<PAGE>   1
                                                                     EXHIBIT 4.2

-------------------------------------------------------------------------------


                          BRIGHAM EXPLORATION COMPANY

                                   Borrower

                                      AND

                   CHASE BANK OF TEXAS, NATIONAL ASSOCIATION

                                    Trustee



                                _______________



                               I N D E N T U R E

                          Dated as of August 20, 1998



                                _______________



                                  $50,000,000
                  Senior Subordinated Secured Notes due 2003
<PAGE>   2
 
                               TABLE OF CONTENTS
<TABLE>
<S>                                                                           <C>
PRELIMINARY STATEMENT......................................................... 1
 
ARTICLE I
     DEFINITIONS.............................................................. 1
     Section 1.01  Definitions................................................ 1
     Section 1.02  Accounting Procedures and Interpretation...................16
 
ARTICLE II
     ISSUE, DESCRIPTION, FORM, EXECUTION, REGISTRATION 
     OF TRANSFER AND EXCHANGE OF NOTES........................................17
     Section 2.01  Form and Dating............................................17
     Section 2.02  Execution and Authentication...............................17
     Section 2.03  Denomination of Notes and Record Date......................17
     Section 2.04  Manual Execution...........................................18
     Section 2.05  Transfer and Exchange......................................18
     Section 2.06  Replacement Notes..........................................19
     Section 2.07  Cancellation of Notes......................................20
     Section 2.08  No Third Party Benefit.....................................20
 
ARTICLE III
     SUBORDINATION............................................................20
 
ARTICLE IV
     SECURITY FOR THE OBLIGATIONS.............................................20
     Section 4.01  Security...................................................20
 
ARTICLE V
     [RESERVED]...............................................................22
 
ARTICLE VI
     [RESERVED]...............................................................22
 
ARTICLE VII
     AFFIRMATIVE COVENANTS....................................................22
     Section 7.01  Financial Statements and Reports...........................22
     Section 7.02  Litigation.................................................24
     Section 7.03  Maintenance, Etc...........................................24
     Section 7.04  Environmental Matters......................................25
     Section 7.05  Further Assurances.........................................25
     Section 7.06  Performance of Obligations.................................26
     Section 7.07  Engineering Reports........................................26
     Section 7.08  Intentionally Omitted......................................27
</TABLE>

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<TABLE>
<S>                                                                           <C>
     Section 7.09  Additional Collateral......................................27
     Section 7.10  ERISA Information and Compliance...........................28
     Section 7.11  Subsidiary Security........................................28
 
ARTICLE VIII
     NEGATIVE COVENANTS.......................................................29
     Section 8.01  Debt.......................................................29
     Section 8.02  Liens......................................................30
     Section 8.03  Investments, Loans and Advances............................30
     Section 8.04  Dividends, Distributions and Redemptions...................31
     Section 8.05  Sales and Leasebacks.......................................32
     Section 8.06  Nature of Business.........................................32
     Section 8.07  Mergers, Etc...............................................32
     Section 8.08  Proceeds of Notes..........................................32
     Section 8.09  ERISA Compliance...........................................32
     Section 8.10  Sale of Oil and Gas Properties.............................33
     Section 8.11  Environmental Matters......................................34
     Section 8.12  Transactions with Affiliates...............................34
     Section 8.13  Negative Pledge Agreements.................................34
     Section 8.14  Gas Imbalances, Take-or-Pay Prepayments....................34
     Section 8.15  Borrower as Operator.......................................34
     Section 8.16  Consolidated Interest Coverage Ratio.......................35
     Section 8.17  Current Ratio..............................................35
 
ARTICLE IX
     PAYMENT OF THE NOTES.....................................................35
     Section 9.01  Repayment..................................................35
     Section 9.02  Interest...................................................35
     Section 9.03  Payments and Computations..................................38
 
ARTICLE X
     DEFAULT AND REMEDIES.....................................................39
     Section 10.01  Events of Default.........................................39
     Section 10.02  Remedies..................................................41
     Section 10.03  Production and Proceeds...................................42
     Section 10.04  Set-Off...................................................42
 
ARTICLE XI
     THE AGENT................................................................42
     Section 11.01  Authorization and Action..................................42
     Section 11.02  Agent's Reliance, Etc.....................................43
     Section 11.03  The Agent and Its Affiliates..............................43
     Section 11.04  Noteholders Loan Decision.................................43
     Section 11.05  Indemnification...........................................44
     Section 11.06  Successor Agent...........................................44
</TABLE>


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<PAGE>   4

<TABLE>
<S>                                                                           <C>
ARTICLE XII
     TRUSTEE..................................................................45
     Section 12.01  Duties of Trustee.........................................45
     Section 12.02  Rights of Trustee.........................................46
     Section 12.03  Individual Rights of Trustee..............................47
     Section 12.04  Trustee's Disclaimer......................................47
     Section 12.05  Notice of Defaults........................................47
     Section 12.06  Reports by Trustee to Noteholders.........................47
     Section 12.07  Compensation and Indemnity................................48
     Section 12.08  Replacement of Trustee....................................49
     Section 12.09  Successor Trustee by Merger, etc..........................50
     Section 12.10  Eligibility, Disqualification.............................50
     Section 12.11  Preferential Collection of Claims Against Borrower........50
     Section 12.12  Appointment of Co-Trustee.................................50
     Section 12.13  No Conflict...............................................51
 
ARTICLE XIII
     MISCELLANEOUS............................................................51
     Section 13.01  Interpretation and Survival of Provisions.................51
     Section 13.02  Costs, Expenses and Taxes.................................52
     Section 13.03  No Waiver; Modifications in Writing.......................54
     Section 13.04  Binding Effect; Assignment................................54
     Section 13.05  Communications............................................55
     Section 13.06  Governing Law.............................................56
     Section 13.07  Arbitration...............................................56
     Section 13.08  Confidentiality...........................................57
     Section 13.09  Execution in Counterparts.................................58
     Section 13.10  Trust Indenture Act Controls..............................58
     Section 13.11  Communication by Noteholders with Other Noteholders.......58
     Section 13.12  Certificate and Opinion as to Conditions Precedent........58
     Section 13.13  Statements Required in Certificate or Opinion.............59
     Section 13.14  Rules by Trustee and Agents...............................59
     Section 13.15  Legal Holidays............................................59

EXHIBITS

     Exhibit A  Form of Note
     Exhibit B  Form of Guaranty Agreement
     Exhibit C  Form of Subordination Agreement
     Exhibit D  Form of Security Agreement
     Exhibit E  Form of Security Agreement
     Exhibit F  Form of Mortgage, Deed of Trust, Assignment of Production,
                    Security Agreement and Financing Statement
     Exhibit G  Acceptance of Appointment
</TABLE>

                                     -iii-
<PAGE>   5
 
     INDENTURE, dated as of August 20, 1998, between BRIGHAM EXPLORATION
COMPANY, a corporation duly organized and existing under the laws of the State
of Delaware (hereinafter sometimes referred to as the "Borrower"), and CHASE
BANK OF TEXAS, NATIONAL ASSOCIATION, a national banking association existing
under the laws of the United States (hereinafter sometimes referred to as the
"Trustee").

                             PRELIMINARY STATEMENT

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


                                   ARTICLE I
                                  DEFINITIONS

     Section 1.01  Definitions.

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

     "Adjusted Consolidated Net Tangible Assets" or "ACNTA" means (without
duplication), as of the date of determination, (a) the sum of (i) the discounted
future net revenue from proved crude oil and natural gas reserves of the
Borrower and its Consolidated Subsidiaries calculated in accordance with
Commission guidelines before any state or federal income taxes, as estimated in
the most current Reserve Report, as increased by, as of the date of
determination, the discounted future net revenue of (A) estimated proved crude
oil and natural gas reserves of the Borrower and its Consolidated Subsidiaries
attributable to acquisitions consummated since the date of such Reserve Report,
and (B) estimated proved crude oil and natural gas reserves of the Borrower and
its Consolidated Subsidiaries attributable to extensions, discoveries and other
additions and upward determinations of estimates of proved crude oil and natural
gas reserves due to exploration, development or exploitation, production or
other activities which reserves were not reflected in the most current Reserve
Report which would, in the case of determination made pursuant to clauses (A)
and (B), in accordance with standard industry practice, result in such
determinations, in each case calculated in accordance with Commission guidelines
(utilizing the Commission guideline prices utilized in the most current Reserve
Report), and decreased by, as of the date of determination, the discounted
future net revenue attributable to (C) estimated proved crude oil and natural
gas reserves of the Borrower and its Consolidated Subsidiaries reflected in the
most current Reserve Report produced or disposed of since the date of such
Reserve Report and (D) reductions in the estimated proved crude oil and natural
gas reserves of the Borrower and its Consolidated Subsidiaries reflected in such
Reserve Report since the date of such Reserve Report attributable to downward
determinations of estimates of proved crude oil and natural gas reserves due to
exploration, development or exploitation, production

                                      -1-
<PAGE>   6

or other activities conducted or otherwise occurring since the date of the most
current Reserve Report which would, in the case of determinations made pursuant
to clauses (C) and (D), in accordance with standard industry practice, result in
such determinations, in each case calculated in accordance with Commission
guidelines (utilizing the Commission guideline prices utilized in the most
current Reserve Report); provided, however, that, in the case of each of the
determinations made pursuant to clauses (A) through (D), such increases and
decreases shall be as estimated by the Borrower's engineers, except that if as a
result of such acquisitions, dispositions, discoveries, extensions or revisions,
there is a net increase in the ACNTA which exceeds $10,000,000, the Agent shall
have the right to require that such increases and decreases in the discounted
future net revenue be confirmed in writing by an independent petroleum engineer,
at the Borrower's expense, (ii) the capitalized costs that are attributable to
seismic and undeveloped oil and gas leases of the Borrower and its Consolidated
Subsidiaries to which no proved crude oil and natural gas reserves are
attributed, based on the Borrower's books and records as of a date no earlier
than the date of the Borrower's latest annual or quarterly financial statements,
(iii) the Net Working Capital on a date no earlier than the date of the
Borrower's latest annual or quarterly financial statements and (iv) the greater
of (I) the net book value on a date no earlier than the date of the Borrower's
latest annual or quarterly financial statements and (II) the appraised value, as
estimated by independent appraisers reasonably acceptable to the Agent, of other
tangible assets of the Borrower and its Consolidated Subsidiaries as of a date
no earlier than the date of the Borrower's latest audited financial statements,
minus (b) to the extent not otherwise taken into account in the immediately
preceding clause (a), the sum of (i) minority interests, (ii) any natural gas
balancing liabilities and credits of the Borrower and its Consolidated
Subsidiaries reflected in the Borrower's latest audited financial statements,
(iii) the discounted future net revenue, calculated in accordance with
Commission guidelines (utilizing the Commission guideline prices utilized in the
Borrower's most current Reserve Report), attributable to reserves subject to
participation interests, overriding royalty interests or other interests of
third parties, pursuant to participation, partnership, vendor financing or other
agreements then in effect, or which otherwise are required to be delivered to
third parties, (iv) the discounted future net revenue, calculated in accordance
with Commission guidelines (utilizing the Commission guideline prices utilized
in the Borrower's most current Reserve Report), attributable to reserves that
are required to be delivered to third parties to fully satisfy the obligations
of the Borrower and its Consolidated Subsidiaries with respect to volumetric
production payments and (v) the discounted future net revenue, calculated in
accordance with Commission guidelines, attributable to reserves subject to
dollar-denominated production payments that, based on the estimates of
production included in determining the discounted future net revenue specified
in the immediately preceding clause (a) (i) (utilizing the Commission guideline
prices utilized in the Borrower's most current Reserve Report), would be
necessary to satisfy fully the obligations of the Borrower and its Consolidated
Subsidiaries with respect to dollar-denominated production payments.

     "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 

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<PAGE>   7
 
or more members of such immediate family and any Person who is controlled by any
such member or trust. For purposes of this definition, any Person which owns
directly or indirectly 20% or more of the securities having ordinary voting
power for the election of directors or other governing body of a corporation or
20% or more of the partnership or other ownership interests of any other Person
(other than as a limited partner of such other Person) will be deemed to
"control" (including, with its correlative meanings, "controlled by" and "under
common control with") such corporation or other Person.

     "Agent" means JEDI-II in its capacity as agent pursuant to Article XI and
includes any successor agent pursuant to Section 11.06.

     "Agent's Account" shall have the meaning specified in Section 9.03.

     "Average Share Price" means $9.50.

     "Basic Documents" means, collectively, this Indenture, the Securities
Purchase Agreement and the other Loan Documents.

     "Board of Directors" means the Board of Directors of the Borrower.

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

     "Business Day" means any day other than a Saturday, Sunday, or a legal
holiday for commercial banks in Houston, Texas, or New York, New York.

     "Business Opportunities Agreement" means the Corporate Shareholders'
Agreement dated as of even date herewith between the Purchasers and the
Borrower.

     "Capital Stock" of any Person means any and all shares, interests,
participations, or other equivalents (however designated) of, or rights,
warrants, or options to purchase, corporate stock, partnership interests, or any
other equity interest (however designated) of or in such Person.

     "Change in Control" means (i) a transaction, including any merger or
consolidation of Borrower with any other Person, in which the shareholders of
the Borrower immediately prior to such transaction (treating the holders of the
Warrants as holders of voting shares) do not own at least fifty-one percent
(51.0%) of the voting shares of stock of the Borrower (or the surviving 
entity in the case of a merger or consolidation) immediately following the
consummation of such transaction, or (ii) a transaction, including any merger or
consolidation of Borrower with any other Person, in which the members of the
Board of Directors immediately prior to such transaction do not comprise at
least a majority of the board of directors of the Borrower (or the surviving
entity in the case of a merger or consolidation) for a period of twelve (12)
months immediately following the consummation of such transaction, or (iii) an
event, including any merger or consolidation of Borrower with any other Person,
such that Mr. Ben Brigham no longer manages the Borrower (or the surviving

                                      -3-
<PAGE>   8
 
entity in the case of a merger or consolidation), other than as a result of his
death or disability.

     "Closing" has the meaning provided therefor in Section 2.02 of the
Securities Purchase Agreement.

     "Closing Date" means the date upon which the Closing occurs as provided in
Section 2.02 of the Securities Purchase Agreement.

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

     "Collateral" means the properties, property interests and rights described
in Section 4.01 hereof, or otherwise covered by the Collateral Documents, as
security for the Obligations.

     "Collateral Documents" means collectively the documents required by the
Agent or the Noteholders to obtain the security interests in the Collateral, as
described in Section 4.01 hereof, and all other agreements, documents and
instruments required in Section 4.01, as the same may from time to time be
amended or supplemented.

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

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

     "Consolidated Indebtedness" means all Debt of the Borrower and its
Consolidated Subsidiaries.

     "Consolidated Interest Coverage Ratio" means, as of the date of
determination, the ratio of (i) EBITDA for the preceding four calendar quarters
to (ii) Interest Expense for the same four calendar quarters.

     "Consolidated Net Income" means with respect to the Borrower and its
Consolidated Subsidiaries, for any period, the aggregate of the net income (or
loss) of the Borrower and its Consolidated Subsidiaries after allowance for
taxes for such period, determined on a consolidated basis in accordance with
GAAP; provided that there shall be excluded from the calculation of such net
income (to the extent otherwise included therein) the following: (i) the net
income of any Person in which Borrower or any Consolidated Subsidiary has an
interest (which interest does not cause the net income of such other Person to
be consolidated with the net income of Borrower and its Consolidated
Subsidiaries in accordance with GAAP), except to the extent of the amount of
dividends or distributions actually paid in such period by such other Person to
the Borrower or to a Consolidated Subsidiary, as the case may be; (ii) the net
income (but not loss) of any Consolidated Subsidiary to the extent that 

                                      -4-
<PAGE>   9
 
the declaration or payment of dividends or similar distributions or transfers or
loans by that Consolidated Subsidiary is not at the time permitted by operation
of the terms of its charter or any agreement, instrument or Governmental
Requirement applicable to such Consolidated Subsidiary, or is otherwise
restricted or prohibited, in each case determined in accordance with GAAP; (iii)
the net income (or loss) of any Person acquired in a pooling-of-interests
transaction for any period prior to the date of such transaction; (iv) any
extraordinary gains or losses, including gains or losses attributable to
Property sales not in the ordinary course of business; and (v) the cumulative
effect of a change in accounting principles and any gains or losses attributable
to writeups or writedowns of assets.

     "Consolidated Subsidiaries" shall mean each Subsidiary of the Borrower
(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 Borrower in accordance with GAAP.

     "corporate trust office" of the Trustee means the office of the Trustee at
the address set out in Section 13.05 or at any other office or agency so
designated by the Trustee.

     "Debt" means, for any Person the sum of the following (without
duplication): (i) all obligations of such Person for borrowed money or evidenced
by bonds, debentures, notes or other similar instruments (including principal
and earned but unpaid issuance fees); (ii) all obligations of such Person
(whether contingent or otherwise) in respect of bankers' acceptances, letters of
credit, surety or other bonds and similar instruments; (iii) all obligations of
such Person to pay the deferred purchase price of Property or services (other
than for borrowed money) excluding Trade Payables but including Schedule 8.02
Payables; (iv) all obligations under leases which shall have been, or should
have been, in accordance with GAAP, recorded as capital leases in respect of
which such Person is liable (whether contingent or otherwise); (v) all
obligations under leases (other than capital leases and oil and gas leases)
which require such Person or its Affiliate to make payments exceeding $100,000
(or $500,000 in the aggregate) over the term of such lease, including payments
at termination, which are substantially equal to at least 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 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 

                                      -5-
<PAGE>   10
 
of which such Person directly or indirectly received payment; and (xiv) all
obligations of such Person under Hedging Agreements, provided that "Debt" shall
not include (a) interest or fees (other than earned but unpaid issuance fees) on
any of the foregoing, (b) obligations associated with bid, performance, surety
or appeal bonds (including those required by Governmental Requirements in
connection with Oil and Gas Properties), (c) gas balancing obligations (whether
volumetric or dollar denominated), (d) intercompany obligations among the
Borrower and its Consolidated Subsidiaries, (e) indemnity obligations which have
not matured into fixed liabilities, and (f) purchase price adjustments and
similar post-closing obligations (but excluding the deferred payment of any
purchase price) incurred in connection with the permitted purchase and sale of
Property or stock, and which is to be determined and payable no later than 180
days following the closing of such purchase and sale.

     "Default" shall mean an Event of Default or an  event which with notice or
lapse of time, or both, would become, an Event of Default.

     "Default Rate" means, for any applicable period, an interest rate equal to
the then applicable rate of interest on the Notes (for cash payments of
interest) plus 4.00% per annum, but in no event shall the Default Rate exceed
the Maximum Rate.

     "EBITDA" shall mean, for any period, the sum of Consolidated Net Income for
such period plus the following expenses or charges to the extent deducted from
Consolidated Net Income in such period: interest, taxes, depreciation, depletion
and amortization, and other non-cash charges, minus all non-cash income added to
Consolidated Net Income in such period.

     "ECT" means Enron Capital & Trade Resources Corp., a Delaware corporation.

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

     "Employee Plan" means any employee benefit plan, program or policy with
respect to which the Borrower 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 Borrower
or any Subsidiary is conducting or at any time has conducted business, or where
any Property of the Borrower 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 

                                      -6-
<PAGE>   11
 
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 "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 Borrower 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 Borrower or any Subsidiary of the Borrower
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.

     "Event of Default" shall have the meaning assigned such term in Section
10.01.

     "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, 

                                      -7-
<PAGE>   12
 
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 obligations and other obligations of a like nature
incurred in the ordinary course of business; and (vii) Liens permitted by the
Loan Documents.

     "Federal Funds Rate" means, for any day, a fluctuating interest rate per
annum (rounded upwards, if necessary, to the nearest 1/100 of 1%) equal to the
weighted average of the rates on overnight federal funds transactions with
members of the Federal Reserve System arranged by federal funds brokers on such
day, as published for such day (or, if such day is not a Business Day, for the
next preceding Business Day) by the Federal Reserve Bank of New York, or, if
such rate is not so published for any day which is a Business Day, the average
of the quotations for any such day on such transactions received by the Agent
from three federal funds brokers of recognized standing selected by it.

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

     "First Reserve Report" shall have the meaning set out in Section 7.07(a).

     "Funding Date" means the first Business Day following the date all of the
conditions precedent to funding in Article VI of the Securities Purchase
Agreement 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
Borrower, the Subsidiaries or any of their Property or the Agent or any
Noteholder.

     "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 Section 7.11.

                                      -8-
<PAGE>   13
 
     "Guaranty Agreements" means the agreements executed by the Guarantors
substantially in the form of Exhibit B 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.

     "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 this instrument as originally executed, or, if amended or
supplemented as herein provided, as so amended or supplemented.

     "Initial Reserve Report" means the report of Cawley, Gillespie & Associates
with respect to the Oil and Gas Properties of BOG as of November 30, 1997, a
copy of which has been delivered to Agent.

     "Interest Expense" means, for each applicable period for which EBITDA is to
be calculated, the sum of all required cash payments of interest during such
period on borrowed money. Interest on the Notes, for purposes of this
definition, shall be deemed cash payments, calculated at the cash interest rate,
whether paid in cash or in kind, except that if a payment of interest is made in
kind on any Interest Payment Date, an amount equal to the cash payment of
interest that would have been due on such Interest Payment Date if payment in
kind had not been made shall be deemed subtracted from Interest Expense for the
four quarter period ending on the last day of the fiscal quarter preceding such
Interest Payment Date (but not for any other four quarter period for which
Interest Expense is calculated).

     "Interest Payment Date" means each November 20, February 20, May 20, and
August 20 following the Funding Date until and including the Maturity Date.

     "JEDI-II" means Joint Energy Development Investments II Limited
Partnership, a Delaware limited partnership.

     "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,

                                      -9-
<PAGE>   14
 
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 Indenture, a Person
shall be deemed to be the owner of any Property which it has acquired or holds
subject to a conditional sale agreement, or leases under a financing lease or
other arrangement pursuant to which title to the Property has been retained by
or vested in some other Person in a transaction intended to create a financing.

     "Loan Documents" means this 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 Borrower or any
Subsidiary or Affiliate of the Borrower (other than the Equity Documents and any
assignments, participation or similar agreements between any Noteholder and any
other lender or creditor with respect to any Obligations pursuant to this
Indenture) in connection with, or as security for the payment or performance of,
the Notes or this Indenture, as such agreements may be amended, supplemented or
restated from time to time.

     "Majority Noteholders" means, at any time, the Noteholders holding more
than 50% of the outstanding principal balance of the Notes.

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

     "Maturity Date" means August 20, 2003, or in the event of an acceleration
of the Obligations, such earlier date as the Obligations become due and payable
in full.

     "Maximum Rate" means at any particular time in question, the maximum
nonusurious rate of interest, if any, which under applicable law may then be
charged on the Notes. If such maximum rate changes after the date hereof, the
Maximum Rate shall be automatically increased or decreased, as the case may be,
without notice to the Borrower from time to time as the effective date of each
change in such maximum rate.

     "Mortgage" means the "Mortgage" referred to in Section 4.01(c) or
4.01(f)(ii) and any other mortgages executed pursuant to Section 7.09 hereof.

     "Mortgaged Property" means the Property owned by the Borrower and its
Subsidiaries which is subject to the Liens existing and to exist under the Loan
Documents.

                                      -10-
<PAGE>   15
 
     "Multiemployer Plan" means a Plan defined as such in Section 3(37) or
4001(a)(3) of ERISA.

     "NASDAQ" means  the National Association of Securities Dealers Automated
Quotation System.

     "Net Working Capital" means, for any Person or group of Persons and as of
any date of its determination, the difference (shown on the balance sheets of
such Person or group as of the end of the most recent fiscal quarter of such
Person or group for which internal financial statements are available) between
(i) all current assets of such Person or group and (ii) all current liabilities
of such Person or group, except the current portion of long-term Debt.

     "Notes" means the Senior Subordinated Secured Notes issued pursuant to
Section 2.03 of the Securities Purchase Agreement, in the aggregate face amount
of $50,000,000, dated as of the date hereof, made by the Borrower and payable to
the order of the Noteholders in their respective Participations.

     "Noteholders" 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 in
whose name a Note may be registered in the Note Register kept for that purpose.

     "Noteholder's Account" means for any Noteholder, the account specified by
such Noteholder as its Noteholder's Account by notice in writing to the Agent.

     "Note Register" and "Note Registrar" have the respective meanings specified
in Section 2.05.

     "Obligations" means any and all amounts, liabilities and obligations owing
from time to time by Borrower to the Agent or the Noteholders, pursuant to any
of the Basic Documents and all renewals, extensions and/or rearrangements
thereof, whether such amounts, liabilities or obligations be liquidated or
unliquidated, now existing or hereafter arising, absolute or contingent.

     "Officers' Certificate" means a certificate signed by the Chairman of the
Board, the President or any Vice President and by the Treasurer or any Assistant
Treasurer or the Secretary or any Assistant Secretary of the Borrower. Each such
certificate shall include the statements provided for in Section 13.13, if and
to the extent required by the provisions thereof.

     "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; 

                                      -11-
<PAGE>   16
 
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-of-way, easements and servitudes together with all additions,
substitutions, replacements, accessions and attachments to any and all of the
foregoing.

     "Opinion of Counsel" means an opinion in writing signed by legal counsel
who shall be reasonably satisfactory to the Trustee and may be counsel to the
Borrower. Each such opinion shall include the statements provided for in Section
13.13, if and to the extent required by the provisions thereof.

     "outstanding", when used with reference to Notes, means, as of any
particular time, all Notes authenticated and delivered by the Trustee under this
Indenture, except

          (a) Notes that have been canceled by the Trustee or delivered to the
     Trustee for cancellation;

          (b) Notes for which monies in the necessary amount for payment or
     redemption shall have been deposited in trust with the Trustee or with any
     paying agent (other than the Borrower), provided that, if such Notes are to
     be redeemed, notice of such redemption shall have been given as provided in
     Article IV or provision satisfactory to the Trustee shall have been made
     for giving such notice; and

          (c) Notes in lieu of or in substitution for which other Notes shall
     have been authenticated and delivered pursuant to the terms of Section
     2.06.

     "Participation" means, for each Noteholder, such Noteholder'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%.

                                      -12-
<PAGE>   17
 
     "PBGC" means the Pension Benefit Guaranty Corporation or any entity
succeeding to any or all of its functions.

     "Permitted Debt" means:

          (a) The Senior Loan, up to the lesser of $75,000,000 or the "Borrowing
     Base" under the Senior Credit Agreement;

          (b) The Notes or other Obligations arising under the Loan Documents or
     any guaranty of or suretyship arrangement for the Notes or other
     Obligations arising under the Loan Documents;

          (c) Debt of the Borrower which is existing on the Closing Date and is
     reflected in the Financial Statements or which constitutes Schedule 8.02
     Payables, and any renewals or extensions (but not increases) thereof;

          (d) Accounts payable for the deferred purchase price of Property or
     services (other than Trade Payables) from time to time incurred in the
     ordinary course of business which, if greater than 60 days past the invoice
     or billing date, are being contested in good faith by appropriate
     proceedings if reserves adequate under GAAP shall have been established
     therefor;

          (e) Debt of the Borrower under capital leases (as required to be
     reported on the financial statements of the Borrower pursuant to GAAP) not
     to exceed $2,000,000;

          (f) Debt of the Borrower under Hedging Agreements with a Senior Lender
     or another investment grade counterparty the notional amounts on which do
     not exceed 75% of Borrower's anticipated oil and/or gas production to be
     produced during the term of such Hedging Agreements entered into as a part
     of its normal business operations as a risk management strategy and/or
     hedge against changes resulting from market conditions related to the
     Borrower's and its Subsidiaries' operations; and

          (g) Debt of the Borrower not described in clauses (a) through (f)
     which, in the aggregate, does not exceed $1,000,000 at any one time
     outstanding.

     "Person" means any individual, corporation, company, voluntary association,
partnership, joint venture, trust, limited liability company, unincorporated
organization or government or any agency, instrumentality or political
subdivision thereof, or any other form of entity.

     "Plan" means any employee pension benefit plan, as defined in Section 3(2)
of ERISA, which (i) is currently or hereafter sponsored, maintained or
contributed to by the Borrower, any Subsidiary or an ERISA Affiliate or (ii) was
at any time during the preceding 

                                      -13-
<PAGE>   18
 
six calendar years sponsored, maintained or contributed to, by the Borrower, 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.

     "Registration Rights Agreement" means the Registration Rights Agreement
dated as of the date hereof, made by the Borrower 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" means a report, in form satisfactory to the Senior Loan
Agent (or if there is no Senior Loan or requirement for a Reserve Report under
the Senior Loan, the Agent), setting forth, as of the dates set forth in
Sections 7.07(a) and (b) (or such other date in the event of an unscheduled
redetermination); (i) the proved oil and gas reserves attributable to the
Borrower's and its Subsidiaries' Hydrocarbon Interests together with a
projection of the rate of production and future net income, taxes, operating
expenses and capital expenditures with respect thereto as of such date, based
upon the pricing assumptions consistent with Commission reporting requirements
at the time and (ii) such other information as the Senior Loan Agent (or, if
there is no Senior Loan, or requirement for a Reserve Report under the Senior
Loan, the Agent) may reasonably request.  The term "Reserve Report" shall also
include the Initial Reserve Report, the First Reserve Report, the supplemental
Reserve Reports described in Section 7.07(b), and the information to be provided
by the Borrower each year pursuant to Section 7.07(d).

     "Responsible Officer" means, as to any Person, the Chief Executive Officer,
the President, any Vice President or the Chief Financial Officer of such Person.
Unless otherwise specified, all references to a Responsible Officer herein shall
mean a Responsible Officer of the Borrower.  "Responsible Officer" when used
with respect to the Trustee means the chairman or the vice-chairman of the board
of directors, the chairman of the executive committee of the board of directors,
the president, any vice president, any second or assistant vice president, the
cashier, any assistant cashier, the secretary, any assistant secretary, the
treasurer, any assistant treasurer, any senior trust officer or trust officer,
or any other officer or assistant officer of the Trustee customarily performing
functions similar to those performed by the persons who at the time shall be
such officers, respectively, or to whom any corporate trust matter is referred
because of his knowledge of and familiarity with the particular subject.

     "Schedule 8.02 Payables" means payables owing under the agreements listed
on Schedule 8.02 which are outstanding more than 75 days after they become fixed
and owing, provided that the aggregate amounts of such payables under each such
agreement do not exceed the amount set forth for each such agreement on such
schedule.

                                      -14-
<PAGE>   19
 
     "Scheduled Redetermination Date"  means the last Business Day of each
September and  March during the term of the Notes, commencing September 1999.

     "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.

     "Securities Purchase Agreement" means the Securities Purchase Agreement
dated of even date herewith between the Noteholders and the Borrower.

     "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 with banks or other financial
institutions 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 or the Borrower 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 Borrower and
ECT Securities Corp. dated as of the date hereof.

                                      -15-
<PAGE>   20
 
     "Subordination Agreement" means the Intercreditor and Subordination
Agreement dated as of even date herewith, by and among the Trustee, the Senior
Loan Agent, the Senior Lenders, the Agent, the Noteholders, the Borrower and
certain Subsidiaries, substantially in the form of Exhibit C 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 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 Borrower.
Quest Resources L.L.C. and Venture Acquisitions L.P. shall not be considered
Subsidiaries of Borrower.

     "TIA" (except as herein otherwise expressly provided or unless the context
otherwise requires) means the Trust Indenture Act of 1939, as amended, as in
force at the date of this Indenture as originally executed.

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

     "Trustee" means Chase Bank of Texas, National Association, and, subject to
the provisions of Article XII, shall also include its successors and assigns.

     "Warrants" means the Warrants issued by the Borrower to ECT and JEDI-II in
their respective Participations pursuant to Section 2.03 of the Securities
Purchase Agreement, 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 therefore, pursuant to the Warrant Certificate to be issued to ECT
and JEDI-II, forms of which are attached to the Securities Purchase Agreement as
Exhibit A.

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


     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 to the Agent or the Noteholders (including ACNTA
calculations) hereunder shall be prepared, in accordance with GAAP, applied on a
basis consistent with the Financial Statements (except for changes concurred
with by the Borrower's independent public accountants).

                                      -16-
<PAGE>   21
 
                                  ARTICLE II
               ISSUE, DESCRIPTION, FORM, EXECUTION, REGISTRATION
                       OF TRANSFER AND EXCHANGE OF NOTES

     Section 2.01  Form and Dating.  The Notes and the Trustee's certificate of
authentication are to be substantially in the form of Exhibit A, with such
appropriate insertions, omissions, substitutions, amendments, changes and other
variations as are required or permitted by this Indenture, and may have such
letters, numbers or other marks of identification and such legends or
endorsements placed thereon as may be required to comply with the rules of any
securities exchange on which the Notes may be listed or as may, consistently
herewith, be determined by the officers executing such Notes as evidenced by
their execution of the Notes.

     The terms and provisions contained in the Notes and each Guaranty Agreement
shall constitute, and are hereby expressly made, a part of this Indenture and,
to the extent applicable, the Borrower and the Guarantors, by their execution
and delivery of this Indenture and each Guaranty Agreement, expressly agree to
such terms and provisions and to be bound thereby.

     The definitive Notes shall be printed or produced in any manner as may be
determined by the officers executing such Notes, as evidenced by their execution
of such Notes.

     Section 2.02  Execution and Authentication.  The Notes and each Guaranty
Agreement shall be executed by the Borrower and Guarantors, respectively, and be
delivered to the Trustee for authentication, and the Trustee shall thereupon, or
from time to time thereafter, authenticate and deliver said Notes and each
Guaranty Agreement to and upon the written order of the Borrower, signed by its
President or a Vice President and by its Treasurer, Assistant Treasurer,
Secretary or Assistant Secretary, without any further action by the Borrower.

     Section 2.03  Denomination of Notes and Record Date.  The Notes shall be
issuable as registered Notes without coupons in denominations of $1,000 and any
integral multiple thereof.  Each Note shall be dated the date of its
authentication.

     The person in whose name any Note is registered at the close of business on
any record date (as hereinafter defined) with respect to any interest payment
date shall be entitled to receive the interest payable on such interest payment
date. The term "record date" as used with respect to any Interest Payment Date
shall mean the day of the calendar month preceding the day on which such
Interest Payment Date falls.  The principal of, and premium, if any, and
interest on, the Notes shall be payable at the principal office of the Borrower
and any other office or agency of the Borrower designated for that purpose;
provided, however, that principal and interest may be payable at the option of
the Noteholders to the Agent's Account.

                                      -17-
<PAGE>   22
 
     Section 2.04  Manual Execution.  The Notes and Guaranty Agreements shall be
signed manually or by facsimile signature on behalf of the Borrower by its
President or a Vice President attested by the manual or facsimile signature of
its Secretary or an Assistant Secretary.

     Only such Notes as shall bear thereon a certificate of authentication
substantially in the form recited in Exhibit A, manually executed by the
Trustee, shall be entitled to the benefits of this Indenture or be valid or
obligatory for any purpose. Such certificate by the Trustee upon any Note
executed by the Borrower shall be conclusive evidence that the Note so
authenticated has been duly authenticated and delivered hereunder.

     In case any officer of the Borrower who shall have signed any of the Notes
shall cease to be such officer before the Notes so signed shall have been
authenticated and delivered by the Trustee, or disposed of by the Borrower, such
Notes nevertheless may be authenticated and delivered or disposed of as though
the person who signed such Notes had not ceased to be such officer of the
Borrower; and any Note may be signed on behalf of the Borrower by such persons
as, at the actual date of the execution of such Note, shall be the proper
officers of the Borrower, although at the date of the execution of this
Indenture any such person was not an officer.

     Section 2.05  Transfer and Exchange.  The Notes may be exchanged for a like
aggregate principal amount of Notes of other authorized denominations.  Notes to
be exchanged shall be surrendered at the Borrower's principal office, and the
Borrower shall execute and the Trustee shall authenticate and deliver in
exchange therefor the Note or Notes which the Noteholder making the exchange
shall be entitled to receive.

     The Borrower shall keep or cause to be maintained at said office or agency
a register (herein sometimes referred to as the "Note Register") in which,
subject to such reasonable regulations as it may prescribe, the Borrower shall
register Notes and shall register the transfer of Notes as in this Article II
provided. For the purposes of registration, exchange, registration of transfer,
redemption or conversion of Notes, the Trustee is hereby appointed Note
Registrar. Upon surrender for registration of transfer of any Note at said
office or agency, the Borrower shall execute and the Trustee shall authenticate
and deliver in the name of the transferee or transferees a new Note or Notes in
a like aggregate principal amount. At all reasonable times the Note Register
shall be open for inspection by the Trustee. No transfer of any Note shall be
valid unless made at said office or agency.

     All Notes presented or surrendered for registration of transfer, exchange,
conversion or payment shall (if so required by the Borrower or the Trustee) be
accompanied by a written instrument or instruments of transfer, in form
satisfactory to the Borrower and the Trustee, duly executed by the registered
Noteholder or his attorney duly authorized in writing.

     No service charge shall be made for any exchange or registration of
transfer of Notes, or issue of new Notes in case of partial prepayment or
conversion, but the Borrower may 

                                      -18-
<PAGE>   23
 
require payment of a sum sufficient to cover any tax or other governmental
charge that may be imposed in relation thereto.

     The Borrower shall not be required (i) to issue, register the transfer of,
or exchange any Note during a period beginning at the opening of business 15
days before the mailing of a notice of redemption of the Notes selected for
redemption and ending on the day of such mailing, or (ii) to register the
transfer of or exchange any Note so selected for redemption in whole or in part,
except the unredeemed portions of Notes being redeemed in part.

     Section 2.06  Replacement Notes.  In case any Note shall become mutilated
or be destroyed, lost or stolen, the Borrower shall execute, and the Trustee
shall authenticate and deliver, a new Note, in exchange and substitution for the
mutilated Note or in lieu of and substitution for the Note destroyed, lost or
stolen. In every case, the applicant for a substituted Note shall furnish to the
Borrower and the Trustee such security or indemnity as may be required by them
to hold each of them harmless, and, in every case of destruction, loss or theft,
the applicant shall also furnish to the Borrower and to the Trustee evidence to
their satisfaction of the destruction, loss or theft of such Note and of the
ownership thereof. The Trustee may authenticate any such substituted Note and
deliver the same upon the request or authorization of the Borrower.  Upon the
issuance of any substituted Note, the Borrower may require the payment of a sum
sufficient to cover any tax or other governmental charge that may be imposed in
relation thereto and any other expenses connected therewith, including fees and
expenses of the Trustee. In case any Note which has matured or is about to
mature or has been called for prepayment or has been presented for conversion
shall become mutilated or be destroyed, lost or stolen, the Borrower may,
instead of issuing a substitute Note, pay or authorize the payment of the same
(without surrender thereof except in the case of a mutilated Note) if the
applicant for such payment shall furnish the Borrower and the Trustee with such
security or indemnity as may be required by them to hold each of them harmless,
and, in case of destruction, loss or theft, evidence to the satisfaction of the
Borrower and the Trustee of the destruction, loss or theft of such Note and of
the ownership thereof.

     If, after the delivery of such replacement Note, a bona fide purchaser of
the original Note in lieu of which such replacement Note was issued presents for
payment or registration such original Note, the Trustee shall be entitled to
recover such replacement Note from the person to whom it was delivered or any
person taking therefrom, except a bona fide purchaser, and shall be entitled to
recover upon the security or indemnity provided therefor to the extent of any
loss, damage, cost or expense incurred by the borrower or Trustee in connection
therewith.

     Every substituted Note issued pursuant to the provisions of this Section
2.06 upon evidence that any Note is destroyed, lost or stolen shall, with
respect to such Note, constitute an additional contractual obligation of the
Borrower, whether or not the destroyed, lost or stolen Note shall be found at
any time, and shall be entitled to all the benefits of this Indenture equally
and proportionately with any and all other Notes duly issued hereunder. 

                                      -19-
<PAGE>   24
 
All Notes shall be held and owned upon the express condition that the foregoing
provisions are exclusive with respect to the replacement or payment of
mutilated, destroyed, lost or stolen Notes, and shall preclude any and all other
rights or remedies, notwithstanding any law or statute existing or hereafter
enacted to the contrary with respect to the replacement or payment of negotiable
instruments or other securities without their surrender.

     Section 2.07  Cancellation of Notes.  All Notes surrendered for payment,
conversion, registration of transfer or exchange shall, if surrendered to the
Borrower or any paying agent, be delivered to the Trustee for cancellation, or,
if surrendered to the Trustee, shall be canceled by it, and no Notes shall be
issued in lieu thereof except as expressly permitted by any of the provisions of
this Indenture. On request of the Borrower, the Trustee shall deliver to the
Borrower canceled Notes held by the Trustee; provided, however, that the Trustee
may at any time destroy any canceled Notes and deliver to the Borrower a
certificate of such destruction.  If the Borrower shall acquire any of the
Notes, however, such acquisition shall not operate as a redemption or
satisfaction of the indebtedness represented by such Notes unless and until the
same are delivered to the Trustee or surrendered to the Trustee for
cancellation.

     Section 2.08  No Third Party Benefit.  Subject to the terms of the
Subordination Agreement, nothing in this Indenture or in the Notes, expressed or
implied, shall give or be construed to give to any person, firm or corporation,
other than the parties hereto and the Noteholders, any legal or equitable right,
remedy or claim under or in respect of this Indenture, or under any covenant,
condition or provision herein contained; all its covenants, conditions and
provisions being for the sole benefit of the parties hereto and of the
Noteholders.


                                  ARTICLE III
                                 SUBORDINATION

     The Notes shall be subject to the Subordination Agreement.


                                  ARTICLE IV
                         SECURITY FOR THE OBLIGATIONS

     Section 4.01  Security.  The Obligations shall be secured by the following
which, in each case shall be subordinate in priority only to those liens,
security interests or rights granted in the same collateral to secure the
performance of Borrower under the Senior Loan Documents, in accordance with, but
subject to, the terms of the Subordination Agreement:

          (a) (i)  A Security Agreement substantially in the form of Exhibit D
duly executed by the Borrower in favor of the Trustee for the ratable benefit of
the Noteholders granting a security interest in all of the Borrower's right,
title and interest in and to the Capital Stock of Brigham, Inc. and Brigham
Holdings I, LLC, together with proper UCC-1 

                                      -20-
<PAGE>   25
 
Financing Statements duly filed in Texas, (ii) a Security Agreement
substantially in the form of Exhibit D duly executed by Brigham, Inc. in favor
of the Trustee for the ratable benefit of the Noteholders granting a security
interest in all of Brigham, Inc.'s right, title and interest in and to the
Capital Stock of Brigham Holdings II, LLC and BOG, together with proper UCC-1
Financing Statements duly filed in Texas, (iii) a Security Agreement
substantially in the form of Exhibit D duly executed by Brigham Holdings II, LLC
in favor of the Trustee for the ratable benefit of the Noteholders granting a
security interest in all of Brigham Holdings II, LLC's, right, title and
interest in and to the Capital Stock of BOG, together with proper UCC-1
Financing Statements duly filed in Texas and (iv) a Security Agreement
substantially in the form of Exhibit D duly executed by Brigham Holdings I, LLC
in favor of the Trustee for the ratable benefit of the Noteholders granting a
security interest in all of Brigham Holdings I, LLC's right, title and interest
in and to the Capital Stock of BOG, together with proper UCC-1 Financing
Statements duly filed in Texas.

          (b) A Security Agreement, substantially in the form of Exhibit E duly
executed by BOG in favor of the Trustee, as collateral agent for the ratable
benefit of the Noteholders granting a security interest in all of BOG's right,
title and interest in and to all accounts, general intangibles, equipment and
inventory of BOG subject to Liens under the Senior Loan Documents.

          (c) A Mortgage, Deed of Trust, Assignment of Production, Security
Agreement and Financing Statement substantially in the form of Exhibit F
executed by BOG in favor of the Trustee, as collateral agent for the ratable
benefit of the Noteholders covering all of the Property of BOG subject to Liens
under the Senior Loan Documents.

          (d) A Guaranty Agreement duly executed by each of BOG, Brigham, Inc.,
Brigham Holdings I, LLC and Brigham Holdings II, LLC in favor of the Trustee for
the ratable benefit of the Noteholders guarantying the payment and performance
of the Obligations.

          (e)  Stock Powers executed by the Borrower and related stock
certificates of Brigham, Inc.

          (f) (i) Guaranty Agreements from each and every Person now or
hereafter guaranteeing all or any portion of the Senior Loan, (ii) Mortgages
covering any and all real property (including Oil and Gas Property) now or
hereafter pledged as collateral for all or any portion of the Senior Loan, (iii)
security agreements covering any and all Property (other than real property
subject to a Mortgage) now or hereafter pledged as collateral for all or any
portion of the Senior Loan, and (iv) financing statements, stock pledges or
other agreements necessary or appropriate to perfect the liens and/or security
interests granted pursuant to any of the foregoing.  Each of the foregoing
instruments shall be in substantially the same form and substance as those
executed of even date herewith or otherwise.

                                      -21-
<PAGE>   26
 
                                   ARTICLE V
                                  [RESERVED]


                                  ARTICLE VI
                                  [RESERVED]


                                  ARTICLE VII
                             AFFIRMATIVE COVENANTS

     Unless the Agent's prior written consent to the contrary is obtained, the
Borrower will, for the benefit of each of the Noteholders, at all times comply
with the covenants contained in this Article VII (or cause each Subsidiary's
compliance with the applicable covenants), from the date hereof and for so long
as any part of the Obligations is outstanding.

     Section 7.01  Financial Statements and Reports. The Borrower shall
deliver, or shall cause to be delivered, to the Agent with sufficient copies for
each of the Noteholders:

          (a) Annual Financial Statements.  As soon as available and in any
event within 90 days after the end of each fiscal year of the Borrower, the
audited consolidated statements of income, stockholders' equity, changes in
financial position and cash flow of the Borrower and its Consolidated
Subsidiaries for such fiscal year, and the related consolidated and unaudited
consolidating balance sheets of the Borrower and its Consolidated Subsidiaries
as at the end of such fiscal year, and setting forth in each case in comparative
form the corresponding figures for the preceding fiscal year, and accompanied by
the related opinion of independent public accountants of recognized national
standing acceptable to the Senior Loan Agent (or in the absence of a Senior
Loan, the Agent) which opinion shall state that said financial statements fairly
present the consolidated financial condition and results of operations of the
Borrower and its Consolidated Subsidiaries as at the end of, and for, such
fiscal year and that such financial statements have been prepared in accordance
with GAAP except for such changes in such principles with which the independent
public accountants shall have concurred and such opinion shall not contain a
"going concern" or like qualification or exception.

          (b) Quarterly Financial Statements.  As soon as available and in any
event within 60 days after the end of each of the first three fiscal quarterly
periods of each fiscal year of the Borrower, consolidated statements of income,
stockholders' equity, changes in financial position and cash flow of the
Borrower and its Consolidated Subsidiaries for such period and for the period
from the beginning of the respective fiscal year to the end of such period, and
the related consolidated and consolidating balance sheets as at the end of such
period, setting forth in each case in comparative form the corresponding figures
for the corresponding period in the preceding fiscal year, accompanied by the
certificate of a Responsible Officer, which certificate shall state that said
financial statements fairly present 

                                      -22-
<PAGE>   27
 
the consolidated financial condition and results of operations of the Borrower
and its Consolidated Subsidiaries in accordance with GAAP, as at the end of, and
for, such period (subject to normal year-end audit adjustments).

          (c) Notice of Default.  Promptly after the Borrower knows that any
Default or any Material Adverse Effect has occurred, a notice of such Default or
Material Adverse Effect, describing the same in reasonable detail and the action
the Borrower proposes to take with respect thereto.

          (d) Other Accounting Reports.  Promptly upon receipt thereof, a copy
of each other report or letter (excluding routine correspondence and audit
request letters) submitted to the Borrower by independent accountants in
connection with any annual, interim or special audit made by them of the books
of the Borrower, and a copy of any response by the Borrower to such letter or
report (including responses to any audit request letters).

          (e) SEC Filings, Etc.  Promptly upon its becoming available, each
financial statement, report, notice or proxy statement sent by the Borrower to
stockholders generally and each regular or periodic report and any registration
statement, prospectus or written communication (other than transmittal letters)
in respect thereof filed by the Borrower with or received by the Borrower in
connection therewith from any securities exchange or the Commission or any
successor agency.

          (f) Notices Under Other Loan Agreements.  Promptly after the
furnishing thereof, copies of any statement, report or notice furnished to any
Person pursuant to the terms of any indenture, loan or credit or other similar
agreement, other than this Indenture and not otherwise required to be furnished
to the Agent or the Trustee pursuant to any other provision of this Section
7.01.

          (g) Other Matters.  Subject to any applicable restrictions on
disclosure, from time to time such other information regarding the business,
affairs or financial condition of the Borrower (including, without limitation,
any Plan or Multiemployer Plan and any reports or other information required to
be filed under ERISA) as may be requested by and provided to the Senior Lender
or Senior Loan Agent.

          (h) Annual Budgets.  Concurrent with the First Reserve Report and each
January 1 Reserve Report thereafter, a one-year financial projection for the
Borrower and its Subsidiaries in form acceptable to the Senior Loan Agent (or in
the absence of a Senior Loan or Senior Loan Agent, the Agent), which projection
shall include revenues, expenses and capital expenditures.

          (i) Monthly Operating Statements.  As soon as available and in any
event within 30 days after the end of each month, monthly operating statements
of BOG including, without limitation, production reports and general and
administrative cost summaries by lease for its Oil and Gas Properties, which
reports shall include quantities or volume of production, revenue, realized
product prices, taxes, capital expenditures by category and lease 

                                      -23-
<PAGE>   28
 
operating costs which have accrued to BOG's accounts in such period, and such
other information with respect thereto as the Senior Loan Agent (or in the
absence of a Senior Loan or Senior Loan Agent, the Agent) may require.

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 C-2 to the Senior Credit Agreement 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)
setting forth in reasonable detail the computations necessary to determine
whether the Borrower is in compliance with Sections 8.01 and 8.16 as of the end
of the respective fiscal quarter or fiscal year, and (iii) certifying that said
financial statements fairly present the consolidated and consolidating financial
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).

     Section 7.02  Litigation.  The Borrower shall promptly give to the Agent
notice of: (i) all legal or arbitral proceedings, and of all proceedings before
any Governmental Authority involving the Borrower or any Guarantor, except
proceedings which, if adversely determined within any reasonable range of loss,
would not have a Material Adverse Effect, and (ii) of any material litigation or
material proceeding against the Borrower or any Guarantor in which the amount
involved is not covered in full by insurance (subject to normal and customary
deductibles), or in which injunctive or similar relief is sought.  The Borrower
will, and will cause each of the Guarantors to, promptly notify the Agent of any
claim, judgment, Lien or other encumbrance affecting any Property of the
Borrower or any Guarantor if the value of the claim, judgment, Lien, or other
encumbrance affecting such Property shall exceed $1,000,000.

     Section 7.03  Maintenance, Etc.

          (a) The Borrower shall and shall cause each Subsidiary to: upon
reasonable notice, permit representatives of the Agent, during normal business
hours, to examine, copy and make extracts from its financial books and records,
to inspect its Properties, and to discuss its business and affairs with its
officers, all to the extent reasonably required by the Agent; keep, or cause to
be kept, insured by financially sound and reputable insurers all Property of a
character usually insured by Persons engaged in the same or similar business
similarly situated against loss or damage of the kinds and in the amounts
customarily insured against by such Persons and carry such other insurance as is
usually carried by such Persons including, without limitation, environmental
risk insurance to the extent reasonably available; and, where failure to do so
would have a Material Adverse Effect: preserve and maintain its corporate
existence and all of its material attendant rights, privileges and franchises,
keep appropriate books of record and account in relation to its business and
activities, comply with all Governmental Requirements, pay and discharge all
taxes, assessments and governmental charges or levies imposed on it or on its
income or profits or on any of its Property, except for any such tax,
assessment, charge or levy the payment of which is being contested in 

                                      -24-
<PAGE>   29
 
good faith and by proper proceedings and against which adequate reserves are
being maintained.

          (b) Contemporaneously with the delivery of the financial statements
required by Section 7.01(a) to be delivered for each year, the Borrower will
furnish or cause to be furnished to the Agent a certificate of insurance
coverage from the insurer in form and scope reasonably satisfactory to the Agent
and, if required by the Agent, will furnish the Agent copies of the applicable
policies.

          (c) The Borrower will and will cause each Subsidiary to maintain and
operate its Oil and Gas Properties and other material Properties or cause or
make reasonable and customary efforts to cause such Oil and Gas Properties and
other material Properties to be maintained and operated in all material respects
in a good and workmanlike manner in accordance with the practices of the
industry and in compliance with all applicable contracts and agreements and in
compliance in all material respects with all Governmental Requirements.  The
covenants contained in this Section 7.03(c) shall not apply to insignificant
Properties unless a failure of such covenant could have a Material Adverse
Effect.

     Section 7.04  Environmental Matters.

          (a) To the extent that a reasonably prudent owner or operator would do
so under the same or similar circumstances, the Borrower will and will cause
each Subsidiary to establish and implement such procedures as may be reasonably
necessary to periodically determine and assure that all Oil and Gas Properties
of the Borrower and the Subsidiaries and the operations conducted thereon and
other activities of the Borrower and the Subsidiaries are in compliance with and
do not violate the requirements of any Environmental Laws, where failure of the
foregoing would have a Material Adverse Effect.

          (b) The Borrower will promptly notify the Agent in writing of any
threatened action, investigation or inquiry by any Governmental Authority of
which the Borrower has knowledge in connection with any Environmental Laws with
respect to the Property of the Borrower or any Subsidiary, excluding routine
testing, compliance and correction action.

     Section 7.05  Further Assurances.  The Borrower will and will cause each
Guarantor to cure promptly any defects in the creation and issuance of the Notes
and the execution and delivery of the Basic Documents.  The Borrower at its
expense will and will cause each Guarantor to promptly execute and deliver to
the Agent upon request all such other documents, agreements and instruments  to
further evidence and more fully describe the collateral intended as security for
the Notes, or to correct any omissions in the Basic Documents, or to state more
fully the security obligations set out herein or in any of the Basic Documents,
or to perfect, protect or preserve any Liens created pursuant to any of the
Basic Documents, or to make any recordings, to file any notices or obtain any
consents, all as may be necessary or appropriate in connection therewith.

                                      -25-
<PAGE>   30
 
     Section 7.06  Performance of Obligations.  The Borrower will pay the Notes
according to the reading, tenor and effect thereof; and the Borrower will and
will cause each Guarantor to do and perform every act and discharge all of the
obligations to be performed and discharged by them under the Basic Documents, at
the time and times and in the manner specified.

     Section 7.07  Engineering Reports.

          (a) Not less than 30 days prior to the First Borrowing Base
Determination Date, the Borrower shall furnish to the Agent a Reserve Report
prepared as of December 1, 1998 or later (the "First Reserve Report") and as
provided in clause 7.07(b) below.

          (b) On January 31, 1999 and not less than 30 days prior to each
Scheduled Redetermination Date thereafter, commencing with the Scheduled
Redetermination Date to occur on September 30, 1999, the Borrower shall furnish
to the Agent a Reserve Report.  The Reserve Report furnished for the September
30 Scheduled Redetermination Date shall be prepared as of the preceding July 1
and the Reserve Report furnished for the March Scheduled Redetermination Date
(as well as the Reserve Report furnished on January 31, 1999) shall be prepared
as of the preceding January 1.  The Reserve Report furnished on January 31, 1999
and the January 1 Reserve Report of each year beginning January 1, 2000 shall be
prepared by certified independent petroleum engineers or other independent
petroleum consultant(s) acceptable to the Agent and the First Reserve Report and
the July 1 Reserve Report 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 First Reserve
Report or January 1 Reserve Report, as appropriate.  At Borrower's option, the
July 1 Reserve Report 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 on.

          (c) In addition, the Borrower shall furnish to the Agent copies of any
additional Reserve Reports (other than those specified in Sections 7.07(a) and
(b) above) that Borrower or any of its Subsidiaries deliver to the Senior Loan
Agent or Senior Lenders pursuant to the Senior Loan Documents.

          (d) With the delivery of each Reserve Report, the Borrower shall
provide to the Agent:

              (i)    a certificate from a Responsible Officer certifying that,
     to the best of his knowledge and in all material respects: (i) the most
     recently delivered Reserve Report does not in the belief of such officer
     and based upon information in the Borrower's possession, materially
     overstate the oil and gas reserves of the Borrower and the Subsidiaries as
     a whole bearing in mind that reserves are evaluated based upon estimates
     and assumptions with respect to which reasonable minds of competent
     engineers may differ, (ii) except as set forth in such Reserve Report or on

                                      -26-
<PAGE>   31
 
     an exhibit to the certificate, on a net basis there are no gas imbalances,
     take or pay or other prepayments with respect to its Oil and Gas Properties
     evaluated in such Reserve Report which would violate Section 8.14, (iii)
     none of its proved Hydrocarbon Interests have been sold since the date of
     the last Borrowing Base determination except as set forth on an exhibit to
     the certificate, which certificate shall list all of its proved Hydrocarbon
     Interests sold and in such detail as reasonably required by the Agent, (iv)
     attached to the certificate is a list of its proved Hydrocarbon Interests
     added to and deleted from the immediately prior Reserve Report and a list
     showing any change in working interest or net revenue interest in its
     Hydrocarbon Interests occurring, (v) at the Agent's request, attached to
     the certificate is a list of all Persons disbursing proceeds to the
     Borrower from its Oil and Gas Properties and (vi) except as set forth on a
     schedule attached to the certificate all of the proved Hydrocarbon
     Interests evaluated by such Reserve Report are Mortgaged Property; and

              (ii)   a certificate from a Responsible Officer certifying that,
     to the best of his knowledge and in all material respects (i) the
     representations of the Borrower in Section 4.10 are true and correct and
     apply to the Hydrocarbon Interests evaluated in the Reserve Report that are
     described in the Mortgage and (ii) the Borrower has, with respect to those
     material Hydrocarbon Interests that are evaluated in the most recently
     delivered Reserve Report, but that are not covered by a Mortgage, conducted
     overall title due diligence that, in all material respects, equals or
     exceeds industry standards given the applicable facts and circumstances.

          (e) In addition to the foregoing, on August 30, 1998, the Borrower
shall furnish to the Agent a Reserve Report prepared as of July 1, 1998, 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 Initial Reserve
Report.

          (f) Notwithstanding the foregoing, so long as there is a Senior Credit
Agreement in effect which requires the semi-annual delivery to the Senior
Lenders of reserve reports evaluating the Borrower's and its Subsidiaries' Oil
and Gas Properties, delivering the Agent and Noteholders with a copy of each
such reserve report and any accompanying officer's certificate (certified to
Agent and the Noteholders) required thereunder shall satisfy the Borrower's
obligations under this Section 7.07, so long as such reserve report includes a
calculation of reserve value based upon pricing assumptions consistent with
Commission reporting requirements at the time.

     Section 7.08  Intentionally Omitted.

     Section 7.09  Additional Collateral.

          (a) Should any of the Borrower's or any Subsidiary's Properties which
are not Mortgaged Property be pledged as collateral for the payment of all or
any portion of the 

                                      -27-
<PAGE>   32
 
Senior Loan Obligations, the Borrower will simultaneously with such pledge in
favor of the Senior Lenders (or Senior Loan Agent) grant or cause such
Subsidiary to grant to the Trustee as security for the Obligations a second-
priority Lien interest (subject only to Excepted Liens, the matters set out on
Schedule 4.10 of the Securities Purchase Agreement, and any additional
qualifications and exceptions accepted by the Senior Lenders under any mortgage
of such Property to the Senior Agent) in the Borrower's or the Subsidiary's
interest in such Properties not already subject to a Lien of the Basic
Documents, which Lien will be created and perfected by and in accordance with
the provisions of deeds of trust, security agreements and financing statements,
or other Basic Documents, all in form substantially the same as the previous
Collateral Documents and in sufficient executed (and acknowledged where
necessary or appropriate) counterparts for recording purposes.

          (b) Concurrently with the granting of the Lien or other action
referred to in Section 7.09(a) above, the Borrower will provide to the Agent all
title information provided to the Senior Lenders or Senior Loan Agent in
connection therewith and any legal opinion (addressed to the Agent as well)
provided to the Seniors Lenders or Senior Loan Agent in connection therewith.

     Section 7.10  ERISA Information and Compliance.  Immediately after any
Responsible Officer of the Borrower knows or has reason to know any of the
following items are true, the Borrower will deliver to the Agent a certificate
of a Responsible Officer of the Borrower setting forth details as to such
occurrence and such action, if any, the Borrower or any ERISA Affiliate is
required or proposes to take, together with any notices required or proposed to
be given to or filed with or by the Borrower or its ERISA Affiliate with respect
thereto: that a Reportable Event has occurred or that an application may be or
has been made to the Secretary of the Treasury for a waiver or modification of
the minimum funding standard; that a Multiemployer Plan has been or may be
terminated, reorganized, partitioned or declared insolvent under Title IV of
ERISA; that any required contribution which is material to a Plan, Multiemployer
Plan or Employee Plan has not been or may not be timely made; that proceedings
may be or have been instituted under Section 4069(a) of ERISA to impose
liability on the Borrower or an ERISA Affiliate or under Section 4042 of ERISA
to terminate a Plan or appoint a trustee to administer a Plan; that the Borrower
or any ERISA Affiliate has incurred or may incur any liability (including any
contingent or secondary liability) on account of the termination of or
withdrawal from a Plan or a Multiemployer Plan; and that the Borrower or any
ERISA Affiliate may be required to provide security to a Plan under Section
401(a)(29) of the Code; or any other condition(s) exist(s) or may occur with
respect to one or more Plans, Employee Plans and/or Multiemployer Plans which
would reasonably be expected to result, individually or in the aggregate, in a
Material Adverse Effect.

     Section 7.11  Subsidiary Security.  Should the Borrower grant to the
Senior Loan Agent for the benefit of the Senior Lenders, or to the Senior
Lenders, a security interest and pledge of the Capital Stock of any Subsidiary
(whether existing as of the Closing Date or created or acquired thereafter), the
Borrower will, simultaneously with such pledge in favor of the Senior Loan Agent
or Senior Lenders, grant to the Trustee for the benefit of the Noteholders, a
second in priority security interest and pledge of such Capital Stock in form

                                      -28-
<PAGE>   33
 
and substance satisfactory to the Agent and if any Subsidiary should guaranty
all or any portion of the Senior Loan, the Borrower will cause such Subsidiary
to enter into a Guaranty Agreement of the Obligations in substantially the same
form as the Guaranty Agreement given by Brigham, Inc. on the Closing Date or
otherwise in form and substance satisfactory to the Agent.  The delivery of such
security and guaranty shall be accompanied by such back up corporate authority
and opinions of counsel (addressed to the Agent as well as the Senior Loan
Agent) as are provided to the Senior Loan Agent.


                                 ARTICLE VIII
                              NEGATIVE COVENANTS

     Unless the Agent's prior written consent to the contrary is obtained, for
the benefit of each of the Noteholders, the Borrower will at all times comply
with the covenants contained in this Article VIII (or cause each Subsidiary's
compliance with the applicable covenants), from the date hereof and for so long
as any part of the Obligations is outstanding.

     Section 8.01  Debt.  Neither the Borrower nor any Subsidiary will:

          (a) Incur, create or assume any Debt, other than Permitted Debt, such
that the ratio of the Borrower's Adjusted Consolidated Net Tangible Assets (as
at the end of the immediately preceding calendar quarter) to the sum of (i)
Borrower's Consolidated Indebtedness (after such incurrence, creation or
assumption of additional Debt other than Permitted Debt) plus (ii) past due
interest on Debt, is less than 1.5 to 1.0.  This covenant shall also apply to
any such Debt incurred or assumed as a result of a merger or consolidation with
any other Person.  Any such Debt so incurred, created or assumed (without
violation of this Section 8.01) must be fully subordinated to the Obligations
unless the Agent agrees otherwise, provided that, so long as ECT has been given
a first look and right to make a proposal for any future subordinated
indebtedness, up to $25,000,000 (less the maximum potential balance at the time
in question of the Schedule 8.02 Payables) in the aggregate of such Debt may be
incurred that is pari passu in right of payment with the Notes.  Notwithstanding
the foregoing, in the event of any refinancing of the Senior Loan, which
refinancing does not violate, on a proforma basis for the four fiscal quarters
of the Borrower after the refinancing, the interest coverage test of Section
8.16, the current ratio test of Section 8.17, or, provided the amount of such
refinanced Senior Loan is more than $75,000,000, the covenant in the first
sentence of this subsection (a), the refinanced Senior Loan shall remain senior
to (and shall not be subordinate to) the Obligations; or

          (b) Incur, create, suffer or assume any accounts payable for the
deferred purchase price of Property or services or any Trade Payables which are
more than 75 days past the invoice or billing date, unless such accounts payable
are either (i) being contested in good faith by appropriate proceedings and
reserves as required under GAAP shall have been established therefor, or (ii)
Schedule 8.02 Payables which are not past due.

                                      -29-
<PAGE>   34
 
Notwithstanding the foregoing, if at any time the ratio of the Borrower's
Adjusted Consolidated Net  Tangible Assets to the sum of (a) Borrower's
Consolidated Indebtedness plus (b) past due interest on Debt, is less than 1.5
to 1.0, the Agent shall have the right to require, and the Borrower covenants
and agrees to convey (or cause to be conveyed) to the Trustee or the Agent for
the benefit of the Agent and the Noteholders, such additional Potential
Collateral as the Agent shall require (subject to the Senior Lenders' rights to
a first and prior lien in such Potential Collateral).  Such conveyance shall be
made within 30 days following receipt of written notice from the Agent and shall
be deemed a pledge of additional Collateral in accordance with Section 7.09.  As
used in this paragraph, "Potential Collateral" means any of Borrower's or any
Subsidiary's Oil and Gas Properties (which are not already Collateral) which are
identified as containing proved Hydrocarbon reserves, whether currently existing
or hereafter acquired.

     Section 8.02  Liens.  Neither the Borrower nor any Subsidiary will
create, incur, assume or permit to exist any Lien on any of its Properties (now
owned or hereafter acquired), except:

          (a) Liens securing the Senior Loan; provided the Trustee or the Agent
is granted a second Lien in such Property securing the payment of the
Obligations;

          (b) Liens securing the payment of the Obligations;

          (c) Excepted Liens;

          (d) Liens securing leases allowed under clause (e) of the definition
of Excepted Liens but only on the Property under lease;

          (e) Liens disclosed on Schedule 8.02; and

          (f) Any Permitted Encumbrances as described in the Mortgage.

     Section 8.03  Investments, Loans and Advances.  Neither the Borrower nor
any Subsidiary will make or permit to remain outstanding any loans or advances
to or investments in any Person, except that the foregoing restriction shall not
apply to:

          (a) investments, loans or advances reflected in the Financial
Statements or which are disclosed to the Noteholders in Schedule 8.03;

          (b) accounts receivable arising in the ordinary course of business;

          (c) direct obligations of the United States or any agency thereof, or
obligations guaranteed by the United States or any agency thereof, in each case
maturing within one year from the date of creation thereof;

                                      -30-
<PAGE>   35
 
          (d) commercial paper maturing within one year from the date of
creation thereof rated in the highest grade by Standard & Poors Corporation or
Moody's Investors Service, Inc.;

          (e) deposits maturing within one year from the date of creation
thereof with, including certificates of deposit issued by any office located in
the United States, Canada, or England of, any bank or trust company which is
organized under the laws of the United States, Canada, England or any state or
province thereof, which has capital, surplus and undivided profits aggregating
at least $100,000,000.00 (as of the date of such bank or trust company's most
recent financial reports) and has a short term deposit rating of no lower than
A2 or P2, as such rating is set forth from time to time, by Standard & Poors
Corporation or Moody's Investors Service, Inc. (or their successors),
respectively;

          (f) deposits in money market funds investing exclusively in
investments described in Section 8.03(c), 8.03(d) or 8.03(e);

          (g) investments of up to $400,000 in the aggregate in Quest Resources
L.L.C.;

          (h) (i) investments, distributions, loans and advances by the Borrower
in or to any Subsidiary of the Borrower which is a Guarantor, (ii) investments,
distributions, loans and advances by the Borrower in or to any Subsidiary of the
Borrower which is not a Guarantor, provided that such Subsidiary has direct or
indirect ownership interests in Oil and Gas Properties or gas gathering systems,
gas plants, and similar assets related thereto and the aggregate outstanding
amount of such investments, distributions, loans and advances under this clause
(ii) shall not exceed $1,000,000 at any time, or (iii) investments in equity
interests in any Person (other than a Subsidiary as provided in clauses (i) or
(ii)) whose business is the acquisition, exploration and development of Oil and
Gas Properties, gas gathering systems, gas plants, or any line of business which
is closely related thereto, provided that the aggregate outstanding amount of
any such investments under this clause (iii) shall not exceed $1,000,000 at any
time;

          (i) investments, distributions, loans and advances by a Subsidiary to
the Borrower;

          (j) extensions of credit to purchasers, working interest owners,
employees and other persons in the ordinary course of business, up to an
aggregate of $1,000,000 at any one time.

     Section 8.04  Dividends, Distributions and Redemptions.  Neither the
Borrower or any Subsidiary will declare or pay any dividend, purchase, redeem or
otherwise acquire for value any of its stock now or hereafter outstanding,
return any capital to its stockholders or make any distribution of its assets to
its partners, except to the Borrower or any Subsidiary.

                                      -31-
<PAGE>   36
 
     Section 8.05  Sales and Leasebacks.  Neither the Borrower nor any
Subsidiary will enter into any arrangement, directly or indirectly, with any
Person whereby the Borrower or any Subsidiary shall sell or transfer any of its
Property, whether now owned or hereafter acquired, and whereby the Borrower or
any Subsidiary shall then or thereafter rent or lease as lessee such Property or
any part thereof or other Property which the Borrower or any Subsidiary intends
to use for substantially the same purpose or purposes as the Property sold or
transferred.

     Section 8.06  Nature of Business. Neither the Borrower nor any Subsidiary
will allow any material change to be made in the character of its business as an
independent oil and gas exploration and production company.

     Section 8.07  Mergers, Etc.  The Borrower will not and will not permit
any Subsidiary to merge into or with or consolidate with any other Person (other
than the Borrower or a Subsidiary) or sell, lease or otherwise dispose of
(whether in one transaction or in a series of transactions) all or substantially
all of its Property or assets to any other Person (other than the Borrower or a
Subsidiary) unless (i) no Default or Event of Default exists and after giving
effect to such merger, no Default or Event of Default shall exist, (ii) after
giving effect to such merger or consolidation, the surviving entity (as the
Borrower hereunder), or in the event of a merger or consolidation of a
Subsidiary, the Borrower, would be able to incur at least $1 in additional Debt
(other than Permitted Indebtedness), and (iii) the surviving entity ratifies and
confirms its Obligations under the Basic Documents and the Notes to the
reasonable satisfaction of the Agent and each Guarantor whose Guaranty Agreement
is in full force and effect ratifies and confirms its Guaranty Agreement to the
reasonable satisfaction of the Agent.

     Section 8.08  Proceeds of Notes.  The Borrower will not permit proceeds
of the Notes to be used for any purpose other than the partial payment of the
Senior Loan.  Neither the Borrower nor any Person acting on behalf of the
Borrower has taken or will take any action which might cause any of the Basic
Documents to violate Regulation G, U or X or any other regulation of the Board
of Governors of the Federal Reserve System or to violate Section 7 of the
Securities Exchange Act of 1934 or any rule or regulation thereunder, in each
case as now in effect or as the same may hereinafter be in effect.

     Section 8.09  ERISA Compliance.  The Borrower will not at any time:

          (a) Engage in, or permit any ERISA Affiliate to engage in, any
transaction in connection with which the Borrower or any ERISA Affiliate could
be subjected to either a civil penalty assessed pursuant to section 502(c), (i),
or (l) of ERISA or a tax imposed by Chapter 43 of Subtitle D of the Code, which
could reasonably be expected to have a Material Adverse Effect;

          (b) Terminate, or permit any ERISA Affiliate to terminate, any Plan in
a manner, or take any other action with respect to any Plan, which could
reasonably be 

                                      -32-
<PAGE>   37
 
expected to result in any liability of the Borrower or any ERISA Affiliate to
the PBGC, which could have a Material Adverse Effect;

          (c) Permit to exist, or allow any ERISA Affiliate to permit to exist,
any accumulated funding deficiency within the meaning of Section 302 of ERISA or
section 412 of the Code, whether or not waived, with respect to any Plan which,
if funded, could reasonably be expected to have a Material Adverse Effect;

          (d) Permit, or allow any ERISA Affiliate to permit, the actuarial
present value of the benefit liabilities under any Plan maintained by the
Borrower or any ERISA Affiliate which is regulated under Title IV of ERISA to
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 an amount which could, if such benefits become payable,
reasonably be expected to have a Material Adverse Effect.  The term "actuarial
present value of the benefit liabilities" shall have the meaning specified in
section 4041 of ERISA;

          (e) Contribute to or assume an obligation to contribute to, or permit
any ERISA Affiliate to contribute to or assume an obligation to contribute to,
any Multiemployer Plan;

          (f) Incur, or permit any ERISA Affiliate to incur, a liability to or
on account of a Plan under sections 515, 4062, 4063, 4064, 4201 or 4204 of ERISA
which, in the aggregate for all such liabilities, could reasonably be expected
to have a Material Adverse Effect;

          (g) Contribute to or assume an obligation to contribute to, or permit
any ERISA Affiliate to contribute to or assume an obligation to contribute to,
any 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 such entities
in their sole discretion at any time without any material liability; or

          (h) Amend or permit any ERISA Affiliate to amend, a Plan resulting in
an increase in current liability such that Borrower or any ERISA Affiliate is
required to provide security to such Plan under section 401(a)(29) of the Code.

     Section 8.10  Sale of Oil and Gas Properties.  The Borrower will not,
and will not permit any Subsidiary to, sell, assign, farm-out, convey or
otherwise transfer any Hydrocarbon Interests except for (i) the sale of
Hydrocarbons in the ordinary course of business; (ii) assignments, farmouts, and
other disposition of Hydrocarbon Interests which do not contain identified
proved Hydrocarbon reserves, provided such assignments, farmouts, and other
dispositions are in the normal course of business (e.g., in bringing in
participants or disposing of unattractive prospects); (iii) the sale or transfer
of equipment that is no longer necessary for the business of the Borrower or
such Subsidiary or is replaced by equipment 

                                      -33-
<PAGE>   38
 
of at least comparable value and use and (iv) during any consecutive four fiscal
quarters, sales of Hydrocarbon Interests containing identified proved
Hydrocarbon reserves which, when taken together with the proceeds of any
permitted sales of Subsidiaries during such four quarters under the next
sentence of this Section 8.10, shall not exceed $3,000,000 in the aggregate. The
Borrower will not sell, and will not permit the sale of, any interest in any
Subsidiary unless all or substantially all of the Borrower's interest in such
Subsidiary is sold and, during any consecutive four fiscal quarters, the
proceeds of any such sale taken together with the proceeds of any sale of
Hydrocarbon Interests permitted under clause (iv) of this Section 8.10 does not
exceed $3,000,000.

     Section 8.11  Environmental Matters.  Neither the Borrower nor any
Subsidiary will knowingly cause or permit any of its Property to be in violation
of, or knowingly do anything or permit anything to be done which will subject
any such Property to any remedial obligations under any Environmental Laws,
assuming disclosure to the applicable Governmental Authority of all relevant
facts, conditions and circumstances, if any, pertaining to such Property, where
such violations or remedial obligations would have a Material Adverse Effect.

     Section 8.12  Transactions with Affiliates.  Neither the Borrower nor
any Subsidiary will enter into any transaction, including, without limitation,
any purchase, sale, lease or exchange of Property or the rendering of any
service, with any Affiliate (other than the Borrower or a Subsidiary) unless
such transaction (a) is otherwise not in violation of this Indenture, and (b)
unless approved by a majority of the disinterested members of the Board of
Directors, is in the ordinary course of its business and is upon fair and
reasonable terms no less favorable to it than it would obtain in a comparable
arm's length transaction with a Person not an Affiliate.

     Section 8.13  Negative Pledge Agreements.  The Borrower will not and
will not permit any Subsidiary to create, incur, assume or suffer to exist any
contract, agreement or understanding (other than the Basic Documents) which in
any way prohibits or restricts any Subsidiary from paying dividends or making
any other distribution to the Borrower or which requires the consent of a notice
to other Persons in connection with any of the foregoing, other than the
restrictions contained in the Senior Loan Documents as they exist on the day
hereof.

     Section 8.14  Gas Imbalances, Take-or-Pay Prepayments.  The Borrower
will not allow gas imbalances, take-or-pay or other prepayments with respect to
the Hydrocarbon Interests of the Borrower and its Subsidiaries which would
require the Borrower or its Subsidiaries to deliver five percent (5%) or more of
the Borrower'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 8.15  Borrower as Operator.  The Borrower will not and will not
allow any of its Subsidiaries to voluntarily resign as operator of more than
twenty-five percent (25%) of their currently operated Oil and Gas Properties,
unless a substitute operator is appointed 

                                      -34-
<PAGE>   39
 
that is another Subsidiary of the Borrower or is otherwise acceptable to the
Majority Noteholders, approval of such substitute operator not to be
unreasonably withheld.

     Section 8.16  Consolidated Interest Coverage Ratio.  As of the last day
of each fiscal quarter, the Borrower will not permit the Consolidated Interest
Coverage Ratio to be less than (i) 1.5 to 1.0 as of the end of the first four
(4) fiscal quarters following the Closing Date and (ii) 2.0 to 1.0 as of the end
of each fiscal quarter thereafter.

     Section 8.17  Current Ratio.  The Borrower will not permit its ratio of
(i) consolidated current assets of the Borrower and its Consolidated
Subsidiaries (including, without limitation, any unused and available
commitments under the Senior Credit Agreement) to (ii) their consolidated
current liabilities (excluding any principal or interest payments due on the
Senior Loan or the Notes), to be less than .8 to 1.0 at any time.

                                  ARTICLE IX
                             PAYMENT OF THE NOTES

     Section 9.01  Repayment.  The Borrower shall pay to the Noteholders on the
Maturity Date an amount equal to the outstanding principal amount of the Notes
plus the accrued and unpaid interest on the outstanding principal amount of the
Notes.  The Borrower may prepay the Obligations at any time in whole or in part
without penalty or premium.

     Section 9.02  Interest.

          (a) Subject to the provisions of Section 9.02(b), the outstanding
principal amount of the Notes shall bear interest at the following rates per
annum:

<TABLE>
<CAPTION>
                Period                               Rate
<S>                                                 <C>
          Funding Date through August 20, 2001        12%

          August 21, 2001 through August 20, 2002     13%

          August 21, 2002 through Maturity Date       14%
</TABLE>

The foregoing rates shall apply only to interest which is paid in cash.  In the
event the Borrower should elect to make any interest payments in kind as
permitted by Section 9.02(b), the rates applicable to such payments shall be as
set forth in Section 9.02(b).

          (b) So long as there exists no Event of Default, if on any Interest
Payment Date either (i) there exists a "Borrowing Base Deficiency" under the
Senior Credit Agreement or (ii) the payment in cash of interest accrued on the
Notes would cause the Borrower to be in violation of any covenant or other
restriction set forth in the Senior Loan Documents or any Basic Document, the
Borrower may pay such interest in kind, as provided in this Section 9.02(b).  In
such event the accrued interest due on such Interest Payment 

                                      -35-
<PAGE>   40
 
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 under the Notes and, as of the Interest
Payment Date, shall be added to the outstanding principal balance of the Notes
(notwithstanding that the outstanding principal balance may exceed, in the
aggregate, the face amount of the Notes). In order to exercise its option to pay
interest in kind under this Section 9.02(b), the Borrower shall, on or before
the applicable Interest Payment Date, deliver written notice to the Agent
executed by a Responsible Officer specifying the applicable covenant or
restriction of the Senior Loan Documents or the Basic Documents that will be
violated by payment of accrued interest in cash and notifying Agent of its
election to pay interest in kind. Any such election must be made as to all
Notes. 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 cash and any subsequent failure to do so in a timely fashion
(subject to the thirty (30) day grace period provided in Section 10.01(a)) shall
constitute an Event of Default hereunder. Notwithstanding anything contained
herein to the contrary, the Borrower may not pay interest in kind over the term
of the Notes for more than six (6) calendar quarters. In the event the Borrower
elects to pay interest in kind, such interest to be paid shall be calculated at
the following rates commencing on the immediately preceding Interest Payment
Date:

                 Period                              Rate

          Funding Date through August 20, 2001        13%

          August 21, 2001 through August 20, 2002     14%

          August 21, 2002 through Maturity Date       15%

          (c) In the event any sum due and payable hereunder is not paid when
due such past due amount shall accrue interest at the Default Rate from the date
due until paid.  Should an Event of Default occur hereunder, interest on the
Obligations shall accrue at the Default Rate from the date of occurrence of the
Default to which such Event of Default is attributable, until such Event of
Default is cured or waived.

          (d) Interest shall be computed based on a year of 360 days and twelve
30-day months (pro-rated appropriately for the period from the Funding Date
until the first Interest Payment Date and for any period of less than three
months for which interest may be due as a result of the prepayment or
acceleration of the Notes).  The rates of interest applicable to the Notes
provided in Sections 9.02(a) and (b) shall commence on the first day immediately
following the Funding Date or the applicable anniversary of the Funding Date and
remain in effect through the next succeeding anniversary of the Funding Date, or
the Maturity Date, as applicable.

          (e) Accrued interest on the Notes shall be due and payable in cash or,
if permitted by Section 9.02(b), in kind, quarterly on each Interest Payment
Date (including the 

                                      -36-
<PAGE>   41
 
Maturity Date) or, in the event the maturity of the Notes is accelerated
pursuant to the terms of the Basic Documents, such earlier date as the Notes
become due and payable, or the date the Notes are paid in full, whichever first
occurs. If any Interest Payment Date is not a Business Day, the interest payment
that would be due thereon shall instead be due on the next following Business
Day.

          (f) Notwithstanding anything herein or in the other Basic Documents to
the contrary, it is the intention of the parties hereto to conform strictly to
usury laws applicable to this transaction.  Accordingly, if the transactions
contemplated hereby would be usurious under applicable law, then, in that event,
notwithstanding anything to the contrary in the Notes, this Indenture or in any
other Basic Document or agreement entered into in connection with or as security
for the Notes, it is agreed as follows:  (a) the aggregate of all consideration
which constitutes interest under law applicable to the Noteholders that is
contracted for, taken, reserved, charged or received under the Notes, this
Indenture or under any of the other Basic Documents or agreements or otherwise
in connection with this transaction shall under no circumstances exceed the
maximum amount allowed by such applicable law, and any excess shall be canceled
automatically and, if already paid, shall be credited by the Noteholders on the
principal amount of the Obligations (or, to the extent that the principal amount
of the Obligations shall have been or would thereby be paid in full, refunded to
the Borrower); and (b) in the event that the maturity of the Notes is
accelerated by reason of any Event of Default under this Indenture or otherwise,
or in the event of any required or permitted prepayment, then such consideration
that constitutes interest under law applicable to this transaction may never
include more than the maximum amount allowed by such applicable law, and (c)
excess interest, if any, provided for in this Indenture or otherwise in
connection with the Notes shall be canceled automatically and, if already paid,
shall be credited by the Noteholders on the principal amount of the Obligations
(or, to the extent that the principal amount of the Obligations shall have been
or would thereby be paid in full, refunded by the Noteholders to the Borrower).
All sums paid or agreed to be paid to the Noteholders for the use, forbearance
or detention of sums included in the Obligations shall, to the extent permitted
by applicable law, be amortized, prorated, allocated and spread throughout the
full term of the Notes until payment in full so that the rate or amount of
interest on account of the Obligations does not exceed the applicable usury
ceiling, if any.  As used in this Section 9.02(f), the term "applicable law"
shall mean the laws which govern this Indenture as described in Section 12.07
(or the law of any other jurisdiction whose laws may be mandatorily applicable
notwithstanding other provisions of this Indenture), or law of the United States
of America applicable to the Noteholders and the Notes which would permit the
Noteholders to contract for, charge, take, reserve or receive a greater amount
of interest than under any other applicable law.  If the stated rate of interest
under this Indenture ever exceeds the Maximum Rate, then the outstanding
principal amount of the Notes made hereunder shall bear interest at the Maximum
Rate until the difference between the interest which would have been due at the
stated rates of interest and the amount due at the Maximum Rate (the "Lost
Interest") has been recaptured by the Noteholders.  If the Notes are repaid in
full and the Lost Interest has not been fully recaptured by the Noteholders
pursuant to the preceding sentence, then the Notes shall be deemed to have
accrued interest at the Maximum Rate since the date the initial advance under
the Notes was 

                                      -37-
<PAGE>   42
 
made to the extent necessary to recapture the Lost Interest not recaptured
pursuant to the preceding sentence and, to the extent allowed by law, the
Borrower shall pay to the Noteholders the amount of the Lost Interest remaining
to be recaptured by the Noteholders.

     Section 9.03  Payments and Computations.

          (a) All payments and obligations by Borrower under the Notes or any
other Basic Document shall be made to the Agent, without any presentment and
without any notation of such payment being made on the Notes (i) by wire
transfer in immediately available funds to such account as the Agent may
designate from time to time by written notice to the Borrower (the "Agent's
Account") or (ii) in such other manner as may be designated in writing to the
Borrower by the Agent.

          (b) The Borrower shall make each payment under this Indenture and
under the Notes not later than 2:00 p.m. (Houston, Texas time) on the day when
due in U.S. Dollars to the Agent at the location specified in paragraph (a)
above in immediately available funds. All payments by the Borrower hereunder
shall be made without any offset, abatement, withholding, or reduction.

          (c) Whenever any payment under the Basic Documents shall be stated to
be due on a day other than a Business Day, such payment shall be made on the
next succeeding Business Day, and (other than an interest payment subject to
Section 9.02(e) above) such extension of time shall in such case be included in
the computation of payment of interest.  If the time for payment for an amount
payable is not specified in the Basic Documents, or in any other document, the
payment shall be due and payable ten days after the date on which the Agent or
any Noteholder demands payment therefor.

          (d) Following receipt of payment in cash of any obligations due under
the Notes or any other Basic Document the Agent will promptly thereafter cause
to be distributed like funds relating to the payment of principal, interest or
fees ratably to the Noteholders at their respective Noteholder's Account.  If
and to the extent that the Agent receives any payment or prepayment from the
Borrower and fails to distribute such payment or prepayment to the Noteholders
ratably on the basis of their respective Participations on the day the Agent
receives such payment or prepayment (if received prior to 1:00 P.M. (Houston,
Texas time) on such day) or the next Business Day (if received after 1:00 P.M.
(Houston, Texas time) on such day), then the Agent shall pay to each Noteholder
such Noteholder's Participation of such payment or prepayment together with
interest thereon at the Federal Funds Rate for each day from the date such
amount should have been distributed by the Agent until such payment or
prepayment is actually distributed to the Noteholders.  All payments and
prepayments received shall be applied first to accrued interest and second to
the reduction of principal.

          (e) Unless the Agent shall have received written notice from the
Borrower prior to the date on which any payment is due to the Noteholders that
the Borrower will not make such payment in full or will make such payment in
kind pursuant to Section 9.02(b), 

                                      -38-
<PAGE>   43
 
the Agent may assume that the Borrower has made such payment in full, in cash,
to the Agent on such date and the Agent may, in reliance upon such assumption,
cause to be distributed to each Noteholder on such date an amount equal to the
amount then due such Noteholder. If and to the extent the Borrower shall not
have so made such payment in full, in cash, to the Agent, each Noteholder shall
repay to the Agent forthwith on demand such amount distributed to such
Noteholder, together with interest, for each day from the date such amount is
distributed to such Noteholder until the date such Noteholder repays such amount
to the Agent, at the Federal Funds Rate for such day.


                                   ARTICLE X
                             DEFAULT AND REMEDIES

     Section 10.01  Events of Default.  The occurrence of any of the following
shall be an "Event of Default" for the purposes of this Indenture and the Notes:

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

          (b) (i) The Borrower or any Guarantor shall, as to any Debt (other
than the Obligations and the Senior Loan) aggregating more than $2,000,000
default in the payment when due of any principal of or interest thereon, or any
event specified in any note, agreement, indenture or other document evidencing
or relating to any such Debt shall occur if the effect of such event is to
cause, or (with the giving of any notice or the lapse of time or both) to permit
the holder or holders of such Debt (or a trustee or agent on behalf of such
holder or holders) to cause, such Debt to become due prior to its stated
maturity, or (ii) as to the Senior Loan, there shall have occurred a default
thereunder and the holders of the Senior Loan shall have elected to accelerate
the payment of the Senior Loan (or it shall be accelerated automatically or
otherwise be due and payable in full); or

          (c) any representation, warranty or certification made or deemed made
herein or in any other Basic Document by the Borrower or any Guarantor, or any
certificate furnished by the Borrower or any Guarantor to the Trustee, any
Noteholder or the Agent pursuant to the provisions hereof or any other Basic
Document, shall prove to have been false or misleading as of the time made or
furnished in any material and adverse respect and such default shall continue
unremedied for a period of forty-five (45) days after notice thereof to the
Borrower by the Agent; or

          (d) the Borrower shall default in the performance of any of its
obligations under Article VIII which are not capable of being cured, or under
Sections 8.01, 8.16, 8.17  or 7.01(c); or the Borrower shall default in the
performance of any of its obligations under 

                                      -39-
<PAGE>   44
 
Article VIII which are capable of being cured (other than Sections 8.01, 8.16
and 8.17) or any other Article of this Indenture (other than 7.01(c)) or under
any other Basic Document to which it is a party (other than the payment of
amounts due which shall be governed by Section 10.01(a)) and such default shall
continue unremedied for a period of forty-five (45) days after notice thereof to
the Borrower by the Agent; or

          (e) any Guarantor shall default in the performance of its obligation
to pay the Liabilities (as defined in the Guaranty Agreement) at maturity, or
any Guarantor shall default in the performance of any of its other obligations
under its Guaranty Agreement and such default shall continue unremedied for a
period of forty-five (45) days after notice thereof to the Guarantor by the
Agent; or

          (f) the Borrower shall admit in writing its inability to, or be
generally unable to, pay its debts as such debts become due; or

          (g) the Borrower shall (i) apply for a consent to the appointment of,
or the taking of possession by, a receiver, custodian, trustee or liquidator of
itself or of all or a substantial part of its property, (ii) make a general
assignment for the benefit of its creditors, (iii) commence a voluntary case
under the Federal Bankruptcy Code (as now or hereafter in effect), (iv) file a
petition seeking to take advantage of any other law relating to bankruptcy,
insolvency, reorganization, winding-up, liquidation or composition or
readjustment of debts, (v) fail to controvert in a timely and appropriate
manner, or acquiesce in writing to, any petition filed against it in an
involuntary case under the Federal Bankruptcy Code, or (vi) take any corporate
action for the purpose of effecting any of the foregoing, or

          (h) a proceeding or case shall be commenced, without the application
or consent of the Borrower, in any court of competent jurisdiction, seeking (i)
its liquidation, reorganization, dissolution or winding-up, or the composition
or readjustment of its debt; (ii) the appointment of a trustee, receiver,
custodian, liquidator or the like of the Borrower of all or any substantial part
of its assets, or (iii) similar relief in respect of the Borrower under any law
relating to bankruptcy, insolvency, reorganization, winding-up, or composition
or adjustment of  debts, and such proceeding or case shall continue undismissed,
or an order, judgement or decree approving or ordering any of the foregoing
shall be entered and continue unstayed and in effect, for a period of 60 days;
or an order for relief against the Borrower shall be entered in an involuntary
case under the Federal Bankruptcy Code; or

          (i) a judgment or judgments for the payment of money in excess of
$2,000,000 in the aggregate shall be rendered by a court against the Borrower
and the same shall not be discharged (or provision shall not be made for such
discharge), or a stay of execution thereof shall not be procured, within forty-
five (45) days from the date of entry thereof and the Borrower shall not, within
said period of 45 days, or such longer period during which execution of the same
shall have been stayed, appeal therefrom and cause the execution thereof to be
stayed during such appeal; or

                                      -40-
<PAGE>   45
 
          (j) any of the Basic Documents after delivery thereof shall for any
reason, except to the extent permitted by the terms thereof, cease to be in full
force and effect and valid, binding and enforceable in all material respects in
accordance with their terms, or cease in any material respect to create a valid
and perfected Lien of the priority required thereby on any of the collateral
purported to be covered thereby, except to the extent permitted by the terms of
this Indenture, or the Borrower or any Guarantor shall so state in writing, and
such Default shall continue unremedied for a period of forty-five (45) days
after notice thereof to the Borrower by the Agent; or

          (k) any Guarantor takes, suffers or permits to exist any of the
events or conditions referred to in paragraphs (f), (g), (h) or (i) hereof or if
any Guaranty Agreement related thereto shall for any reason cease to be valid
and binding on such Guarantor in all material respects or if such Guarantor
shall so state in writing, and such Default shall continue unremedied for a
period of forty-five (45) days after notice thereof to the Guarantor by the
Agent; or

          (l) there occurs a Change in Control; or

          (m) any annual audited financial statement delivered to Agent pursuant
to Section 7.01(a) is qualified (as to going concern or similar qualifications).

     Section 10.02  Remedies.

          (a) At any time during the continuance of any Event of Default
specified in Section 10.01 (other than clauses (f), (g) or (h) of Section
10.01), or in clause (k) as it relates to clauses (f), (g) or (h) thereof, the
Agent may by written notice to the Borrower declare the entire principal amount
of all Obligations then outstanding, including interest accrued thereon, to be
immediately due and payable without presentment, demand, protest, notice of
protest or dishonor, notice of intent to accelerate,  or other notice of default
of any kind, all of which are hereby expressly waived by the Borrower.  Once an
acceleration has been declared pursuant to the foregoing, no subsequent cure of
the Event of Default shall negate such acceleration or the rights and remedies
of the Trustee, Agent or Noteholders with respect thereto without the express
written consent of the Agent.

          (b) Upon the happening of any Event of Default specified in clauses
(f), (g) or (h) of Section 10.01, or clause (k) as it relates to clauses (f),
(g) or (h), the entire principal amount of all Obligations then outstanding,
including interest accrued thereon, shall, without notice or action by the
Trustee, the Agent or the Noteholders be immediately due and payable without
presentment, demand, protest, notice of protest or dishonor, notice of intent to
accelerate or other notice of default of any kind, all of which are hereby
expressly waived by the Borrower.

          (c) In addition to the foregoing, upon the happening of any of the
events described in subsections (a) and (b) above, the Trustee, at the direction
of the Agent may 

                                      -41-
<PAGE>   46
 
exercise any of the rights or remedies provided in the Collateral Documents and
other Basic Documents or avail itself of any rights or remedies provided by
applicable law.

          (d) All proceeds received after maturity of the Notes, whether by
acceleration or otherwise shall be applied first to reimbursement of expenses
and indemnities provided for in the Basic Documents; second to accrued interest
on the Notes; third to fees; fourth pro rata to principal outstanding on the
Notes and other Obligations; and any excess shall be paid to the Borrower or as
otherwise required by any Governmental Requirement.

     Section 10.03 Production and Proceeds.  Notwithstanding that, by the terms
of the various Mortgages and other Basic Documents, the Borrower and any other
mortgagors are and will be assigning to the Trustee all of the Hydrocarbons
covered thereby and all of the products thereof and proceeds and revenues
attributable thereto and all payments in lieu of such Hydrocarbons (in this
section collectively called the "Production and Proceeds"), so long as no
Default has occurred and is continuing (a) the Borrower and such mortgagors may
continue to receive all such Production and Proceeds, subject, however, to the
Liens created under the Mortgages and other Basic Documents, and (b) upon the
Borrower's request the Agent will confirm to any purchasers of Hydrocarbons,
title examiners, or other Persons that the Borrower and such mortgagors continue
to have the right so to receive such Production and Proceeds until notification
by the Agent of the occurrence of a Default.  During the continuance of an Event
of Default, however, the Trustee at the direction of the Agent may (subject to
all rights of the Senior Loan Agent and the Senior Lenders under the Senior Loan
Documents) exercise its rights and remedies granted under the Mortgages and the
other Basic Documents, including the rights and remedies granted under the
Mortgages and the other Basic Documents, including the right to obtain
possession of all Production and Proceeds then held by the Borrower and such
mortgagors and to receive directly from the purchasers of Hydrocarbons all other
Production and Proceeds.  In no case shall any failure by the Trustee to collect
directly any such Production and Proceeds constitute in any way a release of any
of its or the Agent's rights under the Basic Documents.

     Section 10.04 Set-Off.  Upon the occurrence of any Event of Default, any
Noteholder shall have the right to set-off any funds of the Borrower in the
possession of the Noteholder against any Debt (or accrued interest on Debt) then
due by the Borrower to the Noteholder.  The Borrower agrees that any holder of
Notes or a participation in the Notes may exercise any and all rights of
counter-claim, set-off, banker's lien and other liens with respect to any and
all monies owing by the Borrower to such holder as fully as if such holder of a
participation were a holder of a Note in the amount of such participation.

                                  ARTICLE XI
                                   THE AGENT

     Section 11.01  Authorization and Action.  Each Noteholder hereby appoints
and authorizes the Agent to take such action on behalf of such Noteholder and to
exercise such powers under this Indenture as are delegated to the Agent by the
terms hereof and of the other Basic Documents, together with such powers as are
reasonably incidental thereto.  As 

                                      -42-
<PAGE>   47
 
to any matters not expressly provided for by this Indenture or any other Basic
Document (including, without limitation, enforcement or collection of the
Notes), the Agent shall not be required to exercise any discretion or take any
action, but shall be required to act or to refrain from acting (and shall be
fully protected in so acting or refraining from acting) only upon the
instructions of the Majority Noteholders, and such instructions shall be binding
upon Noteholders; provided, however, that the Agent shall not be required to
take any action which exposes the Agent to personal liability or which is
contrary to this Indenture, any other Basic Document, or applicable law.

     Section 11.02  Agent's Reliance, Etc.  Neither the Agent nor any of the
Agent's directors, officers, agents or employees shall be liable for any action
taken or omitted to be taken (including the Agent's own negligence) by it or
them under or in connection with this Indenture or the other Basic Documents,
except for its or their own gross negligence or willful misconduct.  Without
limitation of the generality of the foregoing, the Agent:  (a) may treat the
payee of any Note as the holder thereof until the Agent receives written notice
of the assignment or transfer thereof signed by such payee and in form
satisfactory to the Agent; (b) may consult with legal counsel (including counsel
for the Borrower), independent public accountants and other experts selected by
it and shall not be liable for any action taken or omitted to be taken in good
faith by it in accordance with the advice of such counsel, accountants or
experts; (c) makes no warranty or representation to any Noteholder and shall not
be responsible to any Noteholder for any statements, warranties or
representations made in or in connection with this Indenture or the other Basic
Documents; (d) shall not have any duty to ascertain or to inquire as to the
performance or observance of any of the terms, covenants or conditions of this
Indenture or any other Basic Document on the part of the Borrower or any
Subsidiary or to inspect the Property (including the books and records) of such
Persons; (e) shall not be responsible to any Noteholder for the due execution,
legality, validity, enforceability, genuineness, sufficiency or value of this
Indenture or any other Basic Document; and (f) shall incur no liability under or
in respect of this Indenture or any other Basic Document by acting upon any
notice, consent, certificate or other instrument or writing (which may be by
telecopy) reasonably believed by it to be genuine and signed or sent by the
proper party or parties.

     Section 11.03  The Agent and Its Affiliates.  With respect to its
Participation, and the Note issued to it, the Agent shall have the same rights
and powers under this Indenture as any other Noteholder and may exercise the
same as though it were not an Agent hereunder.  The term "Noteholder" or
"Noteholders" shall, unless otherwise expressly indicated, include the Agent in
its individual capacity.  The Agent and its Affiliates may accept deposits from,
lend money to, act as trustee under indentures of, and generally engage in any
kind of business with, the Borrower or any Subsidiary, and any Person who may do
business with or own securities of the Borrower, or any Subsidiary, all as if
the Agent were not an agent hereunder and without any duty to account therefor
to the Noteholders.

     Section 11.04 Noteholders Loan Decision. Each Noteholder acknowledges that
it has, independently and without reliance upon the Agent or any other
Noteholder and based on the Financial Statements and such other documents and
information as it has deemed

                                      -43-
<PAGE>   48
 
appropriate, made its own credit analysis and decision to enter into the Basic
Documents. Each Noteholder also acknowledges that it will, independently and
without reliance upon the Agent or any other Noteholder and based on such
documents and information as it shall deem appropriate at the time, continue to
make its own credit decisions in taking or not taking action under this
Indenture.

     Section 10.05  Indemnification.  The Noteholders severally agree to
indemnify the Agent and each Affiliate thereof and their respective directors,
officers, employees and agents (to the extent not reimbursed by the Borrower),
according to their respective Participations from and against any and all
liabilities, obligations, losses, damages, penalties, actions, judgments, suits,
costs, expenses or disbursements of any kind or nature whatsoever which may be
imposed on, incurred by, or asserted against the Agent in any way relating to or
arising out of this Indenture or any action taken or omitted by the Agent under
this Indenture or any other Basic Document (INCLUDING THE AGENT'S OWN
NEGLIGENCE), provided that no Noteholder shall be liable for any portion of such
liabilities, obligations, losses, damages, penalties, actions, judgments, suits,
costs, expenses or disbursements resulting from the Agent's gross negligence or
willful misconduct.  Without limitation of the foregoing, each Noteholder agrees
to reimburse the Agent promptly upon demand for its ratable share of any out-of-
pocket expenses (including counsel fees) incurred by the Agent in connection
with the preparation, execution, delivery, administration, modification,
amendment or enforcement (whether through negotiations, legal proceedings or
otherwise) of, or legal advice in respect of rights or responsibilities under,
this Indenture or any other Basic Document, to the extent that the Agent is not
reimbursed for such expenses by the Borrower.

     Section 11.06 Successor Agent. The Agent may resign at any time by giving
written notice thereof to the Noteholders and the Borrower and may be removed at
any time with cause by the Majority Noteholders upon receipt of written notice
from the Majority Noteholders to such effect. Upon receipt of notice of any such
resignation or removal, the Majority Noteholders shall have the right to appoint
a successor Agent with, if no Default exists, the consent of the Borrower, which
consent shall not be unreasonably withheld. If no successor Agent shall have
been so appointed by the Majority Noteholders with the consent of the Borrower,
if required, and shall have accepted such appointment, within 30 days after the
retiring Agent's giving of notice of resignation or the Majority Noteholders,
removal of the retiring Agent, then the retiring Agent may, on behalf of the
Noteholders and the Borrower, appoint a successor Agent. Upon the acceptance of
any appointment as Agent by a successor Agent, such successor Agent shall
thereupon succeed to and become vested with all the rights, powers, privileges
and duties of the retiring Agent, and the retiring Agent shall be discharged
from its duties and obligations under this Indenture and the other Basic
Documents. After any retiring Agent's resignation or removal hereunder as Agent,
the provisions of this Article XI shall inure to its benefit as to any actions
taken or omitted to be taken by it while it was Agent this Indenture and the
other Basic Documents.

                                      -44-
<PAGE>   49
 
                                  ARTICLE XII
                                    TRUSTEE

     Section 12.01  Duties of Trustee.

          (a) If an Event of Default has occurred and is continuing, the Trustee
shall exercise such rights and powers vested in it by this Indenture and use the
same degree of care and skill in such exercise as a prudent person would
exercise or use under the circumstances in the conduct of such person's own
affairs.

          (b) Except during the continuance of an Event of Default:

              (i)    The Trustee need perform only those duties that are
     specifically set forth (or incorporated by reference) in this Indenture and
     no others.

              (ii)   In the absence of bad faith on its part, the Trustee may
     conclusively rely, as to the truth of the statements and the correctness of
     the opinions expressed therein, upon certificates or opinions furnished to
     the Trustee and conforming to the requirements of this Indenture.  However,
     in the case of any such certificates or opinions which by any provision
     hereof are specifically required to be furnished to the Trustee, the
     Trustee shall be under a duty to examine the same to determine whether or
     not they conform to the requirements of this Indenture (but need not
     confirm or investigate the accuracy of mathematical calculations or other
     facts stated therein).

          (c) The Trustee may not be relieved from liability for its own
negligent action, its own negligent failure to act, or its own willful
misconduct, except that:

              (i)    This paragraph (c) does not limit the effect of paragraph
     (b) of this Section.

              (ii)   The Trustee shall not be liable for any error of judgment
     made in good faith by an officer of the Trustee, unless it is proved that
     the Trustee was negligent in ascertaining the pertinent facts.

               (iii) The Trustee shall not be liable with respect to action it
     takes or omits to take in good faith in accordance with a direction
     received by it from the Agent, and the Trustee shall be entitled from time
     to time to request such a direction.

          (d) Every provision of this Indenture and each Collateral Document
that in any way relates to the Trustee is subject to paragraphs (a), (b) and (c)
of this Section.

          (e) The Trustee shall be under no obligation and may refuse to perform
any duty or exercise any right or power unless it receives indemnity
satisfactory to it against any loss, liability or expense.  No provision of this
Indenture or any Collateral Document shall 

                                      -45-
<PAGE>   50
 
require the Trustee to expend or risk its own funds or otherwise incur financial
liability in the performance of any of its duties hereunder or in the exercise
of any of its rights or powers, if it shall have reasonable grounds to believe
that repayment of such funds or adequate indemnity against such risk or
liability is not reasonably assured to it.

          (f) The Trustee shall not be liable for interest on any money received
by it except as the Trustee may agree in writing with the Borrower.  Money held
in trust by the Trustee need not be segregated from other funds except to the
extent required by law.

          (g) The Trustee shall not be required to take notice, and shall not be
deemed to have notice, of any Default or Event of Default hereunder, unless the
Trustee shall be notified specifically of the Default or Event of Default in a
written instrument or document delivered to it by the Borrower or any Guarantor,
or by the Agent or the Majority Noteholders.  In the absence of delivery of a
notice satisfying those requirements, the Trustee may assume that there is no
Default or Event of Default, except as noted above.

     Section 12.02  Rights of Trustee.

          (a) The Trustee may conclusively rely on and shall be fully protected
in acting or refraining from acting upon any document believed by it to be
genuine and to have been signed or presented by the proper person.  The Trustee
shall not be bound to make any investigation into the facts or matters stated in
any resolution, certificate, statement, instrument, opinion, report, notice,
request, direction, consent, order, bond, debenture or other paper or document,
but the Trustee, in its discretion, may make such further inquiry or
investigation into such facts or matters as it may see fit, and, if the Trustee
shall determine to make such further inquiry or investigation, it shall be
entitled to examine the books, records and premises of the Borrower, personally
or by agent or attorney, to the extent reasonably required by such inquiry or
investigation at the sole expense of the Borrower and shall incur no liability
or additional liability of any kind by reason of such inquiry or investigation.

          (b) Before the Trustee acts or refrains from acting, it may require an
Officers, Certificate or an Opinion of Counsel.  The Trustee shall not be liable
for any action it takes or omits to take in good faith in reliance on such
certificate or opinion.

          (c) The Trustee may act through agents and shall not be responsible
for the misconduct or negligence of any agent appointed with due care.

          (d) The Trustee shall not be liable for any action it takes or omits
to take in good faith which it believes to be authorized or within its rights or
powers.

          (e) The Trustee may consult with counsel of its selection and the
advice of such counsel or any Opinion of Counsel shall be full and complete
authorization and protection in respect of any action taken, suffered or omitted
by it hereunder in good faith and in reliance thereon.

                                      -46-
<PAGE>   51
 
          (f) The Trustee will not, without the consent of the Agent, give any
consent, waiver or approval required under the Collateral Documents or by the
terms hereof with respect to the Collateral or agree to any amendment or
modification of the Collateral Documents.

          (g) The Trustee may settle or compromise at any time any and all
claims against it which may be asserted by any governmental body or private
party for the alleged violation of any Environmental Laws affecting any of the
Collateral, and may disclaim (as to itself, but not as to the Indenture or any
successor Trustee) any power (including, without limitation, the power to sell
the Collateral) granted by the Indenture, the Collateral Documents or any
statute or rule of law, the exercise of which power may, in the sole discretion
of the Trustee, as advised by counsel, cause the Trustee to incur corporate or
personal lability under any Environmental Laws.

     Section 12.03  Individual Rights of Trustee.  The Trustee in its individual
or any other capacity may become the owner or pledgee of Notes and may otherwise
deal with the Borrower or its Subsidiaries or Affiliates with the same rights it
would have if it were not Trustee.  The provision of this Section shall extend
to Affiliates of the Trustee.  Any Agent may do the same with like rights.
However, the Trustee must comply with Sections 12.10 and 12.11.

     Section 12.04  Trustee's Disclaimer.

     The Trustee makes no representation as to the value or condition of the
Collateral or any part thereof, or as to the title of the Borrower or any
Subsidiary thereto, or as to the security afforded thereby or hereby, or as to
the validity or genuineness of any Collateral pledged and deposited with the
Trustee, or the validity or adequacy of this Indenture or the Notes, it shall
not be accountable for the Borrower's use of the proceeds from the Notes or any
offering memorandum or solicitation documents, and it shall not be responsible
for any statement in the Basic Documents other than its certificate of
authentication.

     Section 12.05  Notice of Defaults.

     If a Default occurs and is continuing and if it is actually known to a
Responsible Officer of the Trustee pursuant to Section 12.01(g), the Trustee
shall mail to each Noteholder and the Agent pursuant to Section 13.05 a notice
of the Default within 90 days after it occurs.  Except in the case of a Default
in any payment on any Note, the Trustee may withhold the notice if and so long
as the board of directors, executive committee or a trust committee of officers
in good faith determines that withholding the notice is in the interests of the
Noteholders.

     Section 12.06  Reports by Trustee to Noteholders.

     Within 60 days after each November 15, beginning with the November 15
following the date of this Indenture, the Trustee shall mail to each Noteholder
a brief report dated as 

                                      -47-
<PAGE>   52
 
of such November 15, that complies with TIA (S)313(a), but only if such report
is required in any year under TIA (S)313(a). The Trustee also shall comply with
TIA (SS)313(b) and 313(c).

     A copy of each report at the time of its mailing to Noteholders shall be
filed with the SEC and each stock exchange on which the Notes are listed.  The
Borrower shall promptly notify the Trustee in writing when the Notes become
listed on any national securities exchange or of any delisting thereof.

     Section 12.07  Compensation and Indemnity.

     The Borrower and the Guarantors jointly and severally agree to pay the
Trustee from time to time such compensation as shall be agreed in writing
between the Borrower and the Trustee for its services (which compensation shall
not be limited by any provision of law in regard to the compensation of a
trustee of an express trust).  The Borrower and the Guarantors jointly and
severally agree to reimburse the Trustee upon request for all reasonable out-of-
pocket expenses, disbursements and advances incurred by. it.  Such expenses
shall include when applicable the reasonable compensation and expenses of the
Trustee's agents and counsel.

     The Borrower and the Guarantors jointly and severally agree to indemnify
each of the Trustee and any predecessor Trustee against any and all loss,
liability, damage, claim or expenses, including taxes (other than taxes based on
the income of the Trustee) incurred by it arising out of or in connection with
the acceptance and administration of the trust and its duties hereunder as
Trustee and/or Note Registrar, including the costs and expenses of enforcing
this Indenture against the Borrower (including with respect to this Section
12.07) and of defending itself against any claim or liability in connection with
the exercise or performance of any of its powers or duties hereunder.  The
Trustee shall notify the Borrower and the Guarantors of any claim for which it
may seek indemnity; however, unless the position of the Borrower is materially
prejudiced by such failure, the failure of the Trustee to promptly notify the
Borrower shall not limit its right to indemnification.  The Borrower shall
defend each such claim and the Trustee shall cooperate in the defense.  The
Trustee may retain separate counsel and the Borrower shall reimburse the Trustee
for the reasonable fees and expenses of such counsel if the Borrower is advised
by an Opinion of Counsel that the Trustee has separate defenses and that
separate representation is appropriate or if the Trustee reasonably determines
that such joint defense would otherwise involve a conflict of interest.  The
Borrower need not pay for any settlement made without its consent.

     Neither the Borrower nor the Guarantors shall be obligated to reimburse any
expense or indemnify against any loss or liability incurred by the Trustee
through the Trustee's breach of the applicable standard of care for its conduct
under Section 12.01.

     When the Trustee incurs expenses or renders services after the occurrence
of any Event of Default specified in Sections 10.01(f), (g) or (h), the expenses
and the compensation 

                                      -48-
<PAGE>   53
 
for the services are intended to constitute expenses of administration under any
Bankruptcy Law.

     The provisions of this Section 12.07 shall survive the satisfaction and
discharge or other termination of this Indenture.

     Section 12.08  Replacement of Trustee.

     The Trustee may resign by so notifying the Borrower and the Guarantors.
The Agent may remove the Trustee by so notifying the Trustee, in writing.  The
Borrower may remove the Trustee if.

          (a) the Trustee fails to comply with Section 12.10;

          (b) the Trustee is adjudged a bankrupt or an insolvent;

          (c) a receiver or other public officer takes charge of the Trustee or
its property; or

          (d) the Trustee becomes incapable of acting as Trustee hereunder.

     If the Trustee resigns or is removed or if a vacancy exists in the office
of Trustee for any reason, the Borrower shall promptly appoint a successor
Trustee.  Within one year after the successor Trustee takes office, the Agent
may appoint a successor Trustee to replace the successor Trustee appointed by
the Borrower.

     A successor Trustee shall deliver a written acceptance of its appointment
to the retiring Trustee and to the Borrower and the Guarantors.  Immediately
after that, the retiring Trustee shall transfer all property held by it as
Trustee to the successor Trustee the resignation or removal of the retiring
Trustee shall become effective, and the successor Trustee shall have all the
rights, powers and duties of the Trustee under this Indenture.  A successor
Trustee shall mail notice of its succession to each Noteholder.

     If a successor Trustee does not take office within 30 days after the
retiring Trustee resigns or is removed, the retiring Trustee, the Borrower or
the Agent may petition, at the expense of the Borrower, any court of competent
jurisdiction for the appointment of a successor Trustee.

     If the Trustee fails to comply with Section 12.10, the Agent may petition
any court of competent jurisdiction for the removal of the Trustee and the
appointment of a successor Trustee.  Any successor Trustee shall comply with TIA
(S)310(a)(5).

                                      -49-
<PAGE>   54
 
     Section 12.09  Successor Trustee by Merger, etc.

     If the Trustee consolidates, merges or converts into, or transfers all or
substantially all of its corporate trust business to, another corporation, the
successor corporation without any further act shall be the successor Trustee;
provided such corporation or association shall be otherwise eligible and
qualified under this Article.

     Section 12.10  Eligibility, Disqualification.

     This Indenture shall always have a Trustee which satisfies the requirements
of TIA (S)310(a)(1) and (5). The Trustee shall always have a combined capital
and surplus of at least $50,000,000 as set forth in its most recent published
annual report of condition. The Trustee shall also comply with TIA (S)310(b).

     Section 12.11  Preferential Collection of Claims Against Borrower.

     The Trustee shall comply with TIA (S)311(a), excluding any creditor
relationship listed in TIA (S)311(b). A Trustee who has resigned or been removed
shall be subject to TIA (S)311(a) to the extent indicated therein.

     Section 12.12  Appointment of Co-Trustee.

     If the Trustee deems it necessary or desirable in connection with the
Collateral and/or the enforcement of the Collateral Documents, the Trustee may
appoint a co-Trustee with such powers of the Trustee as may be designated by the
Trustee at the time of such appointment (including acting as separate trustee of
any Collateral), and the Borrower shall, on request, execute and deliver to such
co-Trustee any deeds, conveyances or other instruments required by such co-
Trustee so appointed by the Trustee to more fully and certainly vest in and
confirm to such co-Trustee its rights, powers, trusts, duties and obligations
hereunder.

     All rights (including rights to indemnification hereunder), powers, duties
and obligations conferred or imposed upon the Trustee shall be conferred or
imposed upon and exercised or performed by the Trustee or jointly by the Trustee
and such co-Trustees, except to the extent that under any law of any
jurisdiction in which any particular act or acts are to be performed the Trustee
shall be incompetent or unqualified to perform such act or acts, in which event
such rights, powers, duties and obligations shall be exercised and performed by
such co-Trustees.  No Trustee or co-Trustee shall be personally liable by reason
of any act or omission of any other Trustee or co-Trustee hereunder.  Any co-
Trustee appointed pursuant to this Section 12.12 may be removed by the Trustee
pursuant to the terms of this Indenture and may be removed and may resign
pursuant to the provisions of the applicable Collateral Document and of this
Indenture.

     A co-Trustee shall not be responsible for and makes no representation as to
the value or condition of the Collateral or any part thereof, or as to the title
of the Borrower thereto, or as to the security afforded thereby or hereby, or as
to the validity or genuineness of any 

                                      -50-
<PAGE>   55
 
Collateral pledged and deposited with such co-Trustee, or the validity or
adequacy of this Indenture or the Notes; a co-Trustee shall not be accountable
for the Borrower's use of the proceeds from the Notes, and it shall not be
responsible for any statement of the Borrower in this Indenture or any document
issued in connection with the sale of the Notes or any statement in the Notes. A
co-Trustee makes no representations with respect to the effectiveness or
adequacy of this Indenture or any Basic Document or the validity or perfection,
if any, of Liens granted under this Indenture or the Collateral Documents. A co-
Trustee shall not be responsible for independently ascertaining or maintaining
such validity or perfection, if any, and shall be fully protected in relying
upon certificates and opinions delivered to it in accordance with the terms of
this Indenture or the Collateral Documents.

     Section 12.13 No Conflict.

     It is the purpose of this section of the Indenture to remove any potential
conflict of interest in the instance in which Chase Bank of Texas, National
Association ("Chase") is acting as Trustee and, in its commercial banking
capacity, has or may develop a lending relationship with the Borrower or any of
its Subsidiary Guarantors.  Accordingly, in the event that Chase, in its
commercial banking capacity, has or may develop a lending relationship with the
Borrower or any of Subsidiary Guarantors, Chase may, but is not obligated to,
resign as Trustee, such resignation to be effective automatically upon receipt
by the Trustee of notice from the successor Trustee evidencing its assumption of
the duties of Trustee hereunder, without notice to and without prior approval of
any party.  In the event Chase resigns as trustee pursuant to this Section
12.13, First Union National Bank, a national banking association duly organized
and existing under the laws of the United States of America with a corporate
trust office in Jacksonville, Florida, or any successor appointed pursuant to
the "Acceptance of Appointment" attached hereto as Exhibit G, has agreed to and
shall automatically become successor Trustee hereunder for all purposes.  Chase
shall give notice of its resignation in writing to the Borrower, the Agent and
the Noteholders as soon as possible but in any event not less than forty-five
(45) days after its resignation, provided that failure to give such notice shall
not impair the effectiveness of such resignation.  The provisions of this
section shall extend to Affiliates of Chase.


                                 ARTICLE XIII
                                 MISCELLANEOUS

     Section 13.01  Interpretation and Survival of Provisions.  Article,
Section, Schedule, and Exhibit references are to this Indenture, 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 Borrower has an obligation under
the Basic Documents, the expense of complying with that obligation shall be an
expense of the Borrower unless otherwise specified.  Whenever any determination,
consent, or approval is to be made or given by the Noteholders, such action
shall be in the Noteholders' sole discretion unless 

                                      -51-
<PAGE>   56
 
otherwise specified in this Indenture. 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 Indenture, 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 Borrower or the Noteholders or (b) acceptance of any of
the Notes and payment therefor and repayment or repurchase thereof. All
indemnification obligations of the Borrower and the provisions of Section 13.02
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 Indenture or any other
Basic Document.

     Section 13.02  Costs, Expenses and Taxes.

          (a) Intentionally Deleted.

          (b) The Borrower agrees to indemnify the Agent and the Noteholders,
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, 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 Borrower of the
proceeds of any sale of the Notes, (ii) the operations of the business of the
Borrower 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 Borrower or any
Subsidiary to comply with any Governmental Requirement, or (vi) any other aspect
of this Indenture and the other Basic 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 Noteholders or
any Noteholder and the Agent or any Noteholder's shareholders against the Agent
or any Noteholder or by reason of the gross negligence or wilful misconduct of
any Indemnitee).

          (c) The Borrower agrees to pay and hold the Noteholders harmless from
and against any and all present and future stamp and other similar taxes with
respect to this 

                                      -52-
<PAGE>   57
 
Indenture and Basic Documents and save the Noteholders 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 Noteholders for the full amount of
taxes paid by the Noteholders in respect of payments made or to be made under
this Indenture, any Note, or any other Basic 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) The Borrower agrees to indemnify and hold harmless from time to
time the Noteholders, and their respective Related Parties, together with the
Trustee, from and against any and all losses, claims, cost recovery actions,
administrative orders or proceedings, damages, and liabilities to which any such
Person may become subject (i) under any Environmental Law applicable to the
Borrower, any Subsidiary, or any of their respective Properties, (ii) as a
result of the breach or non-compliance by the Borrower or any Subsidiary with
any Environmental Law applicable to the Borrower or any Subsidiary, or any of
their respective Properties, (iii) due to the ownership by the Borrower or any
Subsidiary of their respective Properties or any activity on any of their
respective Properties, or any past activity on any of their respective
Properties which, though lawful and fully permissible at the time, could result
in present liability, (iv) the presence, use, release, storage, treatment, or
disposal of hazardous substances on or at any of the properties owned or
operated by the Borrower or any Subsidiary, or (v) any other environmental,
health, or safety condition in connection with this Indenture or any other Basic
Document.

          (e) In the case of any indemnification hereunder, the Noteholder or
other Person indemnified hereunder shall give notice to the Borrower within a
reasonable period of time of any such claim or demand being made against the
Noteholder or other indemnified Person and the Borrower at its sole cost and
expense shall provide a defense of such claim, provided, however, that (i) if
the Borrower 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
Borrower 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 Borrower
or such Subsidiary or if the interests of the indemnified party reasonably may
be deemed to conflict with the interests of the  Borrower 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 Borrower as incurred.

          (f) 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 13.02.

                                      -53-
<PAGE>   58
 
          (g) This Section 13.02 shall not apply to actions, suits, proceedings,
investigations, demands, losses, liabilities, claims, damages, deficiencies,
interest, judgments, 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).

          (h) The Borrower's obligations under this Section 13.02 shall survive
any termination of this Indenture and the payment of the Obligations.

     Section 13.03  No Waiver; Modifications in Writing.

          (a) No failure or delay on the part of the Trustee, the Borrower, the
Agent or the Noteholders 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 Borrower, the Trustee, the Agent or the Noteholders 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 Indenture, the
Notes or any other Basic Document, shall be effective unless signed by the
Borrower and the Majority Noteholders.  The Noteholders have all rights to take
such actions under this Indenture and the other Basic Documents without the
consent or joinder of any holder of the Acquired Shares or Warrants. Any
amendment, supplement or modification of or to any provision of this Indenture
or the Notes or any other Basic Document, any waiver of any provision of this
Indenture, the Notes or any other Basic Document, and any consent to any
departure by the Borrower from the terms of any provision of this Indenture, the
Notes or any other Basic Document, shall be effective only in the specific
instance and for the specific purpose for which made or given.  Except where
notice is specifically required by this Indenture, no notice to or demand on the
Borrower in any case shall entitle the Borrower to any other or further notice
or demand in similar or other circumstances.

     Section 13.04  Binding Effect; Assignment.  This Indenture shall be
binding upon the Borrower, the Trustee, the Agent and the Noteholders, and their
respective successors and permitted assigns. Except as expressly provided in
this Indenture, this Indenture shall not be construed so as to confer any right
or benefit upon any Person other than the Borrower, Trustee, Agent and
Noteholders, and their respective successors and permitted assigns.  Subject to
applicable federal law and state securities law, all or any portion of the
rights and obligations of the Noteholders under this Indenture with respect to
the Basic Documents may be sold, assigned or pledged by any Noteholder.  Upon
any assignment of the Basic Documents, the acquiring Noteholder shall succeed to
all of the selling Noteholder's rights and obligations under the Basic Documents
to the extent assigned and the selling Noteholder 

                                      -54-
<PAGE>   59
 
shall be automatically released from any such obligations hereunder with respect
to the Basic Documents to the extent assigned.

     Section 13.05  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 Trustee:

     Chase Bank of Texas, National Association
     Global Trust Services
     600 Travis Street, Suite 1150
     Houston, Texas  77002
     Attention:  Mauri J. Cowen
     Telephone:  (713) 216-6686
     Telecopier: (713) 216-5474


     If to the Agent:

     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

     Attention:  Donna Lowry
     Telecopier: (713) 646-4039

     If to the Noteholders:

     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

                                      -55-
<PAGE>   60
 
     Enron Capital & Trade Resources Corp.
     1400 Smith Street
     Houston, Texas  77002
     Attention:  Donna Lowry
     Telecopier: (713) 646-4039

     If to the Borrower:

     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 Borrower, Agent or any Noteholder 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.  Notwithstanding the foregoing, notices to the Trustee shall
be effective only upon receipt.

     Section 13.06  Governing Law.  This Indenture will be construed in
accordance with and governed by the laws of the State of Texas without regard to
principles of conflicts of laws.

     Section 13.07  Arbitration.

          (a) Binding Arbitration.  Subject to the provisions of subparagraph
(e), on the request of either the Borrower, the Agent or any Noteholder, 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 Indenture (a "Dispute") shall be resolved by binding
arbitration in accordance with the terms hereof.  Either the Borrower, the Agent
or any Noteholder 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 

                                      -56-
<PAGE>   61
 
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 Borrower, the Agent and the Noteholders each agree to
keep all Disputes and arbitration proceedings strictly confidential except for
disclosure of information required by applicable law.

          (e) Parties' Rights.  Nothing in the preceding paragraph shall require
arbitration prior to the Agent's or the Noteholders' exercise of any rights and
remedies under Article X.  In addition, nothing in this Section 13.07, nor the
exercise of any right to arbitrate thereunder, shall limit the right of the
Borrower, the Agent, the Trustee or any Noteholder: (a) to foreclose against any
Collateral by the exercise of the power of sale under, or to secure direct
payment of the proceeds of any Collateral as provided under, any deed of trust,
mortgage, or other security agreement or instrument or applicable law; (b) to
exercise self-help remedies such as setoff or repossession; or (c) to obtain
provisional or ancillary remedies or relief such as replevin, injunctive relief,
attachment or appointment of a receiver from a court having jurisdiction,
before, during or after the pendency of any arbitration proceeding.  Any
foreclosure action, or the institution and maintenance of any action for such
judicial relief, or pursuit of provisional or ancillary remedies, or exercise of
self-help remedies shall not constitute a waiver of the right of the exercising
party to submit any claim or dispute to arbitration.

          (f) Costs of Arbitration.  All fees of the arbitrator and any
engineer, accountant or other consultant engaged by the arbitrator, shall be
paid by the Borrower (as to 50%) and the Noteholders (as to 50%) unless
otherwise awarded by the arbitrator.

     Section 13.08  Confidentiality.  In the event that the Borrower or any
Guarantor (hereinafter called the "Subject Entities") provides to the Agent or
the Noteholders written confidential information or, if communicated as
confidential, oral confidential information belonging to any Subject Entity, the
Agent and the Noteholders shall thereafter maintain such information in
confidence in accordance with the standards of care and diligence that each
utilizes in maintaining its own confidential information.  This obligation of
confidence shall 

                                      -57-
<PAGE>   62
 
not apply to such portions of the information which (i) are in the public
domain, (ii) hereafter become part of the public domain without the Agent or the
Noteholders breaching their obligation of confidence to any Subject Entity,
(iii) are previously known by the Agent or the Noteholders from some source
other than any Subject Entity, (iv) are hereafter developed by the Agent or the
Noteholders without using a Subject Entity's information, (v) are hereafter
obtained by or available to the Agent or the Noteholders from a third party who
owes no obligation of confidence to any Subject Entity with respect to such
information, (vi) are disclosed with a Subject Entity's consent, (vii) must be
disclosed either pursuant to any Governmental Requirement or to Persons
regulating the activities of the Agent or the Noteholders, or (viii) may be
required to be disclosed by law or regulation or order of any Governmental
Authority in any judicial, arbitration or governmental proceeding. Further, the
Agent or a Noteholder may disclose any such information to any other Noteholder,
any independent petroleum engineers or consultants, any independent certified
public accounts, any legal counsel employed by such Person in connection with
this Indenture or any other Basic Document, including without limitation, the
enforcement or exercise of all rights and remedies thereunder, or, subject to
Section 13.04, any assignee or participant (including prospective assignees and
participants) in the Obligations; provided, however, that the Agent or the
Noteholders shall receive a confidentiality agreement from the Person to whom
such information is disclosed such that said person shall have the same
obligation to maintain the confidentiality of such information as is imposed
upon the Agent or the Noteholders hereunder. Notwithstanding anything to the
contrary provided herein, this obligation of confidence shall cease three (3)
years from the date the information was furnished, unless the Borrower requests
in writing at least thirty (30) days prior to the expiration of such three (3)
year period, to maintain the confidentiality of such information for an
additional three year period.

     Section 13.09  Execution in Counterparts.  This Indenture 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.

     Section 13.10 Trust Indenture Act Controls. Whether prior to or following
the qualification of this Indenture under the TIA, if any provision of this
Indenture limits, qualifies, or conflicts with the duties imposed by operation
of TIA (S)318(c) upon an Indenture qualified under the TIA, the imposed duties
shall control under this Indenture.

     Section 13.11 Communication by Noteholders with Other Noteholders.
Noteholders may communicate pursuant to TIA (S)312(b) with other Noteholders
with respect to their rights under this Indenture or the Notes. The Company, the
Guarantors, the Trustee, the Registrar and anyone else shall have the protection
of TIA (S)312(c).

     Section 13.12  Certificate and Opinion as to Conditions Precedent.  Upon
any request or application by the Borrower or any Guarantor to the Trustee to
take any action under this Indenture, the Borrower or such Guarantor, as the
case may be, shall furnish to the Trustee:

                                      -58-
<PAGE>   63
 
          (a) an Officers' Certificate (which shall include the statements set
forth in Section 13.13) stating that, in the opinion of the signers, the
conditions precedent, if any, provided for in this Indenture relating to the
proposed action have been complied with;

          (b) an Opinion of Counsel stating that, in the opinion of such
counsel, such conditions precedent have been complied with; and

          (c) any Opinion of Counsel may assume the existence of non-existence
of facts necessary to support such Opinion unless such counsel has actual
knowledge that such assumption would be contrary to the actual facts.

     Section 13.13  Statements Required in Certificate or Opinion.  Each
certificate or opinion with respect to compliance with a condition or covenant
provided for in this Indenture shall include:

          (a) a statement that each person making such certificate or opinion
has read such covenant or condition;

          (b) a brief statement as to the nature and scope of the examination or
investigation upon which the statements or opinions contained in such
certificate or opinion are based;

          (c) a statement that, in the opinion of each such person, he has made
such examination or investigation as is necessary to enable him to express an
informed opinion as to whether or not such covenant or condition has been
complied with; and

          (d) a statement as to whether or not, in the opinion of each such
person, such covenant or condition has been complied with.

     Section 13.14  Rules by Trustee and Agents.  The Trustee may make
reasonable rules for action by or a meeting of the Noteholders.  The Note
Registrar may make reasonable rules for its functions.

     Section 13.15  Legal Holidays.  A "Legal Holiday" is a Saturday, a
Sunday, or a day on which banks and trust companies in the City of New York are
not required by law or executive order to be open.  If a payment date is a Legal
Holiday at a place of payment, payment may be made at the place on the next
succeeding day that is not a Legal Holiday, without additional interest.

                                      -59-
<PAGE>   64
 
     IN WITNESS WHEREOF, BRIGHAM EXPLORATION COMPANY has caused this Indenture
to be signed by its President or one of its Vice Presidents, and CHASE BANK OF
TEXAS, NATIONAL ASSOCIATION has caused this Indenture to be signed by one of its
duly authorized trust officers, all as of the day and year first above written.

                              BRIGHAM EXPLORATION COMPANY


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



                              CHASE BANK OF TEXAS, NATIONAL
                              ASSOCIATION, as Trustee


                              By: /s/ MAURI COWEN
                                 -----------------------------------
                              Name:   Mauri J. Cowen
                                   ---------------------------------
                              Title:  Vice President & Trust Officer
                                    --------------------------------

                                      -60-
<PAGE>   65
 
STATE OF TEXAS      (S)
                    (S)
COUNTY OF HARRIS    (S)

     BEFORE ME, the undersigned authority, a Notary Public in and for said
state, on this day personally appeared Craig M. Fleming known to me to be the
person and officer whose name is subscribed to the foregoing instrument and
acknowledged to me that the same was the act of the said BRIGHAM EXPLORATION
COMPANY, a Delaware corporation, and that he executed the same as the act of
said corporation for the purposes and consideration therein expressed, and in
the capacity therein stated.

     GIVEN UNDER MY HAND AND SEAL OF OFFICE, this 20th day of August, 1998.


                              -------------------------------------------
                              Notary Public in and for the State of Texas

My commission expires:

---------------------------

STATE OF TEXAS      (S)
                    (S)
COUNTY OF HARRIS    (S)

     BEFORE ME, the undersigned authority, a Notary Public in and for said
state, on this day personally appeared __________________, known to me to be the
person and officer whose names are subscribed to the foregoing instrument and
acknowledged to me that the same was the act of the said CHASE BANK OF TEXAS,
NATIONAL ASSOCIATION, a national banking association, and that she executed the
same as the act of said national banking association for the purposes and
consideration therein expressed, and in the capacity therein stated.

     GIVEN UNDER MY HAND AND SEAL OF OFFICE, this 20th day of August, 1998.


                              ------------------------------------------- 
                              Notary Public in and for the State of Texas
My commission expires:

---------------------------

                                      -61-