment of accrued interest in kind on the next applicable
                   Interest Payment Date. Should Borrower deliver such notice in
                   a timely fashion, Borrower shall be deemed to have
                   irrevocably elected to make payment of accrued interest in
                   cash and any subsequent failure to do so in a timely fashion
                   (subject to the five (5) day grace period provided in Section
                   10.01(a)) shall constitute an Event of Default hereunder. In
                   order to exercise its option under the second sentence of
                   this Section 9.02(b), the Borrower must, on or before
                   September 7, 2000, deliver written notice to the Agent
                   executed by a Responsible Officer certifying to Agent that
                   Borrower has satisfied the conditions set forth in the second
                   sentence of this Section 9.02(b), together with reasonable
                   supporting evidence, and notifying Agent of its election to
                   pay interest in kind on the November 20, 2000 Interest
                   Payment Date. Should Borrower fail to deliver such written
                   notice in a timely fashion, Borrower shall be deemed to have
                   irrevocably elected not to make payment of accrued interest
                   in kind on the November 20, 2000 Interest Payment Date.
                   Should Borrower deliver such notice in a timely fashion,
                   Borrower shall be deemed to have irrevocably elected to make
                   payment of accrued interest in cash and any subsequent
                   failure to do so in a timely fashion (subject to the five (5)
                   day grace period provided in Section 10.01(a)) shall
                   constitute an Event of Default hereunder. In the event the
                   Borrower elects to pay interest in kind, such interest to be
                   paid shall be calculated at 13% per

                                      -13-
<PAGE>   14

                   annum commencing on the immediately preceding Interest
                   Payment Date."

               2.13 Section 10.01. Section 10.01 of the Indenture is amended as
         follows:

               2.13.1 By deleting subsection (a) in its entirety and
         substituting the following therefore:

                   "(a) the Borrower shall default in the payment or prepayment
                   when due of any Obligation, and such default, other than a
                   default of a payment or prepayment of principal (which shall
                   have no cure period), shall continue unremedied for a period
                   of five (5) days after such Obligation becomes due, in the
                   case of interest, or thirty (30) days after the Borrower
                   receives notice from the Agent that such Obligation is due,
                   in the case of Obligations other than principal or interest;
                   or"

               2.13.2 By deleting clause (ii) of subsection (b) in its entirety
         and substituting the following therefor:

                   "(ii) as to the Senior Loan, there shall have (x) occurred a
                   default thereunder in the payment of any principal or
                   interest due on the Senior Loan beyond any cure period
                   contained in the Senior Loan Documents as of the date of the
                   Second Amendment, whether or not the Senior Lenders have
                   waived such default or modified the Senior Loan Documents to
                   extend the due date thereof or any cure period or (y)
                   occurred a default thereunder and the holders of the Senior
                   Loan shall have elected to accelerate the payment of the
                   Senior Loan (or it shall be accelerated automatically or
                   otherwise be due and payable in full); or"

               2.13.3 By deleting the "." at the end of subsection (m) and
         substituting "; or"

               2.13.4 By adding the following new subsection (n) at the end of
         Section 10.01:

                   "(n) BOG, Borrower or any Subsidiary of Borrower, shall
                   default in the performance of its obligations under any Term
                   ORRI Conveyance and such default shall continue unremedied
                   for a period of thirty days after the earlier of (A) the date
                   notice thereof to the Borrower by the Agent or (B) the
                   Borrower's knowledge thereof; provided that the foregoing 30
                   day cure period shall be reduced to five days for any payment
                   default. As used in this Section 10.01(n), "Borrower's
                   knowledge" shall be limited to the actual knowledge of any of
                   the officers of the Borrower or BOG."

                                      -14-
<PAGE>   15

               2.14 Exhibits.

               2.14.1 A new Exhibit "H" is added to the Indenture in the form of
         Exhibit "H" to this Second Amendment.

               2.14.2 A new Exhibit "I" is added to the Indenture in the form of
         Exhibit "I" to this Second Amendment.

               2.14.3 A new Exhibit "J" is added to the Indenture in the form of
         Exhibit "J" to this Second Amendment.

         Section 3. Conditions Precedent. This Amendment shall become binding
only upon receipt by the Agent of the following documents and satisfaction of
the other conditions provided in this Section 3 (the "Closing Date"), each of
which must be satisfactory to the Agent in form and substance:

               3.1 The Second Amendment. Counterparts of this Amendment executed
         by the Borrower and the Trustee.

               3.2 New Mortgage. The Borrower shall have satisfied all of its
         obligations under Section 7.09(a) of the Indenture, including the (i)
         delivery to the Agent of all Mortgages required thereby and (ii)
         evidence that the New Mortgage and the related UCC-1 financing
         statements delivered have been filed in all jurisdictions necessary to
         perfect and protect the security interests, assignments and Liens
         created thereby.

               3.3 Registration Rights. Counterparts of the Second Amendment to
         Registration Rights Agreement executed by the Borrower, JEDI-II and ECT
         Merchant.

               3.4 Financial Statements. All past due financial statements
         through the month of November 1999 described in Section 7.01 of the
         Indenture.

               3.5 Officer's Certificates. All past due officer's certificates
         through the month of November 1999 described in Sections 7.01 and 7.07
         of the Indenture.

               3.6 Accounts Payable. An aged accounts payable and accounts
         receivable listing as of December 31, 1999.

               3.7 Secretary's Certificate. Certificates of the Secretary or an
         Assistant Secretary of the Borrower and each of the Guarantors setting
         forth for each of them (i) the resolutions of its board of directors or
         managers (or if such Guarantor is a partnership, resolutions of the
         general partner of such partnership), as applicable, with respect to
         the authorization to execute and deliver this Amendment and the
         consummation of the transactions contemplated

                                      -15-
<PAGE>   16

         hereby; (ii) the Responsible Officer of such entity authorized to sign
         this Amendment, and (iii) the signature of such authorized Responsible
         Officer of such entity.

               3.8 Term ORRI Conveyance. A Term ORRI Conveyance in the form
         attached hereto as Exhibit I conveying a Term ORRI in all Oil and Gas
         Properties owned by the Borrower, BOG or any other Affiliate of the
         Borrower.

               3.9 Consent by Guarantors. A Consent and Acknowledgment executed
         by BOG and Brigham, Inc.

               3.10 Warrants. Duly executed revised warrants in the form
         attached hereto as Exhibit A, issued by the Borrower to the Noteholders
         in their respective Participations, in substitution for the current
         Warrants issued pursuant to Section 2.03 of the Securities Purchase
         Agreement (and any Warrants issued in substitution therefor), for the
         purchase of an aggregate of 1,000,000 shares of Common Stock, and which
         warrants shall constitute the "Warrants" under the Indenture and the
         Securities Purchase Agreement for all purposes.

               3.11 Opinion of Counsel. An opinion of Thompson & Knight, LLP in
         form satisfactory to the Noteholders.

               3.12 Fees and Expenses. Payment of the expenses of the Agent and
         the Noteholders in accordance with Section 6 hereof.

               3.13 Senior Lenders Consent. A consent executed by each of the
         Senior Lenders and the Senior Loan Agent, consenting to the terms of
         this Amendment and subordinating all of the liens securing the Senior
         Loan to each Term ORRI.

               3.14 Letter. A letter from Borrower in the form attached hereto
         as Exhibit B.

               3.15 Subordination Agreement. An amendment to the Subordination
         Agreement satisfactory to the Noteholders, the Senior Lenders, the
         Agent and the Senior Loan Agent.

               3.16 Closing of Amended Senior Credit Agreement.
         Contemporaneously with the Closing Date, the Borrower and/or its
         Subsidiaries, the Senior Loan Agent and the Senior Lenders shall have
         executed the amended Senior Credit Agreement (in such form as is
         satisfactory to the Noteholders) and all other Senior Loan Documents
         (in such form as is satisfactory to the Noteholders).

               3.17 Other Documents. Such other documents as Agent or its
         counsel may reasonably request.

                                      -16-
<PAGE>   17

         Section 4. Post Closing. Within 30 days as of the Closing Date hereof,
Brigham Holdings I, LLC and Brigham Holdings II, LLC will execute a Consent and
Acknowledgment.

         Section 5. Representations and Warranties.

               5.1 Reaffirmation. The Borrower hereby reaffirms that, as of the
         date of this Amendment, the representations and warranties made by the
         Borrower in the Securities Purchase Agreement and each of the Loan
         Documents are true and correct as though made on and as of the date
         hereof, subject only to the revisions to the schedules to the
         Securities Purchase Agreement and Indenture as are reflected in the
         schedules attached hereto and further, the Borrower represents that,

               5.1.1 As of the date hereof, no Default or Material Adverse
         Effect has occurred and is continuing except as previously disclosed to
         the Agent in writing.

               5.1.2 The execution, delivery and performance by the Borrower or
         the Guarantors of this Amendment and the other Loan Documents and all
         instruments and documents to be delivered by the Borrower or the
         Guarantors, to the extent a party thereto, hereunder and thereunder and
         the creation of all Liens provided for herein and therein: (i) are
         within the Borrower's or such Guarantor's corporate power; (ii) have
         been duly authorized by all necessary or proper corporate action,
         including the consent of stockholders, members and/or partners therein
         or thereof; (c) are not in contravention of any provision of the
         Borrower's or such Guarantor's certificate of incorporation, bylaws or
         similar organizational and/or governing documents; (d) will not violate
         (1) any law or regulation or (2) any order or decree of any court or
         governmental instrumentality; (e) will not conflict with or result in
         the breach or termination of, constitute a default under or accelerate
         any performance required by, any indenture, mortgage, deed of trust,
         lease, agreement or other instrument to which the Borrower or any of
         the Guarantors is a party or by which the Borrower or any of the
         Guarantors or any of their respective property is bound; (f) will not
         result in the creation or imposition of any Lien upon any of the
         property of the Borrower or the Guarantors other than those in favor of
         the Agent pursuant to the terms of this Amendment and the other Loan
         Documents to be delivered in connection herewith; and (g) do not
         require the consent or approval of any governmental body, agency,
         authority or any other Person that has not been duly obtained, made or
         complied with prior to the date hereof. At or prior to the date hereof,
         each of this Amendment and the other Loan Documents to be delivered in
         connection herewith shall have been duly executed and delivered for the
         benefit of or on behalf of the Borrower or the Guarantors, in each case
         to the extent a party thereto, and each shall then constitute a legal,
         valid and binding obligation of the Borrower or such Guarantor,
         enforceable against it in accordance with its terms.

                                      -17-
<PAGE>   18

               5.2 Independent Counsel. Each of the Borrower and the Guarantors
         further represents and warrants, for itself only that it (i) is
         executing this Amendment, and the documents executed in connection
         herewith to which it is a party, after consultation with counsel of its
         own choosing, (ii) has read and understands the release granted by
         Section 5 hereof, (iii) desires to execute this Amendment and such
         documents to which it is a party and (iv) has the requisite authority
         to enter into and be bound by this Amendment and such documents to
         which it is a party, including the release granted by Section 5 hereof.

         Section 6. Release.

               6.1 EACH OF THE RELEASING PARTIES DESIRES AND INTENDS FULLY TO
         COMPROMISE, RELEASE AND SETTLE ANY AND ALL OF THE RELEASED CLAIMS; AND
         EACH OF THE RELEASING PARTIES HEREBY COVENANTS, WARRANTS AND REPRESENTS
         UNTO EACH OF THE RELEASED PARTIES THAT SUCH RELEASING PARTY DOES HEREBY
         FOREVER RELEASE, ACQUIT, WAIVE AND DISCHARGE EACH OF THE RELEASED
         PARTIES OF AND FROM THE RELEASED CLAIMS AND EACH OF THE RELEASING
         PARTIES HEREBY DECLARES THE SAME FOREVER RELEASED, ACQUITTED, WAIVED,
         SETTLED AND DISCHARGED. THIS RELEASE IS EFFECTIVE WITHOUT REGARD TO
         WHETHER (I) SUCH RELEASED CLAIMS ARE KNOWN OR UNKNOWN, (II) DAMAGES
         ARISING OUT OF SUCH RELEASED CLAIMS HAVE YET ACCRUED, (III) SUCH
         RELEASED CLAIMS AROSE COLLATERALLY, DIRECTLY, DERIVATIVELY, OR
         OTHERWISE BETWEEN THE PARTIES HERETO OR (IV) AN ORDINARY PERSON IN THE
         SAME OR SIMILAR CIRCUMSTANCES WOULD OR WOULD NOT, THROUGH THE EXERCISE
         OF DUE CARE, HAVE DISCOVERED SUCH CLAIMS BY THE DATE OF THIS AMENDMENT.
         IN CONNECTION WITH THE FOREGOING RELEASE:

               6.2 Borrower and each of the Guarantors represents and warrants
         that it has the full power and authority to perform the release granted
         in this Section 6 and that it has not in any manner made any assignment
         of any Released Claim to any third party.

               6.3 The release granted in this Section 6 will be effective upon
         execution of this Amendment by all of the parties hereto.

               6.4 Each party executing this Amendment understands and agrees
         that the release granted in this Section 6 is a full, final and
         complete release of the Released Claims and that such release may be
         pleaded as an absolute and final bar to any or all suits which may
         hereafter be filed or prosecuted by any one or more of the Releasing
         Parties or anyone claiming by, through or under any one or more of the
         Releasing Parties in respect of any of the matters released hereby, and
         that no recovery on account of the Released Claims may hereafter be had
         from any of the Released Parties; and that the consideration given for
         such release is not an

                                      -18-
<PAGE>   19

         admission of liability or fault on the part of any of the Released
         Parties (it being the express intent of the parties hereto to obtain
         peace of mind and avoid the expense and uncertainty of potential
         litigation), and that none of the Releasing Parties or those claiming
         by, through or under any of them will ever claim that it is.

               6.5 The parties hereto acknowledge that the release granted by
         this Section 6 does not have any effect with respect to relationships
         between the Borrower and each of the Guarantors and the Noteholders and
         the Agent other than in connection with the Lending Relationship.

         Section 7. Payment of Fees and Expenses; Form of Payment.

               7.1 The Borrower agrees, whether or not the transactions
         contemplated hereby are consummated, to pay all reasonable expenses of
         the Agent and the Noteholders (including, without limitation, all
         reasonable fees and disbursements of counsel and other outside
         consultants for the Agent and/or the Noteholders) in connection with
         the negotiation, investigation, preparation, execution and delivery of,
         recording and filing of, preservation of rights under and enforcement
         of this Amendment and the other Loan Documents to be delivered in
         connection herewith.

               7.2 All payments to be made by the Borrower under this Amendment
         shall be made in Dollars, in immediately available funds, to the Agent
         at such account as the Agent shall specify.

         Section 8. Limitations. The amendments set forth herein are limited
precisely as written and shall not be deemed to (a) be a consent to, or waiver
or modification of, any other term or condition of the Securities Purchase
Agreement or the Indenture or any of the other Loan Documents, or (b) prejudice
any right or rights which the Noteholders or the Agent may now have or may have
in the future under or in connection with the Securities Purchase Agreement or
the Indenture or any of the other Loan Documents. Except as expressly
supplemented, amended or modified hereby, the terms and provisions of the
Securities Purchase Agreement or the Indenture or any other Loan Documents are
and shall remain in full force and effect. In the event of a conflict between
this Amendment and any of the foregoing documents, the terms of this Amendment
shall be controlling.

         Section 9. Governing Law. This Amendment and the rights and obligations
of the parties hereunder and under the Indenture shall be construed in
accordance with and be governed by the laws of the State of Texas and the United
States of America.

                                      -19-
<PAGE>   20

         Section 10. Descriptive Headings, etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 11. Counterparts. This Amendment may be executed  in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.

                                      -20-
<PAGE>   21

         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed as of the date first written above.

             NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION 26.02

THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE PARTIES BEFORE OR
SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF TOGETHER CONSTITUTE A
WRITTEN LOAN AGREEMENT AND REPRESENT THE FINAL AGREEMENT BETWEEN THE PARTIES AND
MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENT BETWEEN THE
PARTIES.

BORROWER:                 BRIGHAM EXPLORATION COMPANY

                          By:
                             ----------------------------------------------
                               Curtis F. Harrell
                               Chief Financial Officer

TRUSTEE:                  CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
                          as Trustee

                          By:
                             ----------------------------------------------
                                 Mauri J. Cowen
                                 Vice President and Trust Officer

<PAGE>   22

The Noteholders have joined herein solely for the purpose of evidencing their
(i) consent to the foregoing, and (ii) authorization to the Trustee to execute
this Amendment:

                            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:
                                         --------------------------------------
                                            Mark Warner
                                            Agent and Attorney-in-Fact

                            ECT MERCHANT INVESTMENTS
                            CORP., a Delaware corporation

                            By:
                               ----------------------------------------------
                                   Mark Warner
                                   Agent and Attorney-in-Fact

<PAGE>   23

                                    EXHIBIT A

                                 Form of Warrant

<PAGE>   24

                                    EXHIBIT B

                                 Form of Letter

                                February 28, 2000

Mr. John S. Hopley
Enron North America Corp.
1400 Smith Street
Houston, Texas 77002-7361

Dear John:

         Brigham Exploration Company ("BEXP") agrees to engage within thirty
days from the date hereof of a reputable investment banking firm mutually
acceptable to Enron North America Corp. and BEXP and to secure from such
investment banking firm advice concerning financial, capitalization, strategic,
sale, merger and restructure options available to BEXP within thirty days after
such engagement. BEXP agrees to present such advice to its board of directors
and to analyze and consider any such advice offered, but shall in no way be
obligated to act on such advice.

                                   Sincerely,

                                   Curtis F. Harrell

CFH/ldl

<PAGE>   25

                                    EXHIBIT H

                                  TITLES, ETC.

(a) The rights and interests afforded Gasco Limited Partnership ("Gasco") and
its successors and assigns under the terms of (i) that certain Expense
Allocation and Participation Agreement dated as of April 1, 1996, by and between
Gasco and BOG, as heretofore and/or hereafter amended, expanded, supplemented,
renewed and/or extended, and (ii) that certain Expense Allocation and
Participation Agreement II dated as of April 1, 1997, by and between Gasco and
BOG, as heretofore and/or hereafter amended, expanded, supplemented, renewed
and/or extended, and (iii) that certain Expense Allocation and Participation
Agreement III dated as of March 1, 1998, by and between Gasco and BOG, as
heretofore amended, expanded, supplemented, renewed and/or extended.

(b) The rights and interests afforded Middle Bay Oil Company ("Middle Bay") and
its successors and assigns under the terms of that certain Expense Allocation
and Participation Agreement dated as of April 1, 1996, by and between Middle Bay
and BOG, as heretofore amended, modified, expanded, supplemented, renewed and/or
extended.

(c) The rights and interests afforded Stephens Production Company ("Stephens")
and its successors and assigns under the terms of that certain Anadarko Basin
Joint Participation Agreement dated as of May 1, 1996, by and between BOG and
Stephens, as heretofore amended, modified, expanded, supplemented, renewed
and/or extended.

(d) The rights and interests afforded Vintage Petroleum, Inc. ("Vintage") and
its successors and assigns under the terms of that certain Anadarko Basin Joint
Participation Agreement dated as of May 1, 1996, by and between BOG and Vintage,
as heretofore amended, modified, expanded, supplemented, renewed and/or
extended.

(e) The rights and interests afforded Brigham-Duke (Delaware) LLC ("Duke") and
its successors and assigns under the terms of that certain Joint Development
Agreement dated as of February 17, 1999, by and between Duke and BOG, as
heretofore amended.

(f) The rights and interests, whether real or equitable, vested or contingent,
afforded third parties under the terms of various farmout, exploration, joint
participation and/or operating agreements, in existence as of the date hereof,
under or in relation to which BOG, Borrower or any Subsidiary agrees to farm-out
to one or more third party(ies) one or more Oil and Gas Property and/or
undertakes with one or more third party(ies) the joint exploration and/or
development of one or more Oil and Gas Properties (which rights and interests
may include, without limitation, rights under Area of Mutual Interests
agreements and rights in respect of forfeiture of all or a portion of Borrower's
interests in an Oil and Gas Property, or part thereof or interest therein, that
is triggered by an election not to participate in a proposed operation; and

<PAGE>   26

(g) consulting agreements in existence as of the date hereof, as same may have
heretofore been amended, expanded, supplemented, renewed and/or extended, with
third party geologists, landmen or other oil and gas industry participants who
agree to perform services in return, in whole or in part, for an overriding
royalty interest or other interest in or relating to any Oil and Gas Properties.

<PAGE>   27

                                    EXHIBIT I

                              Term ORRI Conveyance

<PAGE>   28

                                    EXHIBIT I

                              Hydrocarbon Interests

<PAGE>   29

                                    EXHIBIT J

                        FORM OF CERTIFICATE ACCOMPANYING

                               FINANCIAL STATEMENT

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