Document:

FIRST AMENDMENT
                   TO AMENDED AND RESTATED GUARANTY AGREEMENT

     THIS FIRST AMENDMENT TO AMENDED AND RESTATED GUARANTY AGREEMENT (this
"AMENDMENT") dated as of October 31, 2000, is between BRIGHAM EXPLORATION
COMPANY, a Delaware corporation (the "GUARANTOR") and BANK OF MONTREAL, as agent
("AGENT") for the lenders (the "LENDERS") that are or become parties to the
Credit Agreement defined below.

                                    RECITALS

     A. Brigham Oil & Gas, L.P., a Delaware limited partnership (the
"BORROWER"), the Agent and the Lenders previously entered into that certain
Amended and Restated Credit Agreement dated as of February 17, 2000, as amended
by First Amendment to Amended and Restated Credit Agreement of even date
herewith (as amended, the "CREDIT AGREEMENT"), pursuant to which the Lenders
agreed to make certain loans and extensions of credit to the Borrower.

     B. Pursuant to the terms and conditions stated in the Credit Agreement,
Guarantor executed that certain Amended and Restated Guaranty Agreement dated
February 17, 2000, by Guarantor (the "GUARANTY AGREEMENT").

     C. Guarantor and the Agent now desire to amend certain provisions of the
Guaranty Agreement.

     NOW THEREFORE, in consideration of the mutual covenants and agreements
herein contained, the Guarantor, the Agent and the Lenders hereby agree that the
Guaranty Agreement shall be amended as follows:

     SECTION 1. CERTAIN DEFINITIONS. As used in this Amendment, the terms
"Agent", "Amendment", "Borrower", "Credit Agreement", "Guarantor" and "Lenders"
shall have the meanings indicated above; and unless otherwise defined herein,
all terms beginning with a capital letter which are defined in the Guaranty
Agreement shall have the same meanings herein as therein unless the context
hereof otherwise requires.

     SECTION 2. AMENDMENTS TO GUARANTY AGREEMENT.

     (a) Section 5.2(r) of the Guaranty Agreement is hereby deleted in its
entirety, and the following is substituted therefor:

          "(r) INTEREST COVERAGE RATIO. The Guarantor will not permit its
     Interest Coverage Ratio as of the end of any fiscal quarter of the
     Guarantor (calculated quarterly at the end of each fiscal quarter) to be
     less than the ratio set forth below for such period. INTEREST COVERAGE
     RATIO shall mean the ratio of (i) EBITDA to (ii) the sum of all required
     payments of interest (whether paid in cash or in kind) during such period
     on borrowed money:

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        (i)    not less than .75 to 1.0 for the twelve (12) month period ending
               September 30, 2000;

        (ii)   not less than .80 to 1.0 for the twelve (12) month period ending
               December 31, 2000;

        (iii)  not less than .90 to 1.0 for the twelve (12) month period ending
               March 31, 2001;

        (iv)   not less than 1.3 to 1.0 for the twelve (12) month period ending
               June 30, 2001;

        (v)    not less than 1.5 to 1.0 for the twelve (12) month period ending
               September 30, 2001;

        (vi)   not less than 1.7 to 1.0 for the twelve (12) month period ending
               December 31, 2001;

        (vii)  not less than 2.0 to 1.0 for the twelve (12) month period ending
               March 31, 2002;

        (viii) not less than 2.25 to 1.0 for the twelve (12) month period
               ending June 30, 2002; and

        (ix)   thereafter, not less than 2.50 to 1.0 for the twelve (12) month
               period ending September 30, 2002, and each twelve (12) month
               period ending at the end of each fiscal quarter of Guarantor.

     (b) The phrase "; provided that Guarantor may pay dividends on its
preferred equity securities so long as they are paid in kind and not in cash"
shall be added to the end of subsection 5.2(d).

     SECTION 3. REPRESENTATIONS AND WARRANTIES. Guarantor hereby reaffirms that
as of the effective date of this Amendment, the representations and warranties
made by the Guarantor in Article III of the Guaranty Agreement will be true and
correct as though made on and as of the effective date of this Amendment.

     SECTION 4. RATIFICATION. Guarantor hereby expressly ratifies and affirms
its obligations under the Guaranty Agreement as amended by this Amendment and
agrees that the Guaranty Agreement as amended by this Amendment remains in full
force and effect.

     SECTION 5. GOVERNING LAW. This Amendment and the rights and obligations of
the parties hereunder and under the Credit Agreement shall be construed in
accordance with and be governed by the laws of the State of Texas and the United
States of America.

     SECTION 6. DESCRIPTIVE HEADINGS, ETC. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

                                     - 2 -
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     SECTION 7. COUNTERPARTS. This Amendment may be executed in any number of
counterparts and by different parties on separate counterparts and all of such
counterparts shall together constitute one and the same instrument.

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

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

     THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE PARTIES
BEFORE OR SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF TOGETHER
CONSTITUTE A WRITTEN LOAN AGREEMENT AND REPRESENT THE FINAL AGREEMENT BETWEEN
THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR
SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NOT UNWRITTEN ORAL
AGREEMENTS BETWEEN THE PARTIES.

GUARANTOR:                      BRIGHAM EXPLORATION COMPANY

                                By: /s/ Karen E. Lynch
                                   ---------------------------------------------
                                Name:   Karen E. Lynch
                                     -------------------------------------------
                                Title:  Vice President
                                      ------------------------------------------

AGENT AND LENDER:                BANK OF MONTREAL

                                 By: /s/ Thomas E. McGraw
                                    --------------------------------------------
                                         Thomas E. McGraw
                                         Director

                                     - 3 -SECURITIES PURCHASE AGREEMENT

     This SECURITIES PURCHASE AGREEMENT (this "Agreement"), is entered into as
of November 1, 2000, between Brigham Exploration Company, a Delaware corporation
(the "Company"), DLJ MB Funding III, Inc., a Delaware corporation ("MB"), and
DLJ ESC II, LP, a Delaware limited partnership ("ESC") (collectively referred to
as "Investors").

     WHEREAS, the Company has authorized the sale and issuance of an aggregate
of up to one million, (1,000,000) shares of its Series A Preferred Stock (the
"Shares") and warrants to acquire six million, six hundred sixty-six thousand,
six hundred sixty-seven (6,666,667) shares of its Common Stock, (the
"Warrants"), in the form attached hereto as EXHIBIT A;

     Whereas, Investors desire to purchase the Shares and the Warrants on the
terms and conditions set forth herein; and

     Whereas, the Company desires to issue and sell the Shares and the Warrants
to Investors on the terms and conditions set forth herein;

     NOW, THEREFORE, in consideration of the premises and the mutual covenants
and agreements herein contained, and intending to be legally bound hereby, the
Company and Investors hereby agree as follows:

                                    ARTICLE I

                            TERMS OF THE TRANSACTION

     1.1 AUTHORIZATION OF SHARES. On or prior to the Closing (as defined in
Section 2.1 below), the Company shall have authorized (a) the sale and issuance
to Investors of the Shares and the Warrants and (b) the issuance of such shares
of Common Stock to be issued upon exercise of the Warrants (the "Warrant
Shares"). The Shares shall have the rights, preferences, privileges and
restrictions set forth in the Certificate of Designations of the Company, in the
form attached hereto as EXHIBIT B (the "Certificate of Designations").

     1.2 SALE AND PURCHASE. Subject to the terms and conditions hereof, at the
Closing the Company hereby agrees to issue and sell to MB and ESC, and MB and
ESC agree to purchase from the Company, respectively, 905,500 units (each a
"Unit") and 94,500 Units at a purchase price of Twenty Dollars ($20.00) per
Unit, with each such Unit consisting of (i) one Share and (ii) Warrant to
purchase 6.666667 Warrant Shares.

                                   ARTICLE II

                                     CLOSING

     2.1 CLOSING. The closing of the sale and purchase of the Shares and
Warrants under this Agreement (the "Closing") shall take place at the offices of
Vinson & Elkins L.L.P., 2300 First City Tower, 1001 Fannin, Houston, Texas
77002-6760, at 10:00 a.m., local time, on the date of this Agreement or at such
other time or place as the Company and Investors may mutually agree (the
"Closing Date"). All closing transactions at the Closing shall be deemed to have
occurred simultaneously.

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     2.2 CLOSING DELIVERIES. At the Closing, subject to the terms and conditions
hereof, the Company will deliver to each Investor, against payment of the
purchase price therefor by wire transfer made payable to the Company, a
certificate representing the applicable Shares and a Warrant representing the
applicable Warrants to purchase Warrant Shares.

                                   ARTICLE III

                  REPRESENTATIONS AND WARRANTIES OF THE COMPANY

     The Company represents and warrants to Investors, as of the date hereof,
that:

     3.1 CORPORATE ORGANIZATION. The Company is a corporation duly organized,
validly existing, and in good standing under the laws of the State of Delaware
and has all requisite corporate power and authority in all material respects to
own, lease, and operate its properties and to carry on its business as now being
conducted. No actions or proceedings to dissolve the Company are pending or, to
the best knowledge of the Company, threatened. The Company is duly qualified to
do business as a foreign corporation and is in good standing in each
jurisdiction where such qualification is necessary, except where the failure to
so qualify or to be in good standing would not reasonably be expected to have a
Material Adverse Effect.

     3.2 CAPITALIZATION OF THE COMPANY.

     (a) On the Closing Date, the authorized capital stock of the Company will
consist of 50,000,000 shares of Common Stock and 10,000,000 shares of preferred
stock, $.01 par value, 1,500,000 of which are designated as Series A Preferred
Stock. As of the date hereof, but prior to giving effect to the Enron
Transactions and the Financing Transaction (i) 17,028,175 shares of Common Stock
are outstanding and no shares of preferred stock are outstanding and (ii)
1,426,500 shares of Common Stock are reserved for issuance upon exercise of
outstanding employee, officer and director stock options and 8,212,476 shares of
Common Stock are reserved for issuance upon exercise of outstanding warrants or
conversion rights. All outstanding shares of capital stock of the Company have
been validly issued and are fully paid and nonassessable, and no shares of
capital stock of the Company are subject to, nor have any been issued in
violation of, preemptive or similar rights. On the Closing Date, the rights,
preferences, privileges and restrictions of the Shares will be as stated in the
Certificate of Designations.

     (b) Except as set forth above in subparagraph (a) of this Section 3.2,
there are outstanding (i) no shares of capital stock or other voting securities
of the Company; (ii) no securities of the Company convertible into or
exchangeable for shares of capital stock or other voting securities of the
Company; (iii) no options or other rights to acquire from the Company, and no
obligation of the Company to issue or sell, any shares of capital stock or other
voting securities of the Company or any securities of the Company convertible
into or exchangeable for such capital stock or voting securities; and (iv) no
equity equivalents, interests in the ownership or earnings, or other similar
rights of or with respect to the Company.

     (c) Neither the execution of this Agreement nor the performance of the
Company's obligations hereunder, nor the consummation of any other transaction
currently contemplated by the Company or any of its Subsidiaries, including the
Financing Transaction (as hereinafter defined) and the Enron Transaction (as
hereinafter defined), will trigger or cause any adjustment under any
anti-dilution provisions or any other similar provisions contained in any
agreement as currently in effect that have the effect of (i) causing a decrease
in any exercise price or conversion price in any security exercisable for or
convertible into shares of Common Stock (a "Common Stock Equivalent"), or (ii)
causing an increase in the number of shares of Common Stock that may be acquired
upon conversion or exercise of a Common Stock Equivalent.

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<PAGE>

     3.3 AUTHORITY RELATIVE TO THIS AGREEMENT. The Company has full corporate
power and authority to execute, deliver, and perform this Agreement and to
execute, deliver, and where applicable, perform the Ancillary Documents to which
it is a party and to consummate the transactions contemplated hereby and
thereby. The execution, delivery and performance by the Company of this
Agreement and the execution, delivery, and where applicable, performance by it
of the Ancillary Documents to which it is a party, and the consummation by it of
the transactions contemplated hereby and thereby, have been (or prior to the
Closing will have been) duly authorized by all necessary corporate action of the
Company. This Agreement has been duly executed and delivered by the Company and
constitutes, and each Ancillary Document executed or to be executed by the
Company has been, or when executed will be, duly executed and delivered by the
Company and constitutes, or when executed and delivered will constitute, a valid
and legally binding obligation of the Company, enforceable against the Company
in accordance with its terms, except that such enforceability may be limited by
(i) applicable bankruptcy, insolvency, reorganization, moratorium, and similar
laws affecting creditors' rights generally and (ii) general equitable principles
(regardless of whether such enforceability is considered in a proceeding in
equity or at law).

     3.4 NONCONTRAVENTION. The execution, delivery, and performance by the
Company of this Agreement and the execution, delivery, and where applicable, the
performance by it of Ancillary Documents to which it is a party and the
consummation by it of the transactions contemplated hereby and thereby do not
and will not (i) conflict with or result in a violation of any provision of the
Company's Certificate of Incorporation, as amended, or the Company's Bylaws, as
amended, or the charter, bylaws, partnership agreement or other governing
instruments of any Subsidiary, (ii) conflict with or result in a violation of
any provision of, or constitute (with or without the giving of notice or the
passage of time or both) a default under, or give rise (with or without the
giving of notice or the passage of time or both) to any loss of material
benefit, or of any right of termination, cancellation, or acceleration under,
any Material Agreement, (iii) result in the creation or imposition of any
Encumbrance upon the properties of the Company or any Subsidiary or (iv)
assuming compliance with the matters referred to in Section 3.5, violate any
Applicable Law binding upon the Company or any Subsidiary, except, in the case
of clauses (ii), (iii) and (iv) above, for any such conflicts, violations,
defaults, terminations, cancellations, accelerations, or Encumbrances which
would not, individually or in the aggregate, have a Material Adverse Effect on
the Company.

     3.5 CONSENTS AND APPROVALS. No consent, approval, order, or authorization
of, or declaration, filing, or registration with, any Governmental Entity is
required to be obtained or made by the Company or any Subsidiary in connection
with the execution, delivery, or performance by the Company of this Agreement
and the execution, delivery, and where applicable, performance of Ancillary
Documents to which it is a party or the consummation of the transactions
contemplated hereby and thereby, other than (i) compliance with any applicable
requirements of the Securities Act; (ii) compliance with any applicable
requirements of the Exchange Act; (iii) compliance with any applicable state
securities laws; (iv) filing of the Certificate of Designations with the
Delaware Secretary of State; (v) compliance with any applicable requirements of
the HSR Act as a result of the exercise of any of the Warrants; and (vi) such
consents, approvals, orders, or authorizations which, if not obtained, and such
declarations, filings, or registrations which, if not made, would not,
individually or in the aggregate, have a Material Adverse Effect on the Company.
Except for such consents as are obtained before or contemporaneously with
consummation of the Closing, no consent or approval of any person other than the
Company, Investors or any Governmental Entity is required to be obtained or made
by the Company or any Subsidiary in connection with the execution, delivery, or
performance by the Company of this Agreement and execution, delivery and, where
applicable, performance of the Ancillary Documents to which it is a party or the
consummation of the transactions contemplated hereby and thereby, other than
such consents, approvals, orders, or authorizations which, if not obtained, and
such declarations, filings, or registrations which, if not made, would not,
individually or in the aggregate, have a Material Adverse Effect on the Company.

                                       3
<PAGE>

     3.6 AUTHORIZATION OF ISSUANCE; RESERVATION OF SHARES. When issued and
delivered pursuant to this Agreement and the Certificate of Designations against
payment therefor, the Shares and the Warrants will be validly issued, fully paid
and nonassessable. The Warrant Shares have been duly and validly reserved for
issuance. The issuances of the Shares and the Warrants are not subject to any
preemptive or similar rights.

     3.7 FINANCIAL CONDITION. The audited consolidated balance sheet of the
Company and its Subsidiaries as at December 31, 1999 and the related
consolidated statement of income, stockholders' equity and cash flow of the
Company and its Subsidiaries for the fiscal year ended on said date, with the
opinion thereon of Price Waterhouse heretofore furnished to the Investors and
the unaudited consolidated balance sheet of the Company and its Subsidiaries as
at June 30, 2000, and their related consolidated statements of income,
stockholders' equity and cash flow of the Company and its Subsidiaries for the
six-month period ended on such date hereto fore furnished to the Investors, are
complete and correct and fairly present the consolidated financial condition of
the Company and its Subsidiaries as at said dates and the results of its
operations for the fiscal year and the six-month period on said dates, all in
accordance with GAAP, as applied on a consistent basis (subject, in the case of
the interim financial statements, to normal year-end adjustments). Neither the
Company nor any Subsidiary has on the Closing Date any debt, trade payables,
contingent liabilities, liabilities for taxes, unusual forward or long-term
commitments or unrealized or anticipated losses from any unfavorable
commitments, except as referred to or reflected or provided for in the Financial
Statements or in Schedule 3.7 or except to the extent that the existence of any
of the foregoing would not have a Material Adverse Effect relative to the
Company. Since December 31, 1999, there has been no change or event having a
Material Adverse Effect relative to the Company, except as disclosed to the
Investors in writing. Since the date of the Financial Statements, neither the
business nor the properties of the Company's Subsidiaries, taken as a whole,
have been materially and adversely affected as a result of any fire, explosion,
earthquake, flood, drought, windstorm, accident, strike or other labor
disturbance, embargo, requisition or taking of property or cancellation of
contracts, permits or concessions by any Governmental Entity, riot, activities
of armed forces or acts of God or of any public enemy.

     3.8 LITIGATION. Except as disclosed in Schedule 3.8 hereto, at the Closing
Date there is no litigation, legal, administrative or arbitral proceeding,
investigation or other action of any nature pending or, to the knowledge of the
Company, threatened against or affecting the Company or any Subsidiary which
both (a) involves the possibility of any judgment or liability against the
Company or any Subsidiary not fully covered by insurance (except for normal
deductibles), and (b) would be more likely than not to have a Material Adverse
Effect relative to the Company.

     3.9 ERISA. The Company and each ERISA Affiliate have complied in all
material respects with ERISA and, where applicable, the Code regarding each
Plan. Each Plan is, and has been, maintained in substantial compliance with
ERISA and, where applicable, the Code.

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

     No Plan (other than a defined contribution plan) or any trust created under
any such Plan has been terminated since September 2, 1974. No liability to the
PBGC in excess of $100,000 (other than for the payment of current premiums which
are not past due) by the Company or any ERISA Affiliate has been or is expected
by the Company or any ERISA Affiliate to be incurred with respect to any Plan.
No ERISA Event with respect to any Plan has occurred which could reasonably be
expected to result in liabilities of $100,000 or more.

                                       4
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     Full payment when due has been made of all amounts which the Company or any
ERISA Affiliate is required under the terms of each Plan or applicable law to
have paid as contributions to such Plan, and no accumulated funding deficiency
in an amount of $100,000 or more (as defined in section 302 of ERISA and section
412 of the Code), whether or not waived, exists with respect to any Plan.

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

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

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

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

     3.10 TAXES. The Company has filed all United States Federal income tax
returns and all other tax returns which are required to be filed by it and has
paid all material taxes due pursuant to such returns or pursuant to any
assessment received by the Company, except for any taxes which are being
contested in good faith and by proper proceedings and against which adequate
reserves are being maintained. The charges, accruals and reserves on the books
of the Company in respect of taxes and other governmental charges are, in the
opinion of the Company, adequate. No tax lien has been filed and, to the
knowledge of the Company, no claim is being asserted with respect to any such
tax, fee or other charge, except for any taxes, fees or other charges which are
not material or which are being contested in good faith and by proper
proceedings and against which adequate reserves are being maintained.

     3.11 TITLES, ETC.

     (a) Subject to the matters set out in Schedule 3.11, each of the Company
and the Subsidiaries has good and defensible title, in all material respects, to
the material Oil and Gas Properties that are evaluated in the most recently
delivered reserve report, free and clear of all Liens, other than Excepted
Liens. Except for immaterial divergences, after giving full effect to the
Excepted Liens, the Company owns, in all material respects, the net interests in
production attributable to the Hydrocarbon Interests that are evaluated in the
most recently delivered reserve report, and the ownership of such Hydrocarbon
Interests shall not in any material respect obligate the Company to bear the
costs and expenses relating to the maintenance, development and operations of
each such Hydrocarbon Interest in an amount in excess of the working interest of
such Hydrocarbon Interest (without a corresponding increase in net revenue
interest). The Company does not believe, based upon information in its
possession, that its most recently delivered reserve report materially
overstates its oil and gas reserves, bearing in mind that reserves are evaluated
based upon estimates and assumptions with respect to which reasonable minds of
competent reserve engineers may differ.

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

                                       6
<PAGE>

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

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

     3.12 NO MATERIAL MISSTATEMENTS. Taken as a whole, the written information,
statements, exhibits, certificates, documents and reports furnished to Investors
by the Company or any Subsidiary in connection with the negotiation of this
Agreement do not contain any material misstatement of fact or omit to state a
material fact or any fact necessary to make the statements contained therein not
materially misleading in the light of the circumstances in which made and with
respect to the Company or any Subsidiary. As of the Closing Date, there is no
fact peculiar to the Company or Subsidiary which has a Material Adverse Effect
relative to the Company or in the future is reasonably likely to have (so far as
the Company can now foresee) a Material Adverse Effect and which has not been
set forth in this Agreement or the other documents, certificates and statements
furnished to Investors by or on behalf of the Company or any Subsidiary prior
to, or on, the Closing Date in connection with the transactions contemplated
hereby.

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

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

     3.15 SUBSIDIARIES. Except as set forth on Schedule 3.15, the Company has no
Subsidiaries. Each Subsidiary is a corporation or limited partnership, duly
incorporated or organized, validly existing and in good standing under the laws
of its jurisdiction of incorporation or organization, if applicable, and has all
requisite corporate power and authority in all material respects to own, lease,
and operate its properties and to carry on its business as now being conducted.
Each Subsidiary is duly qualified to do business as a foreign corporation or
limited partnership, if applicable, and is in good standing in each jurisdiction
where such qualification is necessary, except where the failure to so qualify or
to be in good standing would not reasonably be expected to have a Material
Adverse Effect. There are outstanding (i) no securities of any Subsidiary of the
Company convertible into or exchangeable for shares of capital stock or other
voting securities of any Subsidiary of the Company and (ii) no options or other
rights to acquire from any Subsidiary of the Company, and no obligation of any
Subsidiary of the Company to issue or sell, any shares of capital stock or other
voting securities of any Subsidiary of the Company or any securities of any
Subsidiary of the Company convertible into or exchangeable for such capital
stock or voting securities.

     3.16 DEFAULTS. Neither the Company nor any Subsidiary is in default nor has
any event or circumstance occurred which, but for the expiration of any
applicable grace period or the giving of notice, or both, would constitute a
default under any material agreement or instrument to which the Company is a
party or by which the Company is bound, which default would have a Material
Adverse Effect.

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

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     (a) Neither any Oil and Gas Property of the Company or any of its
Subsidiaries nor the operations conducted thereon violate any order or
requirement of any court or Governmental Entity or any Environmental Laws;

     (b) Without limitation of clause (a) above, no Oil and Gas Property of the
Company or any of its Subsidiaries nor the operations currently conducted
thereon or, to the best knowledge of the Company, by any prior owner or operator
of such property or operation, are in violation of or subject to any existing,
pending or threatened action, suit, investigation, inquiry or proceeding by or
before any court or Governmental Entity or to any remedial obligations under
Environmental Laws;

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

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

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

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

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

     3.18 COMPLIANCE WITH THE LAW. Neither the Company nor any Subsidiary has
violated any Governmental Requirement or failed to obtain any license, permit,
franchise or other governmental authorization necessary for the ownership of any
of its Oil and Gas Properties or the conduct of its business, which violation or
failure would have (in the event such violation or failure were asserted by any
Person through appropriate action) a Material Adverse Effect. Except for such
acts or failures to act as would not have a Material Adverse Effect, the Oil and

                                       7
<PAGE>

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

     3.19 INSURANCE. Schedule 3.19 attached hereto contains an accurate and
complete description of all material policies of fire, liability, workmen's
compensation and other forms of insurance owned or held by the Company and each
Subsidiary as of the Closing Date. All such policies are in full force and
effect, all premiums with respect thereto covering all periods up to and
including the Closing Date have been paid, and no notice of cancellation or
termination has been received with respect to any such policy. Such policies are
sufficient for compliance with all requirements of law and of all agreements to
which the Company or any Subsidiary is a party; are valid, outstanding and
enforceable policies; provide adequate insurance coverage in at least such
amounts and against at least such risks (but including in any event public
liability) as are usually insured against in the same general area by companies
engaged in the same or a similar business for the assets and operations of the
Company and each Subsidiary; will remain in full force and effect through the
respective dates set forth in Schedule 3.19 with the payment of additional
premiums; and will not in any way be affected by, or terminate or lapse by
reason of, the transactions contemplated by this Agreement. Schedule 3.19
identifies all material risks, if any, which the Company, the Subsidiaries and
their respective Board of Directors or officers have designated as being self
insured. Neither the Company nor any Subsidiary has been refused any insurance
with respect to its assets or operations, nor has its coverage been limited
below usual and customary policy limits, by an insurance carrier to which it has
applied for any such insurance or with which it has carried insurance during the
last three years.

     3.20 HEDGING AGREEMENTS. Schedule 3.20 sets forth, as of the Closing Date,
a true and complete list of all Hedging Agreements (including commodity price
swap agreements, forward agreements or contracts of sale which provide for
prepayment for deferred shipment or delivery of oil, gas or other commodities)
of the Company and each Subsidiary.

     3.21 MATERIAL AGREEMENTS. Set forth on Schedule 3.21 hereto is a complete
and correct list of all material agreements, leases, indentures, purchase
agreements, obligations in respect of letters of credit, guarantees, joint
venture agreements, and other instruments in effect or to be in effect as of the
Closing Date (other than Hedging Agreements) providing for, evidencing, securing
or otherwise relating to any material Debt of the Company or any Subsidiary, and
all obligations of the Company or any Subsidiary to issuers of surety or appeal
bonds (excluding operator's bonds, plugging and abandonment bonds, and similar
surety obligations obtained in the ordinary course of business) issued for
account of the Company or any such Subsidiary.

     3.22 GAS IMBALANCES. As of the Closing Date, except as set forth in the
most recent Reserve Report furnished to Investors, on a net basis there are no
gas imbalances, take or pay or other prepayments with respect to the Company's
or any Subsidiary's Hydrocarbon Interests which would require the Company or
such Subsidiary to deliver five percent (5%) or more of the monthly production

                                       9
<PAGE>

from the Company'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.

     3.23 BROKERAGE FEES. The Company has not retained any financial advisor,
broker, agent, or finder or paid or agreed to pay any financial advisor, broker,
agent, or finder on account of the sale by the Company and the purchase by
Investors of the Shares pursuant to this Agreement, except for CIBC World
Markets Corp. (or an Affiliate), and the Company hereby agrees to pay all fees
owing to CIBC World Markets Corp. on account of the consummation of such
transaction, which fees are not to exceed $1,200,000.

     3.24 SEC FILINGS. The Company has complied in all material respects with
its obligations to file with the Securities and Exchange Commission all forms,
reports, schedules, statements and other documents required to be filed by it
since May 9, 1997 under the Securities Act and the Exchange Act. All forms,
reports, schedules, statements, and other documents (including all amendments
thereto) filed by the Company with the Securities and Exchange Commission since
such date are herein collectively referred to as the "SEC Filings". The SEC
Filings, at the time filed, complied in all material respects with all
applicable requirements of federal securities laws. None of the SEC Filings,
including, without limitation, any financial statements or schedules included
therein, at the time filed or as same may have been amended, contained any
untrue statement of a material fact or omitted to state any material fact
required to be stated therein or necessary in order to make the statements
contained therein, in light of the circumstances under which they were made, not
misleading.

     3.25 STOCKHOLDER APPROVAL. Neither the execution of this Agreement nor the
consummation of the transactions contemplated hereunder require the approval of
the stockholders of the Company under the applicable listing rules of the Nasdaq
Stock Market, Inc.

                                   ARTICLE IV

                   REPRESENTATIONS AND WARRANTIES OF INVESTORS

     Each Investor represents and warrants to the Company that:

     4.1 ORGANIZATION. MB is a corporation duly organized, validly existing and
in good standing under the laws of the State of Delaware. ESC is a limited
partnership duly organized, validly existing and in good standing under the laws
of the State of Delaware. Each Investor has all requisite corporate power and
authority in all material respects to own, lease, and operate its properties and
to carry on its business as now being conducted. No actions or proceedings to
dissolve either Investor are pending or, to the best knowledge of any Investor,
threatened.

     4.2 AUTHORITY RELATIVE TO THIS AGREEMENT. Each Investor has full corporate
or (if applicable) other power and authority to execute, deliver, and perform
this Agreement and execute, deliver and, where applicable, perform the Ancillary
Documents to which it is a party and to consummate the transactions contemplated
hereby and thereby. The execution, delivery, and performance by each Investor of
this Agreement and execution, delivery, and, where applicable, performance of
the Ancillary Documents to which it is a party, and the consummation by it of
the transactions contemplated hereby and thereby, have been duly authorized by
all necessary corporate (if applicable) action of such Investor. This Agreement
has been duly executed and delivered by each Investor and constitutes, and each
Ancillary Document executed or to be executed by each Investor has been, or when
executed will be, duly executed and delivered by such Investor and constitutes,
or when executed and delivered will constitute, a valid and legally binding
obligation of such Investor, enforceable against such Investor in accordance
with its terms, except that such enforceability may be limited by (i) applicable
bankruptcy, insolvency, reorganization, moratorium, and similar laws affecting
creditors' rights generally and (ii) general equitable principles (regardless of
whether such enforceability is considered in a proceeding in equity or at law).

                                       9
<PAGE>

     4.3 NONCONTRAVENTION. The execution, delivery, and performance by each
Investor of this Agreement and the execution, delivery and, where applicable,
performance of Ancillary Documents to which it is a party and the consummation
by it of the transactions contemplated hereby and thereby do not and will not
(i) conflict with or result in a violation of any provision of MB's Certificate
of Incorporation or Bylaws or ESC's Certificate of Limited Partnership or
partnership agreement, (ii) conflict with or result in a violation of any
provision of, or constitute (with or without the giving of notice or the passage
of time or both) a default under, or give rise (with or without the giving of
notice or the passage of time or both) to any right of termination,
cancellation, or acceleration under, any bond, debenture, note, mortgage,
indenture, lease, agreement or other instrument or obligation to which any
Investor is a party or by which Investor or any of its properties may be bound,
(iii) result in the creation or imposition of any Encumbrance upon the
properties of any Investor, or (iv) violate any Applicable Law binding upon any
Investor, except, in the case of clauses (ii), (iii) and (iv) above, for any
such conflicts, violations, defaults, terminations, cancellations,
accelerations, or Encumbrances which would not, individually or in the
aggregate, have a Material Adverse Effect on any Investor.

     4.4 CONSENTS AND APPROVALS. No consent, approval, order, or authorization
of, or declaration, filing, or registration with, any Governmental Entity is
required to be obtained or made by Investors in connection with the execution,
delivery, or performance by Investors of this Agreement. No consent or approval
of any person other than any Governmental Entity is required to be obtained or
made by any Investor in connection with the execution, delivery or performance
by Investors of this Agreement and the execution, delivery and, where
applicable, performance of the Ancillary Documents to which it is a party.

     4.5 PURCHASE FOR INVESTMENT. Each Investor understands that none of the
Shares, the Warrants or the Warrant Shares have been registered under the
Securities Act. Each Investor also understands that the Shares, the Warrants and
the Warrant Shares are being offered and sold pursuant to an exemption from
registration contained in the Securities Act based in part upon Investors'
representations contained in the Agreement. Each Investor hereby represents and
warrants as follows:

     (a) INVESTOR BEARS ECONOMIC RISK. Each Investor has substantial experience
in evaluating and investing in private placement transactions of securities in
companies similar to the Company so that it is capable of evaluating the merits
and risks of its investment in the Company and has the capacity to protect its
own interests. Without limiting the generality of the foregoing, each Investor
further represents that it has such knowledge regarding the oil and gas industry
and the business of the Company and the current circumstances surrounding such
industry and business that it is capable of evaluating the merits and risks of
the acquisition of the Shares, the Warrants and the Warrant Shares. Each
Investor must bear the economic risk of this investment indefinitely unless the
Shares, the Warrants or the Warrant Shares are registered pursuant to the
Securities Act, or an exemption from registration is available. Each Investor
understands that the Company has no present intention of registering the Shares,
the Warrants or the Warrant Shares. Each Investor also understands that there is
no assurance that any exemption from registration under the Securities Act will
be available and that, even if available, such exemption may not allow an
Investor to transfer all or any portion of the Shares, Warrants or Warrant
Shares under the circumstances, in the amounts or at the times an Investor might
propose.

     (b) ACQUISITION FOR OWN ACCOUNT. Each Investor is acquiring the Shares, the
Warrants and Warrant Shares for such Investor's own account for investment only,
and not with a view towards their distribution.

                                       10
<PAGE>

     (c) INVESTOR CAN PROTECT ITS INTEREST. Each Investor represents that by
reason of its, or of its management's, business or financial experience, such
Investor has the capacity to protect its own interests in connection with the
transactions contemplated in this Agreement and the Ancillary Agreements.
Further, neither Investor is aware of no publication of any advertisement in
connection with the transactions contemplated in the Agreement.

     (d) ACCREDITED INVESTOR. Each Investor represents that it is an accredited
investor within the meaning of Regulation D under the Securities Act.

     (e) COMPANY INFORMATION. Each Investor has had access to the Company's SEC
Filings and has had an opportunity to discuss the Company's business, management
and financial affairs with directors, officers and management of the Company and
has had the opportunity to review the Company's operations and facilities. Each
Investor has also had the opportunity to ask questions of, and receive answers
from, the Company and its management regarding the terms and conditions of this
investment. Each Investor hereby acknowledges and affirms that it has completed
its own independent investigation, analysis, and evaluation of the Company and
its subsidiaries, that it has made all such reviews and inspections of the
business, assets, results of operations, condition (financial or otherwise), and
prospects of the Company and its subsidiaries as it has deemed necessary or
appropriate, and that in making its decision to enter into this Agreement and to
consummate the transactions contemplated hereby it has relied solely on its own
independent investigation, analysis, and evaluation of the Company and its
subsidiaries, or that of its own independent advisers in evaluating its
investment in the Shares, Warrants and Warrant Shares.

     (f) RULE 144. Each Investor acknowledges and agrees that the Shares and the
Warrants, and, if issued, the Warrant Shares, must be held indefinitely unless
they are subsequently registered under the Securities Act or an exemption from
such registration is available. Each Investor has been advised or is aware of
the provisions of Rule 144, which permits limited resale of shares purchased in
a private placement subject to the satisfaction of certain conditions,
including, among other things: the availability of certain current public
information about the Company, the resale occurring following the required
holding period under Rule 144 and the number of shares being sold during any
three-month period not exceeding specified limitations.

     (g) TRANSFER RESTRICTIONS. Each Investor acknowledges and agrees that the
Shares, the Warrants and the Warrant Shares are subject to restrictions on
transfer as set forth in Section 5.5, below, and further understands that the
Shares, the Warrants and the Warrant Shares will not have been registered
pursuant to the Securities Act or any applicable state securities laws, that the
Shares, the Warrants and the Warrant Shares will be characterized as "restricted
securities" under federal securities laws, and that under such laws and
applicable regulations the Shares, the Warrants and the Warrant Shares cannot be
sold or otherwise disposed of without registration under the Securities Act or
an exemption therefrom. In this connection, each Investor represents that it is
familiar with Rule 144 promulgated under the Securities Act, as currently in
effect, and understands the resale limitations imposed thereby and by the
Securities Act. Appropriate stop transfer instructions may be issued to the
transfer agent for securities of the Company (or a notation may be made in the
appropriate records of the Company) in connection with the Shares, the Warrants
or the Warrant Shares.

     (h) CONFIRMATION. The acquisition of the Shares by an Investor at the
Closing shall constitute such Investor's confirmation of the foregoing
representations.

     4.6 NO OTHER SHARES. Except for such rights as may be conferred on an
Investor by this Agreement and the Ancillary Documents, Investors do not
beneficially own, directly or indirectly, any shares of capital stock or other
securities of the Company or any of its Subsidiaries.

     4.7 FINANCIAL RESOURCES. Each Investor has the financial resources
available to it as are necessary to perform its obligations to acquire the
Shares pursuant to the terms of this Agreement.

                                       11
<PAGE>

     4.8 BROKERAGE FEES. No Investor has retained any financial advisor, broker,
agent, or finder or paid or agreed to pay any financial advisor, broker, agent,
or finder on account of the sale by the Company and the purchase by Investors of
the Shares pursuant to this Agreement.

                                    ARTICLE V

                              ADDITIONAL AGREEMENTS

     5.1 REASONABLE BEST EFFORTS.

     (a) Each party hereto agrees that it will use its reasonable best efforts
to take, or cause to be taken, all action and to do, or cause to be done, all
things reasonably necessary, proper, or advisable under Applicable Laws to
consummate the transactions contemplated by this Agreement, including, without
limitation, (i) cooperation in determining whether any consents, approvals,
orders, authorizations, waivers, declarations, filings, or registrations of or
with any Governmental Entity or third party are required in connection with the
consummation of the transactions contemplated hereby; (ii) reasonable best
efforts to obtain any such consents, approvals, orders, authorizations, and
waivers and to effect any such declarations, filings, and registrations; (iii)
reasonable best efforts to cause to be lifted or rescinded any injunction or
restraining order or other order adversely affecting the ability of the parties
to consummate the transactions contemplated hereby; (iv) reasonable best efforts
to defend, and cooperation in defending, all lawsuits or other legal proceedings
challenging this Agreement or the consummation of the transactions contemplated
hereby; and (v) the execution of any additional instruments necessary to
consummate the transactions contemplated hereby.

     (b) Without limiting the generality of Section 5.1(a), to the extent
required by the HSR Act, each of the parties hereto shall (i) file or cause to
be filed, as promptly as practicable but in no event later than five (5)
consecutive Business Days after the execution and delivery of this Agreement,
with the Federal Trade Commission and the United States Department of Justice,
all reports and other documents required to be filed by such party under the HSR
Act concerning the transactions contemplated hereby and (ii) promptly comply
with or cause to be complied with any requests by the Federal Trade Commission
or the United States Department of Justice for additional information concerning
such transactions, in each case so that the waiting period applicable to this
Agreement and the transactions contemplated hereby under the HSR Act shall
expire as soon as practicable after the execution and delivery of this
Agreement. Each party hereto agrees to request, and to cooperate with the other
party or parties in requesting, early termination of any applicable waiting
period under the HSR Act. Notwithstanding the foregoing, if any report or other
document is required to be filed by any Investor under the HSR Act solely as
result of the purchase and sale of the Shares or the Warrants (with no regard to
any other securities held by such Investor or its Affiliates), the Company shall
pay any and all fees and expenses, including filing fees and legal expenses,
incurred by such Investor in connection with the filing of such reports or other
documents and any other actions required to comply with the provisions of the
HSR Act.

     5.2 PRESS RELEASES. Except as may be required by Applicable Law or by the
rules of any national securities exchange or registered securities association,
prior to the Closing, neither Investors nor the Company shall issue any press
release with respect to this Agreement or the transactions contemplated hereby
without the prior consent of the other party (which consent shall not be
unreasonably withheld under the circumstances). Any such press release required
by Applicable Law or by the rules of any national securities exchange or
registered securities association shall only be made after reasonable notice to
the other party.

     5.3 FEES AND EXPENSES. Except as otherwise expressly provided in this
Agreement, all fees and expenses, including fees and expenses of counsel,
financial advisors and accountants, incurred in connection with this Agreement
and the transactions contemplated hereby shall be paid by the party incurring
such fee or expense.

                                       12
<PAGE>

         5.4 SURVIVAL. The representations and warranties made herein shall
survive the Closing, regardless of any investigation made by or on behalf of any
party, until the second anniversary of the Closing Date; provided, however, the
representations and warranties contained in Sections 3.9, 3.10 and 3.18 shall
survive until the expiration of the applicable statute limitations relating to
the subject matters of such representations and warranties (the "Survival
Date".) All statements as to factual matters contained in any certificate or
other instrument delivered by or on behalf of the Company pursuant hereto in
connection with the transactions contemplated hereby shall be deemed to be
representations and warranties by the Company herein for purposes of this
Section 5.5. No action may be brought with respect to a breach of any
representation or warranty after the Survival Date unless, prior to such time,
the party seeking to bring such an action has notified the other parties of such
claim, specifying in reasonable detail the nature of the loss suffered.

     5.5 TRANSFER RESTRICTIONS.

     (a) Notwithstanding any provision contained in this Agreement to the
contrary, each Investor agrees that it will not, directly or indirectly, sell,
assign, transfer, pledge, encumber, or otherwise dispose of any of the Shares,
Warrants or Warrant Shares except:

          (i) In compliance with Rule 144; provided, however, that the Investor
     shall provide the Company with copies of all filings made with the
     Securities and Exchange Commission with respect to sales of securities
     under Rule 144 and with such other information and documents as the Company
     shall reasonably require in order to assure full compliance with Rule 144;
     or

          (ii) Pursuant to a no-action letter or other interpretive statement or
     release of the Securities and Exchange Commission to the effect that the
     proposed sale or other disposition may be effected without registration
     under the Securities Act; or

          (iii) Pursuant to an applicable exemption (other than Rule 144) under
     the Securities Act; provided, however, that the Investor shall have
     furnished the Company with an opinion of counsel, which opinion and counsel
     shall be reasonably acceptable to the Company, to the effect that such
     disposition does not require registration of such securities under the
     Securities Act; provided further, however, that no opinion of counsel shall
     be required in the case of a transfer to an affiliate (as defined in Rule
     405 of the Securities Act) of Investor if such affiliate shall have
     furnished the Company with the representations contained in Section 4.5 of
     this Agreement and shall have agreed with the Company to be subject to the
     terms of this Agreement to the same extent as if an original holder of
     securities pursuant hereto.

          (iv) Pursuant to an effective registration statement filed under the
     Securities Act.

     (b) It is agreed and understood by each Investor that the certificates or
instruments representing the Shares, Warrants and Warrant Shares shall each be
stamped or otherwise imprinted with a legend in substantially the following
form:

     "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE STATE SECURITIES
LAWS, AND MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR
AN EXEMPTION THEREFROM. SUCH SECURITIES ARE SUBJECT TO THE RESTRICTIONS AND
PRIVILEGES SPECIFIED IN A SECURITIES PURCHASE AGREEMENT, DATED AS OF __________,
2000, BETWEEN BRIGHAM EXPLORATION COMPANY AND THE INITIAL HOLDERS OF SECURITIES
NAMED THEREIN, A COPY OF WHICH IS ON FILE WITH THE SECRETARY OF BRIGHAM
EXPLORATION COMPANY AND WILL BE FURNISHED WITHOUT CHARGE TO THE HOLDER HEREOF
UPON WRITTEN REQUEST, AND THE HOLDER OF THIS CERTIFICATE AGREES TO BE BOUND
THEREBY."

                                       13
<PAGE>

     5.6 TRANSACTION FEE. The sum of Two Hundred Thousand Dollars ($200,000),
plus all reasonable out-of-pocket expenses incurred by the investors, including
attorneys fees, shall be paid by the Company to Investors on the Closing Date
upon Closing; provided, however, that in no event shall the Company be obligated
to pay more than $235,000 pursuant to this Section 5.6.

     5.7 SPECIAL MEETING OF STOCKHOLDERS.

     (a) The Company shall take all action necessary in accordance with
applicable law and the Company's Certificate of Incorporation and Bylaws to duly
call, give notice of, convene, and hold a special meeting of its stockholders as
promptly as practicable after the date hereof to consider and vote upon the
matters described in the Stockholders Voting Agreement dated as of October 31,
2000 by and among the Company and certain of its stockholders (the "Stockholder
Approval"). The Company shall not mail or otherwise distribute the proxy
statement or information statement (or any related proxy materials or amendments
or supplements thereto, if any) relating to such special meeting to its
stockholders without consultation with Investors and their counsel, and such
proxy statement or information statement and such other items shall be in such
form as Investors and their counsel shall approve (such approval not to
unreasonably withheld.

     (b) The Company covenants and agrees that, prior to obtaining the
Stockholder Approval, it shall not take any action that would cause an
adjustment, pursuant to the terms of the Warrants, to the Exercise Price (as
defined in the Warrant Certificates evidencing the Warrants) of the Warrants but
for the requirements of Section 2(i) of such Warrant Certificates.

     5.8 CAPITALIZATION CERTIFICATION. The Company shall provide, immediately
after the Closing, a schedule reflecting the capitalization of the Company as of
immediately after the transactions contemplated by this Agreement and those
contemplated in the Enron Transactions and the Financing Transaction, including
at least the information provided in the representation in Section 3.2 and
indicating the number of fully-diluted shares of Common Stock, and certified by
the Chief Financial Officer of the Company (the "Certificate"). Until the second
anniversary of the Closing Date, the Company shall amend the Certificate at any
time after the Closing to reflect any changes to the Certificate (which in all
cases shall reflect the capitalization of the Company as of immediately after
the transactions contemplated by this Agreement and those contemplated in the
Enron Transactions and the Financing Transaction) if the Company learns that the
Certificate is incorrect or not complete in any respect. Notwithstanding any
provision contained in this Agreement, the Registration Rights Agreement and the
Warrant Certificate, if the number of fully-diluted shares of Common Stock as
reflected in the Certificate at any time is more than 32,531 shares in excess of
32,531,187 shares of Common Stock, then the number of shares purchasable upon
exercise of the Warrant shall be increased to a number of shares equal to 20.49%
of the fully-diluted shares of Common Stock. Upon any such adjustment to the
number of shares to be acquired upon exercise of the Warrant, the holder of the
Warrant shall deliver to the Company the Warrant Certificate for cancellation
and immediately thereupon the Company shall issue a new Warrant Certificate
reflecting the adjusted number of shares purchasable thereunder. For purposes of
this Section 5.8, the term "fully-diluted shares of Common Stock" means the sum
of shares of Common Stock outstanding, plus all shares of Common Stock issuable
pursuant to (i) the conversion or exchange of securities that are convertible
into or exchangeable for shares of Common Stock or the exercise of any option,
warrant or other right to acquire shares of Common Stock from the Company, (ii)
the conversion or exchange of any security that is convertible into or
exchangeable for any securities referenced in 5.8(i) or the exercise of any
security that is exercisable for any securities referenced in 5.8(i), and (iii)
the exercise of any rights under any agreement regarding equity equivalents,
interests in the ownership or earnings, or other similar rights of or with
respect to the Company.

                                       14
<PAGE>

                                   ARTICLE VI

                    CONDITIONS TO OBLIGATIONS OF THE COMPANY

     The obligations of the Company to consummate the transactions contemplated
by this Agreement shall be subject to the fulfillment on or prior to the Closing
Date of each of the following conditions:

     6.1 REPRESENTATIONS AND WARRANTIES. All the representations and warranties
of Investors contained in this Agreement shall be true and correct in all
material respects, except as affected by transactions contemplated or permitted
by this Agreement.

     6.2 COVENANTS AND AGREEMENTS. Investors shall have performed and complied
with in all material respects all covenants and agreements required by this
Agreement to be performed or complied with by them on or prior to the Closing
Date.

     6.3 HSR ACT. All waiting periods (and any extensions thereof) applicable to
this Agreement and the transactions contemplated hereby under the HSR Act shall
have expired or been terminated.

     6.4 LEGAL PROCEEDINGS. No Proceeding shall, on the Closing Date, be pending
or threatened seeking to restrain, prohibit or obtain damages or other relief in
connection with this Agreement or the consummation of the transactions
contemplated hereby.

     6.5 CONSENTS. All consents, approvals, orders, authorizations and waivers
of, and all declarations, filings and registrations with, third parties
(including Governmental Entities) required to be obtained or made by or on the
part of the parties hereto, or otherwise reasonably necessary for the
consummation of the transactions contemplated hereby, shall have been obtained
or made, and all thereof shall be in full force and effect at the time of
Closing.

     6.6 ENRON TRANSACTIONs. All conditions precedent to the closing of the
Enron Transactions (other than conditions with respect to the consummation,
simultaneously with such closing, of the transactions contemplated hereby) shall
have been satisfied or waived at or prior to the Closing, and such closing shall
have occurred prior to or be occurring simultaneously with the Closing. For
purposes of this Agreement, the "Enron Transactions" mean (i) the repurchase by
the Company from affiliates of Enron North America Corp. of an aggregate of
1,052,632 shares of the Company's Common Stock, warrants to purchase an
aggregate of 1,000,000 shares of the Company's common stock and (ii) the
repayment in full (and/or repurchase or cancellation) of the Company's Senior
Subordinated Secured Notes due 2003, for an aggregate repurchase/repayment price
of no more than $20,000,000 in cash, excluding fees and commissions.

     6.7 FINANCING. All conditions precedent to the closing of a Financing
Transaction (other than conditions with respect to the consummation,
simultaneously with such closing, of the transactions contemplated hereby) shall
have been satisfied or waived at or prior to the Closing, and such closing shall
have occurred prior to or be occurring simultaneously with the Closing. For
purposes of this Agreement, a "Financing Transaction" means the financing
arrangements described in the Subordinated Credit Agreement dated as of October
31, 2000 among Brigham Oil & Gas, L.P. and Shell Capital, Inc.

                                       15
<PAGE>

                                   ARTICLE VII

                     CONDITIONS TO OBLIGATIONS OF INVESTORS

     The obligations of Investors to consummate the transactions contemplated by
this Agreement shall be subject to the fulfillment on or prior to the Closing
Date of each of the following conditions:

     7.1 REPRESENTATIONS AND WARRANTIES. All the representations and warranties
of the Company contained in this Agreement shall be true and correct in all
material respects, except as affected by transactions contemplated or permitted
by this Agreement (or the announcement thereof).

     7.2 COVENANTS AND AGREEMENTS. The Company shall have performed and complied
with in all material respects all covenants and agreements required by this
Agreement to be performed or complied with by it on or prior to the Closing
Date.

     7.3 HSR ACT. All waiting periods (and any extensions thereof) applicable to
this Agreement and the transactions contemplated hereby under the HSR Act shall
have expired or been terminated.

     7.4 LEGAL PROCEEDINGS. No Proceeding shall, on the Closing Date, be pending
or threatened seeking to restrain, prohibit or obtain damages or other relief in
connection with this Agreement or the consummation of the transactions
contemplated hereby.

     7.5 LEGAL OPINION. Thompson & Knight, L.L.P., counsel to the Company, shall
have delivered to the Investors a legal opinion satisfactory in form and
substance to the Investors.

     7.6 CONSENTS. All consents, approvals, orders, authorizations and waivers
of, and all declarations, filings and registrations with, third parties
(including Governmental Entities) required to be obtained or made by or on the
part of the parties hereto, or otherwise reasonably necessary for the
consummation of the transactions contemplated hereby, shall have been obtained
or made, and all thereof shall be in full force and effect at the time of
Closing.

     7.7 APPOINTMENT OF DIRECTOR. On or before the Closing Date, Steven A.
Webster shall be appointed as a member of the Board of Directors of the Company.

     7.8 ENRON TRANSACTIONS. All conditions precedent to the closing of the
Enron Transactions (other than conditions with respect to the consummation,
simultaneously with such closing, of the transactions contemplated hereby) shall
have been satisfied at or prior to the Closing, and such closing shall have
occurred prior to or be occurring simultaneously with the Closing.

     7.9 FINANCING. All conditions precedent to the closing of a Financing
Transaction (other than conditions with respect to the consummation,
simultaneously with such closing, of the transactions contemplated hereby) shall
have been satisfied at or prior to the Closing, and such closing shall have
occurred prior to or be occurring simultaneously with the Closing.

     7.10 CLOSING DELIVERIES. Investors shall have received the certificates,
instruments and documents required to be delivered by the Company by Section
2.2.

                                       16
<PAGE>

                                  ARTICLE VIII

                              BOARD REPRESENTATION

     The Company covenants to nominate one representative of the Investors
appointed by MB to serve as a member of the Board of Directors of the Company
(the "Board") for so long as the Investors or their Affiliates own at least 10%
of the Shares or at least 5% of the outstanding shares of Common Stock of the
Company. Notwithstanding the foregoing, should a representative of the Investors
not be elected to the Board at a meeting of the stockholders of the Company, the
Company shall provide such representative with notice of each meeting of the
Board and shall provide such representative with access to such meeting as an
observer.

                                   ARTICLE IX

                                    COVENANTS

     9.1 AFFIRMATIVE COVENANTS. The Company covenants and agrees that, so long
as any of the Shares are outstanding:

          (a) FINANCIAL STATEMENTS AND OTHER REPORTS. The Company shall deliver,
     or shall cause to be delivered, to the Investors:

               (i) ANNUAL FINANCIAL STATEMENTS. As soon as available and in any
          event within 90 days after the end of each fiscal year of the Company
          and its consolidated Subsidiaries for such fiscal year, and the
          related consolidated and unaudited consolidating balance sheets of the
          Company 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 which opinion
          shall state that said financial statements fairly present the
          consolidated financial condition and results of operations of the
          Company 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.

               (ii) 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 Company,
          consolidated statements of income, stockholders' equity, changes in
          financial position and cash flow of the Company 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.

               (iii) MONTHLY FINANCIAL STATEMENTS. As soon as available and in
          any event within forty-five (45) days after the end of each calendar
          month that is not also the end of one of the Company's first three
          fiscal quarterly periods or of the Company's fiscal year, consolidated
          statements of income and changes in financial position of the Company
          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 balance sheets as at the end of
          such period and beginning statements setting forth in each case in
          comparative form the corresponding figures for the corresponding
          period in the preceding fiscal year.

          (b) SEC FILINGS, ETC. Promptly, upon its becoming available, each
     financial statement, report, notice or proxy statement sent by the Company
     to stockholders generally.

                                       17
<PAGE>

          (c) ENGINEERING REPORTS. Not later than April 30 and October 30 of
     each year, the Company shall furnish to the Investors a Reserve Report as
     of the preceding December 31 and June 30, respectively. The Reserve Report
     to be furnished in April of each year shall be prepared by certified
     independent petroleum engineers or other independent petroleum
     consultant(s) and the Reserve Reports to be furnished in October of each
     year shall be prepared by or under the supervision of the chief engineer or
     Vice President of Operations of the Company who shall certify such Reserve
     Report to have been prepared in accordance with the procedures used in the
     immediately preceding April Reserve Report. At Company's option, the
     Reserve Report to be furnished in October 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 Company on any wells previously
     reported in the Reserve Report described in the immediately preceding
     April.

          (d) EXCHANGE ACT REPORTS. At all times (i) timely file all reports
     required to be filed by the Company under Section 13(d) or Section 15 of
     the Exchange Act and the rules and regulations thereunder, and (ii) if the
     Company is no longer subject to the requirements of the Exchange Act,
     provide holders of the Shares reports in substantially the same form and at
     the same times as would be required if the Company were subject to the
     Exchange Act.

          (e) NASDAQ LISTING. Maintain at all times a valid listing for the
     Common Stock on a national securities exchange or the National Market
     System or SmallCap Market of the Nasdaq Stock Market, Inc.

          (f) FURTHER ASSURANCES. The Company at its expense will promptly
     execute and deliver to the Investors upon request all such other documents,
     agreements and instruments to comply with or accomplish the covenants and
     agreements of the Company in this Agreement or any other agreements and
     documents executed by and between the Company and the Investors.

     9.2 NEGATIVE COVENANTS. The Company covenants and agrees that, so long as
at least 10% of the Shares are outstanding, without the prior written consent of
the persons holding 75% of the then outstanding Shares:

          (a) DIVIDENDS, DISTRIBUTIONS AND REDEMPTIONS. The Company will not
     declare or pay any dividend, purchase, redeem, or otherwise acquire for
     value any of its Parity Security or Junior Security now or hereafter
     outstanding, return any capital or make a distribution of its assets to its
     stockholders.

          (b) NATURE OF BUSINESS. Neither the Company nor Brigham Oil & Gas,
     L.P. will allow any material change to be made in the character of its
     business as an independent oil and gas exploration and production company.

          (c) ENVIRONMENTAL MATTERS. Neither the Company 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.

          (d) TRANSACTIONS WITH AFFILIATES. Neither the Company nor any
     Subsidiary will enter into any transaction, including, without limitation,
     any purchase, sale, lease or exchange of Property or the rendering of any
     service, with any Affiliate unless such transactions are otherwise not in
     violation of this Agreement, and are 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.

                                       18
<PAGE>

                                    ARTICLE X

                              AMENDMENT AND WAIVER

     10.1 AMENDMENT. This Agreement may not be amended except by an instrument
in writing signed by or on behalf of all the parties hereto.

     10.2 WAIVER. No failure or delay by a party hereto in exercising any right,
power, or privilege hereunder shall operate as a waiver thereof nor shall any
single or partial exercise thereof preclude any other or further exercise
thereof or the exercise of any other right, power, or privilege. The provisions
of this Agreement may not be waived except by an instrument in writing signed by
or on behalf of the party against whom such waiver is sought to be enforced.

                                   ARTICLE XI

                                  MISCELLANEOUS

     11.1 NOTICES. All notices, requests, demands, and other communications
required or permitted to be given or made hereunder by any party hereto shall be
in writing and shall be deemed to have been duly given or made if (i) delivered
personally, (ii) sent by prepaid overnight courier service, or (iii) sent by
telecopy or facsimile transmission, answer back requested, to the parties at the
following addresses (or at such other addresses as shall be specified by the
parties by like notice):

         (a)      If to the Company:
                  Brigham Exploration Company
                  6300 Bridge Point Parkway
                  Building 2, Suite 500
                  Austin, TX  78730
                  Attention: Chief Financial Officer
                  Telefax:  512-427-3400

         with a copy to:

                  Thompson & Knight L.L.P.
                  1700 Pacific Avenue, Suite 3300
                  Dallas, Texas 75201
                  Attention: Joe Dannenmaier
                  Telefax: 214-969-1751

         (b)      If to either Investor, to such Investor at:

                  277 Park Avenue
                  New York, New York 10172
                  Attention: Michael Isikow
                  Telefax: 212-892-2689

         with a copy to:

                  Gardere Wynne Sewell, LLP
                  1000 Louisiana, Suite 3400
                  Houston, Texas 77002
                  Attention: N.L. Stevens III
                  Telefax: 713-276-5807

                                       19
<PAGE>

Such notices, requests, demands, and other communications shall be effective (i)
if delivered personally or sent by courier service, upon actual receipt by the
intended recipient, or (ii) if sent by telecopy or facsimile transmission, when
the answer back is received.

     11.2 ENTIRE AGREEMENT. This Agreement, together with the Schedules,
Exhibits, Annexes, and other writings referred to herein or delivered pursuant
hereto, constitutes the entire agreement between the parties hereto with respect
to the subject matter hereof and supersedes all prior agreements and
understandings, both written and oral, between the parties and their Affiliates
with respect to the subject matter hereof.

     11.3 BINDING EFFECT; ASSIGNMENT; NO THIRD PARTY BENEFIT. This Agreement
shall be binding upon and inure to the benefit of the parties hereto and their
respective successors and permitted assigns. Except as otherwise expressly
provided in this Agreement, neither this Agreement nor any of the rights,
interests or obligations hereunder shall be assigned by any of the parties
hereto without the prior written consent of the other party. Nothing in this
Agreement, express or implied, is intended to or shall confer upon any person
other than the parties hereto, and their respective heirs, legal
representatives, successors, and permitted assigns, any rights, benefits or
remedies of any nature whatsoever under or by reason of this Agreement.

     11.4 SEVERABILITY. If any provision of this Agreement is held to be
unenforceable, then this Agreement shall be considered divisible and such
provision shall be deemed inoperative to the extent it is deemed unenforceable,
and in all other respects this Agreement shall remain in full force and effect
to the maximum extent permitted by Applicable Law.

     11.5 INJUNCTIVE RELIEF. The parties hereto acknowledge and agree that
irreparable damage would occur in the event any of the provisions of this
Agreement were not performed in accordance with their specific terms or were
otherwise breached. It is accordingly agreed that the parties shall be entitled
to an injunction or injunctions to prevent breaches of the provisions of this
Agreement, and shall be entitled to enforce specifically the provisions of this
Agreement, in any court of the United States or any state thereof having
jurisdiction, in addition to any other remedy to which the parties may be
entitled under this Agreement or at law or in equity.

     11.6 GOVERNING LAW. THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED AND
ENFORCED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT REGARD TO
THE PRINCIPLES OF CONFLICTS OF LAWS THEREOF.

                                       20
<PAGE>

     11.7 JURISDICTION. Except as otherwise expressly provided in this
Agreement, any suit, action or proceeding seeking to enforce any provision of,
or based on any matter arising out of or in connection with, this Agreement or
the transactions contemplated hereby may be brought in the United States
District Court for the Southern District of New York or any other New York State
court sitting in New York City, and each of the parties hereby consents to the
jurisdiction of such courts (and of the appropriate appellate courts therefrom)
in any such suit, action or proceeding and irrevocably waives, to the fullest
extent permitted by law, any objection which it may now or hereafter have to the
laying of the venue of any such suit, action or proceeding in any such court or
that any such suit, action or proceeding which is brought in any such court has
been brought in an inconvenient forum. Process in any such suit, action or
proceeding may be served on any party anywhere in the world, whether within or
without the jurisdiction of any such court. Without limiting the foregoing, each
party agrees that service of process on such party as provided in Section 10.01
shall be deemed effective service of process on such party.

     11.8 COUNTERPARTS. This Agreement may be executed by the parties hereto in
any number of counterparts, each of which shall be deemed an original, but all
of which shall constitute one and the same agreement. Each counterpart may
consist of a number of copies hereof each signed by less than all, but together
signed by all, the parties hereto.

                                   ARTICLE XII

                                   DEFINITIONS

     12.1 CERTAIN DEFINED TERMS. As used in this Agreement, each of the
following terms has the meaning given it in this Article:

          "Affiliate" of any Person shall mean (i) any Person directly or
     indirectly controlled by, controlling or under common control with such
     first Person, (ii) any director or officer of such first Person or of any
     Person referred to in clause (i) above and (iii) if any Person in clause
     (i) above is an individual, any member of the immediate family (including
     parents, spouse and children) of such individual and any trust whose
     principal beneficiary is such individual or one or more members of such
     immediate family and any Person who is controlled by any such member or
     trust. For purposes of this definition, any Person which owns directly or
     indirectly 50% or more of the securities having ordinary voting power for
     the election of directors or other governing body of a corporation or 50%
     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.

          "Ancillary Documents" means each agreement, instrument, and document
     (other than this Agreement) executed or to be executed by the Company or
     any Investor in connection with the sale and purchase of the Shares and the
     other transactions contemplated by this Agreement.

          "Applicable Law" means any statute, law, rule, or regulation or any
     judgment, order, writ, injunction, or decree of any Governmental Entity to
     which a specified person or property is subject.

          "BOG" means Brigham Oil & Gas, L.P.

          "Business Day" shall mean any day other than a Saturday, a Sunday, or
     a day on which banking institutions in Austin, Texas are authorized or
     obligated by law or executive order to close.

                                       21
<PAGE>

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

          "Common Stock" means the common stock, par value of $.01 per share, of
     the Company, and such other class of securities as shall represent the
     common equity of the Company.

          "Debt" shall mean, 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, interest, fees and charges); (ii) all obligations of
     such Person (whether contingent or otherwise) in respect of bankers
     acceptances, letters of credit, surety or other bonds and similar
     instruments; (iii) all obligations of such Person to pay the deferred
     purchase price of Property or services (other than for borrowed money)
     excluding Trade Payables; (iv) all obligations under leases which shall
     have been, or should have been, in accordance with GAAP, recorded as
     capital leases in respect of which such Person is liable (whether
     contingent or otherwise); (v) all obligations under leases (other than
     capital leases and oil and gas leases) which require such Person or its
     Affiliate to make payments exceeding $100,000 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 market 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; (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) the
     undischarged balance of any production payment created by such Person or
     for the creation of which such Person directly or indirectly received
     payment; and (xiii) all obligations of such Person under Hedging
     Agreements.

          "Encumbrances" means liens, charges, pledges, options, mortgages,
     deeds of trust, security interests, claims, restrictions (whether on
     voting, sale, transfer, disposition, or otherwise), easements, and other
     encumbrances of every type and description, whether imposed by law,
     agreement, understanding, or otherwise.

          "Environmental Laws" shall mean any and all Governmental Requirements
     pertaining to the environment in effect in any and all jurisdictions in
     which the Company or any Subsidiary is conducting or at any time has
     conducted business, or where any Oil and Gas Property of the Company or any
     Subsidiary is located, including without limitation, the Oil Pollution Act
     of 1990 ("OPA"), the Clean Air Act, as amended, the Comprehensive
     Environmental, Response, Compensation, and Liability Act of 1980
     ("CERCLA"), as amended, the Federal Water Pollution Control Act, as
     amended, the Occupational Safety and Health Act of 1970, as amended, the
     Resource Conservation and Recovery Act of 1976 ("RCRA"), as amended, the
     Safe Drinking Water ACT, as amended, the Toxic Substances Control Act, as
     amended, the Superfund Amendments and Reauthorization Act of 1986, as
     amended, the Hazardous Materials Transportation Act, as amended, and other
     environmental conservation or protection laws. As used in the provisions
     hereof relating to Environmental Laws, the term "oil" shall have 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 "disposal") have the meanings specified in
     RCRA; provided that to the extent the laws of the state in which any Oil
     and Gas Property of the Company or any Subsidiary is located establish a
     meaning for "oil", "hazardous substance," "release," "solid waste" or
     "disposal" which is broader than that specified in either OPA, CERCLA or
     RCRA, such broader meaning shall apply.

                                       22
<PAGE>

          "ERISA" shall mean 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 Company or any Subsidiary of the
     Company would be deemed to be a "single employer" within the meaning of
     section 4001(b)(1) of ERISA or subsections (b), (c), (m) or (o) of section
     414 of the Code.

          "Excepted Liens" shall mean: (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 workmen'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
     such property subject thereto; (v) encumbrances (other than to secure the
     payment of borrowed money or the deferred purchase price of property or
     services), easements, restrictions, servitudes, permits, conditions,
     covenants, exceptions or reservations in any rights of way or other
     property for the purpose of roads, pipelines, transmission lines,
     transportation lines, distribution lines for the removal of gas, oil, coal
     or other minerals or timber, and other like purposes, or for the joint or
     common use of real estate, rights of way, facilities and equipment, and
     defects, irregularities, zoning restrictions and deficiencies in title of
     any rights of way or other property which in the aggregate do not
     materially impair the use of such rights of way or other property for the
     purposes of 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 (including
     "Excepted Liens") permitted by or created pursuant to the Senior Credit
     Agreement and Liens permitted by or created pursuant to the Subordinated
     Credit Agreement.

          "Exchange Act" means the Securities Exchange Act of 1934, as amended.

          "Governmental Entity" means any court or tribunal in any jurisdiction
     (domestic or foreign) or any public, governmental, or regulatory body,
     agency, department, commission, board, bureau, or other authority or
     instrumentality (domestic or foreign).

                                       23
<PAGE>

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

          "Hedging Agreements" shall mean any commodity, interest rate or
     currency swap, cap, floor, collar, forward agreement or other exchange or
     protection agreements or any option with respect to any such transaction.

          "HSR Act" means the Hart-Scott-Rodino Antitrust Improvements Act of
     1976, as amended.

          "Hydrocarbon Interests" shall mean 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" shall mean oil, gas, casinghead gas, drip gasoline,
     natural gasoline, condensate, distillate, liquid hydrocarbons, gaseous
     hydrocarbons and all products refined or separated therefrom.

          "Lien" shall mean any interest in property securing an obligation owed
     to, or a claim by, a person other than the owner of the property, whether
     such interest is based on the common law, statute or contract, and whether
     such obligation or claim is fixed or contingent, and including but not
     limited to (i) the lien or security interest arising from a mortgage,
     encumbrance, pledge, security agreement, conditional sale or trust receipt
     or a lease, consignment or bailment for security purposes or (ii)
     production payments and the like payable out of Oil and Gas Properties. The
     term "Lien" shall include reservations, exceptions, encroachments,
     easements, rights of way, covenants, conditions, restrictions, leases and
     other title exceptions and encumbrances affecting property. For the
     purposes of this Agreement, a Person shall be deemed to be the owner of any
     property which it has acquired or holds subject to a conditional sale
     agreement, or leases under a financing lease or other arrangement pursuant
     to which title to the Property has been retained by or vested in some other
     Person in a transaction intended to create a financing.

          "Material Adverse Effect" means, relative to the Company or the
     Investors, as the case may be, any change, development, or effect
     (individually or in the aggregate) which is, or is reasonably likely to be,
     materially adverse (i) to the business, assets, results of operations,
     condition (financial or otherwise), or prospects of the Company and the
     Subsidiaries considered as a whole, or the Investors, as the case may be,
     or (ii) to the ability of the Company or the Investors, as the case may be,
     to perform on a timely basis any material obligation of the Company or the
     Investors, as the case may be, under this Agreement or any agreement,
     instrument, or document entered into or delivered in connection herewith.

          "Material Agreement" means (a) any written agreement, contract, lease,
     commitment, understanding, instrument or obligation to which the Company or
     any Subsidiary is a party or by which the Company or any Subsidiary or any
     of their respective properties may be bound involving total value or
     consideration or liability in excess of $500,000, (b) any loan or credit
     agreement, bond, debenture, note, mortgage or indenture by which the
     Company or any Subsidiary or any of their respective properties may be
     bound, or (c) any agreement set forth as an exhibit to the Company's Form
     10-K for the fiscal year ended December 31, 1999.

                                       24
<PAGE>

          "Person" or "person" means any individual, corporation, partnership,
     joint venture, association, joint-stock company, trust, enterprise,
     unincorporated organization, or Governmental Entity.

          "Oil and Gas Properties" shall mean Hydrocarbon Interests; the
     Properties now or hereafter pooled or unitized with Hydrocarbon Interests;
     all presently existing or future unitization, pooling agreements and
     declarations of pooled units and the units created thereby (including
     without limitation all units created under orders, regulations and rules of
     any Governmental Authority) which may affect all or any portion of the
     Hydrocarbon Interests; all operating agreements, contracts and other
     agreements which relate to any of the Hydrocarbon Interests or the
     production, sale, purchase, exchange or processing of Hydrocarbons from or
     attributable to such Hydrocarbon Interests; all Hydrocarbons in and under
     and which may be produced and saved or attributable to the Hydrocarbon
     Interests, including all oil in tanks, the lands covered thereby and all
     rents, issues, profits, proceeds, products, revenues and other incomes from
     or attributable to the Hydrocarbon Interests; all tenements, hereditaments,
     appurtenances and Properties in any manner appertaining, belonging, affixed
     or incidental to the Hydrocarbon Interests; and all Properties, rights,
     titles, interests and estates described or referred to above, including any
     and all Property, real or personal, now owned or hereinafter 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 rigs, automotive equipment or other personal
     property which may be on such premises for the purpose of drilling a well
     or for other similar temporary uses) 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.

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

          "Proceeding" means any action, suit or proceeding, whether civil,
     criminal, administrative, arbitrative or investigative, any appeal in such
     an action, suit or proceeding, and any inquiry or investigation that could
     lead to such an action, suit or proceeding.

          "reasonable best efforts" means a party's best efforts in accordance
     with reasonable commercial practice and without the incurrence of
     unreasonable expense.

          "Rule 144" means Rule 144 promulgated under the Securities Act.

          "Securities Act" means the Securities Act of 1933, as amended.

          "Senior Credit Agreement" means that certain Amended and Restated
     Credit Agreement dated as of February 17, 2000, by and between BOG, Bank of
     Montreal, as Agent, and the Lenders signatory thereto, as amended on
     October 31, 2000, together with the "Loan Documents" described therein.

                                       25
<PAGE>

          "Subordinated Credit Agreement" means the Subordinated Credit
     Agreement dated as of October 31, 2000 by and between BOG, Shell Capital,
     Inc., as Agent, and the Lenders signatory thereto.

          "Subsidiaries" means Brigham Oil & Gas, L.P.; Brigham, Inc.; Brigham
     Holdings I, LLC and Brigham Holdings II, LLC.

     IN WITNESS WHEREOF, the parties have executed this Agreement, or caused
this Agreement to be executed by their duly authorized representatives, all as
of the day and year first above written.

                                  THE COMPANY:

                                  BRIGHAM EXPLORATION COMPANY
Address:

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

                                  Investor:

                                  DLJ MB FUNDING III, INC.

Address:
                                  By: /s/ Ivy B. Dodes
                                     -----------------------------------------
                                          Ivy B. Dodes
                                          Principal

                                  DLJ ESC II, LP

                                  By:     DLJ LBO Plans Management Corporation,
                                          its general partner

Address:

                                  By: /s/ Ivy B. Dodes
                                     -------------------------------------------
                                          Ivy B. Dodes
                                          Principal

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