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                                                                       EXHIBIT 1





                        3,910,000 Shares of Common Stock



                           BRIGHAM EXPLORATION COMPANY



                             UNDERWRITING AGREEMENT



                                         , 1998



BEAR, STEARNS & CO. INC.
DAIN RAUSCHER WESSELS
HOWARD, WEIL, LABOUISSE,
    FRIEDRICHS INCORPORATED
         As Representatives of the
         several Underwriters named in
         Schedule I attached hereto
c/o Bear, Stearns & Co. Inc.
245 Park Avenue
New York, N.Y. 10167

Dear Sirs:

         Brigham Exploration Company, a corporation organized and existing under
the laws of Delaware (the "Company"), proposes, subject to the terms and
conditions stated herein, to issue and sell to the several underwriters named in
Schedule I hereto (the "Underwriters") an aggregate of 3,400,000 shares (the
"Firm Shares") of its common stock, par value $.01 per share (the "Common
Stock"). In addition, for the sole purpose of covering over-allotments in
connection with the sale


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of the Firm Shares, the undersigned selling stockholders of the Company named in
Schedule II hereto (the "Selling Stockholders") propose to sell to the
Underwriters, at the option of the Underwriters, up to an additional 510,000
shares of Common Stock (the "Additional Shares"). The respective amounts of the
Firm Shares to be so purchased by the Underwriters are set forth opposite their
names in Schedule I hereto. The number of Additional Shares to be sold by each
Selling Stockholder is set forth opposite its name in Schedule II hereto. The
Firm Shares and any Additional Shares purchased by the Underwriters are herein
referred to as the "Shares."

         The Shares are more fully described in the Registration Statement
referred to hereafter.

         1.       Representations and Warranties of the Company and the Selling
 Stockholders.

                  (a) The Company and each of the Selling Stockholders jointly
and severally represent and warrant to, and agree with, the Underwriters that:

                  (i) The Company has filed with the Securities and Exchange
         Commission (the "Commission") a registration statement, and may have
         filed an amendment or amendments thereto, on Form S-1 (No. 333-53873),
         for the registration of the Shares under the Securities Act of 1933
         (the "Act"). Such registration statement, including the prospectus,
         financial statements and schedules, exhibits and all other documents
         filed as a part thereof, as amended at the time of effectiveness of the
         registration statement, including any information deemed to be a part
         thereof as of the time of effectiveness pursuant to paragraph (b) of
         Rule 430A or Rule 434 of the Rules and Regulations of the Commission
         under the Act (the "Regulations"), and any additional related
         registration statement filed pursuant to Rule 462(b) of the Act, is
         herein called the "Registration Statement," and the prospectus, in the
         form first filed with the Commission pursuant to Rule 424(b) of the
         Regulations, or filed as part of the Registration Statement at the time
         of effectiveness if no Rule 424(b) or Rule 434 filing is required, is
         herein called the "Prospectus." The term "preliminary prospectus" as
         used herein means a preliminary prospectus as described in Rule 430 of
         the Regulations.

                  (ii) At the time of effectiveness of the Registration
         Statement or the effectiveness of any post-effective amendment to the
         Registration Statement, when the Prospectus is first filed with the
         Commission pursuant to Rule 424(b) or Rule 434 of the Regulations, when
         any supplement to or amendment of the Prospectus is filed with the
         Commission, and at the Closing Date and the Additional Closing Date, if
         any (as hereinafter respectively defined), the Registration Statement
         and the Prospectus and any amendments thereof and supplements thereto
         complied or will comply in all material respects with the applicable
         provisions of the Act and the

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         Regulations and do not or will not contain an untrue statement of a
         material fact and does not or will not omit to state any material fact
         required to be stated therein or necessary in order to make the
         statements therein (i) in the case of the Registration Statement, not
         misleading, and (ii) in the case of the Prospectus, in light of the
         circumstances under which they were made, not misleading. When any
         related preliminary prospectus was first filed with the Commission
         (whether filed as part of the registration statement for the
         registration of the Shares or any amendment thereto or pursuant to Rule
         424(a) of the Regulations) and when any amendment thereof or supplement
         thereto was first filed with the Commission, such preliminary
         prospectus and any amendments thereof and supplements thereto complied
         in all material respects with the applicable provisions of the Act and
         the Regulations and did not contain an untrue statement of a material
         fact and did not omit to state any material fact required to be stated
         therein or necessary in order to make the statements therein in light
         of the circumstances under which they were made not misleading. No
         representation and warranty is made in this subsection (b), however,
         with respect to any information contained in or omitted from the
         Registration Statement or the Prospectus or any related preliminary
         prospectus or any amendment thereof or supplement thereto in reliance
         upon and in conformity with information furnished in writing to the
         Company by or on behalf of any Underwriter through you as herein stated
         or by or on behalf of any Selling Stockholder insofar as it relates to
         such Selling Stockholder, in each case expressly for use in connection
         with the preparation thereof. If Rule 434 is used, the Company will
         comply with the requirements of Rule 434.

                  (iii) Price Waterhouse LLP, which has certified the financial
         statements and supporting schedules included in the Registration
         Statement, are independent public accountants with regard to the
         Company as required by the Act and the Regulations.

                  (iv) Subsequent to the respective dates as of which
         information is given in the Registration Statement and the Prospectus,
         except as set forth in the Registration Statement and the Prospectus,
         there has been no material adverse change or any development involving
         a prospective material adverse change in the business, prospects,
         properties, operations, condition (financial or other) or results of
         operations of the Company and its Subsidiaries (as defined below) taken
         as a whole, whether or not arising from transactions in the ordinary
         course of business, and since the date of the latest balance sheet
         presented in the Registration Statement and the Prospectus, neither the
         Company nor any of its Subsidiaries has incurred or undertaken any
         liabilities or obligations, direct or contingent, which are material to
         the Company and its Subsidiaries taken as a whole, except for
         liabilities or

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         obligations which are reflected in the Registration Statement and the
         Prospectus. Except as disclosed in or contemplated by the Prospectus,
         since the date of the last audited financial statements included in the
         Prospectus, there has been no dividend or distribution of any kind
         declared, paid or made by the Company on any class of its capital
         stock.

                  (v) This Agreement and the transactions contemplated herein
         have been duly and validly authorized by the Company, and this
         Agreement has been duly and validly executed and delivered by the
         Company. This Agreement is a valid and binding obligation of the
         Company, enforceable against the Company in accordance with its terms.

                  (vi) The execution, delivery, and performance of this
         Agreement and the consummation of the transactions contemplated hereby
         do not and will not (i) conflict with or result in a breach of any of
         the terms and provisions of, or constitute a default (or an event which
         with notice or lapse of time, or both, would constitute a default) or
         require consent under, or result in the creation or imposition of any
         lien, charge or encumbrance upon any property or assets of the Company
         or any of its Subsidiaries, pursuant to the terms of any agreement,
         instrument, franchise, license or permit to which the Company or any of
         its Subsidiaries is a party or by which any of such corporations or
         their respective properties or assets may be bound or (ii) violate or
         conflict with any provision of the organizational documents of the
         Company or any of its Subsidiaries or any judgment, decree, order,
         statute, rule or regulation of any court or any public, governmental or
         regulatory agency or body, domestic or foreign, having jurisdiction
         over the Company or any of its Subsidiaries or any of their respective
         properties or assets. No consent, approval, authorization, order,
         registration, filing, qualification, license or permit of or with any
         court or any public, governmental or regulatory agency or body having
         jurisdiction over the Company or any of its Subsidiaries or any of
         their respective properties or assets is required for the execution,
         delivery and performance of this Agreement or the consummation of the
         transactions contemplated hereby, including the issuance, sale and
         delivery of the Shares to be issued, sold and delivered by the Company
         hereunder, except the registration under the Act of the Shares and such
         consents, approvals, authorizations, orders, registrations, filings,
         qualifications, licenses and permits as may be required under state
         securities or Blue Sky laws in connection with the purchase and
         distribution of the Shares by the Underwriters. The Company has full
         power and authority to authorize, issue and sell the Shares as
         contemplated by this Agreement.


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                  (vii)  All of the outstanding shares of Common Stock, 
         including all shares to be sold by the Selling Stockholders, are duly
         and validly authorized and issued, fully paid and nonassessable and
         were not issued and are not now in violation of or subject to any
         preemptive rights. The Shares, when delivered and sold in accordance
         with this Agreement, will be duly and validly issued and outstanding,
         fully paid and nonassessable, and will not have been issued in
         violation of or subject to any preemptive rights. The Company has an
         authorized and outstanding capitalization as set forth in the
         Registration Statement and the Prospectus. The Common Stock, the Firm
         Shares and the Additional Shares conform to the descriptions thereof
         contained in the Registration Statement and the Prospectus.

                  (viii) Each of the Company and its corporate subsidiaries has
         been duly organized and is validly existing as a corporation in good
         standing under the laws of its jurisdiction of incorporation. Each of
         the Company's subsidiaries that is a limited partnership has been duly
         formed and is validly existing as a limited partnership under the laws
         of the state of its formation. Each of the Company's subsidiaries that
         is a limited liability company has been duly formed and is validly
         existing as a limited liability company under the laws of the state of
         its formation. (The corporate subsidiaries, partnership subsidiaries
         and limited liability company subsidiaries are hereinafter sometimes
         referred to as "Subsidiaries.") Each of the Company and its
         Subsidiaries is duly qualified and in good standing as a foreign
         corporation, limited partnership or limited liability company in each
         jurisdiction in which the character or location of its properties
         (owned, leased or licensed) or the nature or conduct of its business
         makes such qualification necessary, except for those failures to be so
         qualified or in good standing which will not in the aggregate have a
         material adverse effect on the Company and its Subsidiaries taken as a
         whole. Each of the Company and its Subsidiaries has all requisite power
         and authority, and all necessary consents, approvals, authorizations,
         orders, registrations, qualifications, licenses and permits of and from
         all public, regulatory or governmental agencies and bodies, to own,
         lease and operate its properties and conduct its business as now being
         conducted and as described in the Registration Statement and the
         Prospectus, and no such consent, approval, authorization, order,
         registration, qualification, license or permit contains a materially
         burdensome restriction not adequately disclosed in the Registration
         Statement and the Prospectus. All of the issued and outstanding shares
         of capital stock of each corporate subsidiary of the Company have been
         duly authorized and validly issued and are fully paid and nonassessable
         and are owned by the Company, directly or through its Subsidiaries,
         free from liens, encumbrances, claims, security interests, restrictions
         on transfer, stockholders' agreement, voting trust and any other
         defects of title. All of the partnership interests of each partnership
         subsidiary of the Company have been duly and validly authorized and
         issued in accordance with the

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         terms of the governing partnership agreement and are owned by the
         Company, directly or through its Subsidiaries, free from liens,
         encumbrances, claims, security interests, restrictions on transfer,
         voting trusts or similar agreements, and any other defect of title. All
         of the membership interests of each limited liability company
         subsidiary of the Company have been duly and validly authorized and
         issued in accordance with the terms of the governing limited liability
         company agreement (or regulations) and are owned by the Company,
         directly or through its Subsidiaries, free from liens, encumbrances,
         claims, security interests, restrictions on transfer, voting trusts or
         similar agreements, and any other defect of title, with the exception
         of (i) Quest Resources, L.L.C., in which the Company holds a 99.55%
         interest in all profits and losses and General Atlantic Partners III,
         L.P. holds a 0.45% interest and (ii) Venture Acquisition, L.P., in
         which Quest Resources, L.L.C. shares profits and losses with RIMCO
         Energy, Inc., RIMCO Production Company, Inc., RIMCO Exploration
         Partners, L.P. I and RIMCO Exploration Partners, L.P. II.

                  (ix) Except as described in or contemplated by the Prospectus,
         there are no outstanding securities of the Company or any Subsidiary
         convertible or exchangeable into or evidencing the right to purchase or
         subscribe for any shares of Common Stock of the Company or shares of
         capital stock, partnership interests or membership interests of any
         Subsidiary, respectively, and there are no outstanding options,
         warrants, or rights of any character obligating the Company or any
         Subsidiary to issue any shares of its capital stock, any partnership
         interests or any membership interests, as applicable, or any securities
         convertible or exchangeable or evidencing the right to purchase or
         subscribe therefor; and except as described in the Prospectus, no
         holder of securities of the Company or any Subsidiary or any other
         person has the right, contractual or otherwise, which has not been
         satisfied or effectively waived, to cause the Company to sell or
         otherwise issue to them, or to permit them to underwrite the sale of,
         any of the Shares.

                  (x) Except as disclosed in the Prospectus, the Company and its
         Subsidiaries have good and marketable title to all the producing oil
         and gas properties described as being owned by them in the Prospectus,
         free and clear of any liens, encumbrances, equities, or claims of any
         nature, except for the liens for taxes not yet due, liens, claims and
         encumbrances under gas sales contracts, operating agreements,
         geophysical exploration agreements, farm-out and farm-in agreements,
         participation agreements, unitization and pooling agreements, and such
         other agreements as are customarily found in connection with comparable
         exploration, drilling, producing and marketing operations, or in
         connection with the acquisition of properties, and other liens, claims,
         contracts, encumbrances and title defects that are, singly and in the
         aggregate, not material in amount and do not materially

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         interfere with the Company's or such Subsidiary's use and enjoyment of
         its oil and gas properties.

                  (xi)   The written engineering reports prepared by Cawley,
         Gillespie & Associates, Inc. ("Cawley, Gillespie"), an oil and gas
         engineering consulting firm, as of December 31, 1997, setting forth the
         engineering values attributed to the oil and gas properties of the
         Company and its Subsidiaries accurately reflect in all material
         respects the ownership interests of the Company and its Subsidiaries in
         the properties therein as of December 31, 1997, except as otherwise
         disclosed in the Prospectus. The information furnished to Cawley,
         Gillespie upon which Cawley, Gillespie based its reports was, at the
         time of delivery thereof, complete and accurate in all material
         respects. No facts have arisen of which the Company has knowledge that
         might cause a reasonable person to believe that any of the information
         supplied to Cawley, Gillespie was incorrect or incomplete in any
         material respect.

                  (xii)  Except as disclosed in the Prospectus, the Company and
         its Subsidiaries possess adequate certificates, authorities or permits
         issued by appropriate governmental agencies or bodies necessary to
         conduct the business now operated by them, except for such
         certificates, authorities or permits the failure of which to obtain
         would not have a material adverse effect on the Company or any of its
         Subsidiaries taken as a whole, and have not received any notice of
         proceedings relating to the revocation or modification of any such
         certificate, authority or permit that, if determined adversely to the
         Company or any of its Subsidiaries, would individually or in the
         aggregate have a material adverse effect on the Company and its
         Subsidiaries taken as a whole.

                  (xiii) No labor dispute with the employees of the Company or
         any Subsidiary exists or, to the knowledge of the Company, is imminent
         that might have a material adverse effect on the Company and its
         Subsidiaries taken as a whole.

                  (xiv)  The Company and its Subsidiaries own, possess or 
         license adequate trademarks, trade names and other rights to
         inventions, know-how, patents, copyrights, confidential information and
         other intellectual property (collectively, "intellectual property
         rights") necessary to conduct the business now operated by them, or
         presently employed by them, and have not received any notice of
         termination of any license or notice of infringement of or conflict
         with asserted rights of others with respect to any intellectual
         property rights that, if determined adversely to the Company or any of
         its Subsidiaries, would individually or in the aggregate have a
         material adverse effect on the Company and its Subsidiaries taken as a
         whole.


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                  (xv)    Except as disclosed in the Prospectus, neither the
         Company nor any of its Subsidiaries is in violation of any statute, any
         rule, regulation, decision or order of any governmental agency or body
         or any court, domestic or foreign, relating to the use, disposal or
         release of hazardous or toxic substances or relating to the protection
         or restoration of the environment or human exposure to hazardous or
         toxic substances (collectively, "environmental laws"), owns or operates
         any real property contaminated with any substance that is subject to
         any environmental laws, is liable for any off-site disposal or
         contamination pursuant to any environmental laws, or is subject to any
         claim relating to any environmental laws, which violation,
         contamination, liability or claim would individually or in the
         aggregate have a material adverse effect on the Company and its
         Subsidiaries taken as a whole; and the Company is not aware of any
         pending investigation which might lead to such a claim.

                  (xvi)   Except as described in the Prospectus, there is no
         litigation or governmental proceeding to which the Company or any of
         its Subsidiaries is a party or to which any property of the Company or
         any of its Subsidiaries is subject or which is pending or, to the
         knowledge of the Company, contemplated against the Company or any of
         its Subsidiaries which might result in any material adverse change or
         any development involving a material adverse change in the business,
         prospects, properties, operations, condition (financial or other) or
         results of operations of the Company and its Subsidiaries taken as a
         whole or which is required to be disclosed in the Registration
         Statement and the Prospectus.

                  (xvii)  The Company has not taken and will not take, directly
         or indirectly, any action designed to cause or result in, or which
         constitutes or which might reasonably be expected to constitute, the
         stabilization or manipulation of the price of the shares of Common
         Stock to facilitate the sale or resale of the Shares.

                  (xviii) The financial statements, including the notes thereto,
         and supporting schedules included in the Registration Statement and the
         Prospectus present fairly the financial position of the Company and its
         Subsidiaries as of the dates indicated and the results of its
         operations and cash flows for the periods specified; except as
         otherwise stated in the Registration Statement, the financial
         statements have been prepared in conformity with generally accepted
         accounting principles applied on a consistent basis; and the supporting
         schedules included in the Registration Statement present fairly the
         information required to be stated therein; and the assumptions used in
         preparing the pro forma financial statements included in the
         Registration Statement and the Prospectus provide a reasonable basis
         for presenting the significant

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         effects directly attributable to the transactions or events described
         therein, the related pro forma adjustments give appropriate effect to
         those assumptions, and the pro forma columns therein reflect the proper
         application of those adjustments to the corresponding historical
         financial statement amounts.

                  (xix)   Except as described in the Prospectus, no holder of
         securities of the Company has any rights to the registration of
         securities of the Company because of the filing of the Registration
         Statement or otherwise in connection with the sale of the Shares
         contemplated hereby.

                  (xx)    The Company is not, and upon consummation of the
         transactions contemplated hereby will not be, subject to registration
         as an "investment company" under the Investment Company Act of 1940.

                  (xxi)   The Common Stock is quoted and the Shares have been
         approved for quotation on the Nasdaq National Market ("NASDAQ").

                  (xxii)  The Company has obtained and delivered to you before
         the date hereof the written agreements of each of its directors and
         officers and General Atlantic Partners, L.L.C. and Resource Investors
         Management Company that, for a period of 90 days after the date of the
         final Prospectus filed with the Commission pursuant to Rule 424(b),
         such persons will not offer, sell, contract to sell, pledge or
         otherwise dispose of, directly or indirectly, or file with the
         Commission a registration statement under the Act relating to, any
         additional shares of the Common Stock or securities convertible into or
         exchangeable or exercisable for any shares of the Common Stock, or
         publicly disclose the intention to make any such offer, sale, pledge,
         disposal or filing, without the prior written consent of Bear, Stearns
         & Co. Inc.

                  (xxiii) Except as disclosed in the Prospectus, there are no
         contracts, agreements or understandings between the Company and any
         person that would give rise to a valid claim against the Company or any
         Underwriter for a brokerage commission, finder's fee or other like
         payment.

                  (xxiv)  There are no outstanding options, warrants, or rights
         of any character obligating the Company to issue any shares of Common
         Stock that are currently exercisable or will become exercisable within
         90 days of the Closing Date or any Additional Closing Date.


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                  (b)   Each Selling Stockholder represents and warrants to, and
agrees with, the several Underwriters that:

                  (i)   Such Selling Stockholder has (i) caused a certificate or
         certificates for the number of Additional Shares to be sold by such
         Selling Stockholder hereunder to be delivered to Brigham Exploration
         Company (the "Custodian"), endorsed in blank or with blank stock powers
         duly executed, with signatures appropriately guaranteed, such
         certificate or certificates to be held in escrow by Brigham Exploration
         Company, in accordance with the terms of a custodian agreement, for
         delivery pursuant to the provisions hereof on the Closing Date, and
         (ii) granted an irrevocable power of attorney to Ben M. Brigham, Anne
         L. Brigham and Craig M. Fleming, or any of them, as such Selling
         Stockholder's attorney-in-fact (each, an "Attorney-In-Fact") in the
         form heretofore delivered to you (the custodian agreements, together
         with the irrevocable powers of attorney, executed by all Selling
         Stockholders being hereinafter collectively referred to as the
         "Custodian Agreement").

                  (ii)  The execution, delivery and performance of this
         Agreement and the Custodian Agreement by or on behalf of such Selling
         Stockholder and the consummation of the transactions contemplated
         hereby and thereby will not (i) conflict with or result in the breach
         of any of the terms and provisions of, or constitute a default (or an
         event which with notice or lapse of time, or both, would constitute a
         default) or require consent under, or result in the creation or
         imposition of any lien, charge or encumbrance upon any property or
         assets of such Selling Stockholder pursuant to the terms of any
         agreement, instrument, franchise, license or permit to which such
         Selling Stockholder is a party or by which such Selling Stockholder or
         any of such Selling Stockholder's property or assets may be bound, or
         (ii) violate or conflict with any judgment, decree, order, statute,
         rule or regulation of any court or any public, governmental or
         regulatory agency or body having jurisdiction over such Selling
         Stockholder or such Selling Stockholder's properties or assets.

                  (iii) Such Selling Stockholder has, and at the time of
         delivery of the Shares to be sold by such Selling Stockholder such
         Selling Stockholder will have, full legal right, power, authority and
         capacity, and, except as required under the Act and state securities
         and Blue Sky Laws, all necessary consents, approvals, authorizations,
         orders, registrations, filings, qualifications, licenses and permits of
         and from all public, regulatory or governmental agencies and bodies, as
         are required for the execution, delivery and performance of this
         Agreement and the Custodian Agreement and the consummation of the
         transactions contemplated hereby and thereby,

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         including the sale, assignment, transfer and delivery of the Shares to
         be sold, assigned, transferred and delivered by such Selling
         Stockholder hereunder.

                  (iv)  Each of this Agreement and the Custodian Agreement has
         been duly and validly authorized, executed and delivered by such
         Selling Stockholder and is a valid and binding obligation of such
         Selling Stockholder, enforceable against such Selling Stockholder in
         accordance with its terms, except to the extent that rights to
         indemnity hereunder may be limited by applicable federal or state
         securities laws or the public policy underlying such laws.

                  (v)   Such Selling Stockholder has good, valid and marketable
         title to the Shares to be sold by such Selling Stockholder pursuant to
         this Agreement, free and clear of all liens, encumbrances, claims,
         security interests, restrictions on transfer, stockholders' agreements,
         voting trusts and other defects in title whatsoever, with full power to
         deliver such Shares hereunder, and, upon the delivery of and payment
         for such Shares as herein contemplated, each of the Underwriters will
         receive good, valid and marketable title to the Shares purchased by it
         from such Selling Stockholder, free and clear of all liens,
         encumbrances, claims, security interests, restrictions on transfer,
         stockholders agreements, voting trusts and other defects in title
         whatsoever.

                  (vi)  Such Selling Stockholder has not taken and will not 
         take, directly or indirectly, any action which has constituted or which
         was designed to constitute or which might be reasonably expected to
         cause or result in stabilization or manipulation of the price of the
         shares of Common Stock.

                  (vii) When the Registration Statement shall become effective,
         when any amendment to the Registration Statement becomes effective,
         when the Prospectus is first filed with the Commission pursuant to Rule
         424(b) of the Regulations, when any amendment of or supplement to the
         Prospectus is filed with the Commission and at the Closing Date, such
         parts of the Registration Statement and the Prospectus and any
         amendments thereof and supplements thereto as relate to such Selling
         Stockholder and are based upon information furnished in writing to the
         Company by or on behalf of such Selling Stockholder expressly for use
         therein will not contain an untrue statement of a material fact and
         will not omit to state any material fact required to be stated therein
         or necessary in order to make the statements therein not misleading;
         and when any related preliminary prospectus was first filed with the
         Commission (whether filed as part of the registration statement for the
         registration of the Shares or any amendment thereto or pursuant to Rule
         424(a) of the Regulations) and when any amendment thereof or supplement
         thereto was first filed with the Commission, such parts of such
         preliminary prospectus and any amendments thereof and

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         supplements thereto as relate to such Selling Stockholder and are based
         on information furnished in writing to the Company by or on behalf of
         such Selling Stockholder expressly for use therein did not contain an
         untrue statement of a material fact and did not omit to state any
         material fact required to be stated therein or necessary in order to
         make the statements therein not misleading.

                  (viii) The sale of the Shares by the Selling Stockholder
         pursuant hereto is not prompted by any information concerning the
         Company which is not set forth in the Registration Statement. The
         information pertaining to the Selling Stockholder under the caption
         "Principal and Selling Stockholders" in the Prospectus is complete and
         accurate in all material respects. If there is any change in such
         information with respect to the Selling Stockholder, the Selling
         Stockholder will immediately notify you of such change.

                  2.     Purchase, Sale and Delivery of the Shares.

                  (a)    On the basis of the representations, warranties, 
covenants and agreements herein contained, but subject to the terms and
conditions herein set forth, the Company agrees to sell to the several
Underwriters and the Underwriters, severally and not jointly, agree to purchase
from the Company, at a purchase price of $______ per share, the number of Firm
Shares set forth opposite the respective names of the Underwriters in Schedule I
hereto, in each case plus any additional number of Shares that the Underwriter
may become obligated to purchase pursuant to the provisions of Section 9 hereof.

                  (b)    Payment of the purchase price for, and delivery of
certificates for, the Firm Shares shall be made at the office of Thompson &
Knight, P.C., 1700 Pacific Avenue, Suite 3300, Dallas, Texas, or such other
place as shall be agreed upon by you and the Company, at 9:00 A.M., Dallas,
Texas time, on the third or fourth business day (as permitted under Rule 15c6-1
under the Exchange Act) (unless such time and date are postponed in accordance
with the provisions of Section 9 hereof) following the date the Registration
Statement becomes effective (or, if the Company has elected to rely upon Rule
430A of the Regulations, the third or fourth business day (as permitted under
Rule 15c6-1 under the Exchange Act) after the determination of the public
offering price of the Shares), or at such other time not later than ten business
days after such date as shall be agreed upon by you and the Company (such time
and date of payment and delivery being herein called the "Closing Date").
Delivery of the certificates for the Firm Shares shall be made to you for the
respective accounts of the several Underwriters against payment by the several
Underwriters through the Representatives of the purchase price for the Firm
Shares by wire transfer of federal (same day) funds, to the account(s)
designated by the Company.


                                       12
<PAGE>   13




                  (c) Certificates for the Firm Shares shall be registered in
such name or names and in such authorized denominations as you may request in
writing at least two full business days prior to the Closing Date. The Company
will permit you to examine and package such certificates for delivery at least
one full business day prior to the Closing Date.

                  (d) In addition, the Selling Stockholders hereby grant to the
several Underwriters the option to purchase up to 510,000 Additional Shares at
the same purchase price per share to be paid by the several Underwriters to the
Company for the Firm Shares as set forth in this Section 2, for the sole purpose
of covering over-allotments in the sale of Firm Shares by the several
Underwriters. The maximum number of Additional Shares to be sold by each Selling
Stockholder is set forth opposite its name on Schedule II hereto. This option
may be exercised at any time in whole or in part on or before the thirtieth day
following the effective date of the Registration Statement, by written notice by
you to the Company and the Custodian. Such notice shall set forth the aggregate
number of Additional Shares as to which the option is being exercised and the
date and time, as reasonably determined by you, when the Additional Shares are
to be delivered (each such date and time being herein sometimes referred to as
an "Additional Closing Date"); provided, however, that the Additional Closing
Date shall not be earlier than the Closing Date or earlier than the second full
business day after the date on which the option shall have been exercised nor
later than the tenth full business day after the date on which the option shall
have been exercised (unless such time and date are postponed in accordance with
the provisions of Section 9 hereof). If the option is exercised in part, the
respective number of Additional Shares to be sold by each Selling Stockholder
listed on Schedule II hereto shall be on a pro rata basis in accordance with the
percentages set forth opposite their names on Schedule II hereto, in each case
as adjusted by you in such manner as to avoid fractional shares. Certificates
for the Additional Shares shall be registered in such name or names and in such
authorized denominations as you may request in writing at least two full
business days prior to the Additional Closing Date. The Company and the
Custodian will permit you to examine and package such certificates for delivery
at least one full business day prior to the Additional Closing Date.

         The number of Additional Shares to be sold to each Underwriter shall be
the number which bears the same ratio to the aggregate number of Additional
Shares being purchased as the number of Firm Shares set forth opposite the name
of such Underwriter in Schedule I hereto (or such number increased as set forth
in Section 9 hereof) bears to 3,400,000, subject, however, to such adjustments
to eliminate any fractional shares as you in your sole discretion shall make.

         Payment for the Additional Shares shall be made by wire transfer of
federal (same day) funds, to the accounts designated by the Company and the
Custodian, upon delivery of the certificates for the Additional Shares to you
for the respective accounts of the Underwriters at the offices of Thompson &
Knight, P.C., 1700 Pacific Avenue, Suite 3300, Dallas, Texas, or such other
place as shall be agreed upon by you and the Company.

                                       13
<PAGE>   14




                  (e) Certificates in negotiable form for the total number of
the Additional Shares that may be sold hereunder by each Selling Stockholder
have been placed in escrow with the Company as Custodian pursuant to the
Custodian Agreement executed by each Selling Stockholder for delivery of all
Additional Shares to be sold hereunder by such Selling Stockholder. Each Selling
Stockholder specifically agrees that the Additional Shares represented by the
certificates held in custody for the Selling Stockholder under the Custodian
Agreement are subject to the interests of the Underwriters hereunder, that the
arrangements made by the Selling Stockholder for such escrow are to that extent
irrevocable, and that the obligations of the Selling Stockholder hereunder shall
not be terminable by any act or deed of the Selling Stockholder (or by any other
person, firm or corporation including the Company, the Custodian or the
Underwriters) or by operation of law (including the death of an individual
Selling Stockholder or the dissolution of a corporate Selling Stockholder) or by
the occurrence of any other event or events, except as set forth in the
Custodian Agreement. If the Underwriters exercise their option, in whole or in
part, to acquire any or all of the Additional Shares and any such event should
occur prior to the delivery to the Underwriters of the Additional Shares
hereunder, certificates for the Additional Shares shall be delivered by the
Custodian in accordance with the terms and conditions of this Agreement as if
such event has not occurred. The Custodian is authorized to receive and
acknowledge receipt of the proceeds of sale of the Shares held by it against
delivery of such Shares.

                  (f) If on the Additional Closing Date, a Selling Stockholder
fails to sell the Additional Shares that such Selling Stockholder has agreed to
sell on such date as set forth in Schedule II hereto, the Company agrees that it
will sell or arrange for the sale of the number of shares of Common Stock to the
Underwriters that represents the Additional Shares which such Selling
Stockholder has failed to so sell, as set forth in Schedule II hereto, or such
lesser number as may be requested by the Representatives. In no event shall this
Section be construed to excuse the Selling Stockholder from the full performance
of its obligations under this Agreement.

                  3. Offering. Upon your authorization of the release of the
Firm Shares, the several Underwriters propose to offer the Firm Shares for sale
to the public upon the terms set forth in the Prospectus. To the extent, if at
all, that any Additional Shares are purchased pursuant to Section 2 hereof, the
Underwriters will offer them to the public on the foregoing terms.

                  4.  Covenants of the Company and the Selling Stockholders.

                  (a) The Company covenants and agrees with the several 
Underwriters that:

                  (i) If the Registration Statement has not yet been declared
         effective, the Company will use its best efforts to cause the
         Registration Statement and any amendments thereto to become effective
         as promptly as possible, and if Rule 430A is used or the filing of the
         Prospectus is otherwise required under Rule 424(b) or Rule

                                       14
<PAGE>   15




         434, the Company will file the Prospectus (properly completed if Rule
         430A has been used) pursuant to Rule 424(b) or Rule 434 within the
         prescribed time period and will provide evidence satisfactory to you of
         such timely filing. If the Company elects to rely on Rule 434, the
         Company will prepare and file a term sheet that complies with the
         requirements of Rule 434.

                  The Company will notify you immediately (and, if requested by
         you, will confirm such notice in writing) (i) when the Registration
         Statement and any amendments thereto become effective, (ii) of any
         request by the Commission for any amendment of or supplement to the
         Registration Statement or the Prospectus or for any additional
         information, (iii) of the mailing or delivery to the Commission for
         filing of any amendment of or supplement to the Registration Statement
         or the Prospectus, (iv) of the issuance by the Commission of any stop
         order suspending the effectiveness of the Registration Statement or any
         post-effective amendment thereto or of the initiation, or the
         threatening, of any proceedings therefor, (v) of the receipt of any
         comments from the Commission, and (vi) of the receipt by the Company of
         any notification with respect to the suspension of the qualification of
         the Shares for sale in any jurisdiction or the initiation or
         threatening of any proceeding for that purpose. If the Commission shall
         propose or enter a stop order at any time, the Company will make every
         reasonable effort to prevent the issuance of any such stop order and,
         if issued, to obtain the lifting of such order as soon as possible. The
         Company will not file any amendment to the Registration Statement or
         any amendment of or supplement to the Prospectus (including the
         prospectus required to be filed pursuant to Rule 424(b) or Rule 434)
         that differs from the prospectus on file at the time of the
         effectiveness of the Registration Statement before or after the
         effective date of the Registration Statement to which you shall
         reasonably object in writing after being timely furnished in advance a
         copy thereof.

                  (ii) If at any time when a prospectus relating to the Shares
         is required to be delivered under the Act any event shall have occurred
         as a result of which the Prospectus as then amended or supplemented
         would, in the judgment of the Underwriters or the Company, include an
         untrue statement of a material fact or omit to state any material fact
         required to be stated therein or necessary to make the statements
         therein, in the light of the circumstances under which they were made,
         not misleading, or if it shall be necessary at any time to amend or
         supplement the Prospectus or Registration Statement to comply with the
         Act or the Regulations, the Company will notify you promptly and
         prepare and file with the Commission an appropriate amendment or
         supplement (in form and substance satisfactory to you) which will
         correct such statement or omission and will use its best efforts to
         have any amendment to the Registration Statement declared effective as
         soon as possible.

                                       15
<PAGE>   16




                  (iii)  The Company will promptly deliver to you four signed
         copies of the Registration Statement, including exhibits and all
         amendments thereto, and the Company will promptly deliver to each of
         the several Underwriters such number of copies of any preliminary
         prospectus, the Prospectus, the Registration Statement, and all
         amendments of and supplements to such documents, if any, as you may
         reasonably request. The Prospectus shall be furnished on or prior to
         3:00 P.M., New York time, on the second business day following the
         later of the execution and delivery of this Agreement or the effective
         time of the Registration Statement.

                  (iv)   The Company will endeavor in good faith, in cooperation
         with you, at or prior to the time the Registration Statement becomes
         effective, to qualify the Shares for offering and sale under the
         securities laws relating to the offering or sale of the Shares of such
         jurisdictions as you may designate and to maintain such qualification
         in effect for so long as required for the distribution thereof, except
         that in no event shall the Company be obligated in connection therewith
         to qualify as a foreign corporation or to execute a general consent to
         service of process.

                  (v)    The Company will make generally available (within the
         meaning of Section 11(a) of the Act) to its security holders and to you
         as soon as practicable, but not later than 45 days after the end of its
         fiscal quarter in which the first anniversary date of the effective
         date of the Registration Statement occurs, an earnings statement (in
         form complying with the provisions of Rule 158 of the Regulations)
         covering a period of at least twelve consecutive months beginning after
         the effective date of the Registration Statement.

                  (vi)   During the period of 90 days from the date of the
         Prospectus, the Company will not, without your prior written consent,
         issue, sell, offer or agree to sell, grant any option for the sale of,
         or otherwise dispose of, directly or indirectly, any Common Stock (or
         any securities convertible into, exercisable for or exchangeable for
         Common Stock), and the Company will obtain the undertaking of each of
         its officers and directors, all of which are listed on Schedule III
         hereto, and General Atlantic Partners, L.L.C. and Resource Investors
         Management Company, not to engage in any of the aforementioned
         transactions on their own behalf, other than the Company's sale of
         Shares hereunder, and the Company's issuance of Common Stock upon the
         exercise of presently outstanding stock options.

                  (vii)  During the period of three years from the effective 
         date of the Registration Statement, the Company will furnish to the
         Representatives copies of (i) all reports to its stockholders; and (ii)
         all reports, financial statements and proxy

                                       16
<PAGE>   17




         or information statements filed by the Company with the Commission or
         any national securities exchange.

                  (viii) The Company will apply the proceeds from the sale of
         the Shares as set forth under "Use of Proceeds" in the Prospectus.

                  (ix)   The Company agrees that it will not accelerate the
         vesting or exercisability of any options, warrants, or rights of any
         character obligating the Company to issue any shares of Common Stock so
         that any such options, warrants, or rights shall become exercisable
         within 90 days of the Closing Date or any Additional Closing Date.

                  (b)    Each Selling Stockholder covenants and agrees with the
several Underwriters that:

                  (i)    During a period of 90 days from the date of the
         Prospectus, such Selling Stockholder will not, without your prior
         written consent, sell, offer or agree to sell, grant any option for the
         sale of, or otherwise dispose of, directly or indirectly, any Common
         Stock (or any securities convertible into, exercisable for or
         exchangeable for Common Stock), except for sales to the Underwriters as
         provided in this Agreement.

                  (ii)   In order to document the Underwriters' compliance with
         the reporting and withholding provisions of the Tax Equity and Fiscal
         Responsibility Act of 1982 and Dividend Tax Compliance Act of 1983 with
         respect to the transactions herein contemplated, such Selling
         Stockholder shall deliver to you prior to or at the Closing Date a
         properly completed and executed United States Treasury Department Form
         W-9 (or other applicable form or statement specified by the Treasury
         Department regulations in lieu thereof).

                  (iii)  Such Selling Stockholder shall not take, directly or
         indirectly, any action designed to cause or result in, or that has
         constituted or might reasonably be expected to constitute, the
         stabilization or manipulation of the price of any securities of the
         Company, and other than as permitted by the Act, the Selling
         Stockholder shall not distribute any prospectus or other offering
         material in connection with the offering of the Shares.

                  5.     Payment of Expense. Whether or not the transactions
contemplated in this Agreement are consummated or this Agreement is terminated,
the Company hereby agrees to pay all reasonable costs and expenses incident to
the performance of the obligations of the Company and


                                       17
<PAGE>   18




the Selling Stockholders hereunder, including those in connection with (i)
preparing, printing, duplicating, filing and distributing the Registration
Statement, as originally filed and all amendments thereof (including all
exhibits thereto), any preliminary prospectus, the Prospectus and any amendments
thereof or supplements thereto (including, without limitation, fees and expenses
of the Company's accountants and counsel), the underwriting documents (including
this Agreement, and the Agreement Among Underwriters) and all other documents
related to the public offering of the Shares (including those supplied to the
Underwriters in quantities as hereinabove stated), (ii) the travel expenses of
the Company's officers and employees and any other expenses of the Company in
connection with attending or hosting meetings with prospective purchasers of the
Shares, (iii) the issuance, transfer and delivery of the Shares to the
Underwriters, including any transfer or other taxes payable thereon, (iv) the
qualification of the Shares under state or foreign securities or Blue Sky Laws,
including the costs of printing and mailing a preliminary and final "Blue Sky
Survey" and the fees of counsel for the Underwriters and such counsel's
disbursements in relation thereto, (v) quotation of the Shares on the NASDAQ,
(vi) filing fees of the Commission and the National Association of Securities
Dealers, Inc., (vii) the cost of printing certificates representing the Shares,
and (viii) the cost and charges of any transfer agent or registrar.

                  6.   Conditions of Underwriters' Obligations. The obligations 
of the several Underwriters to purchase and pay for the Firm Shares and the
Additional Shares, as provided herein, shall be subject to the accuracy of the
representations and warranties of the Company and the Selling Stockholders
herein contained, as of the date hereof and as of the Closing Date (or in the
case of the Additional Shares as of the Additional Closing Date), to the absence
from any certificates, opinions, written statements or letters furnished to you
or to Vinson & Elkins L.L.P. ("Underwriters' Counsel") pursuant to this Section
6 of any material misstatement or omission, to the performance by the Company
and the Selling Stockholders of their respective obligations hereunder, and to
the following additional conditions:

                  (a)  The Registration Statement, including any related
registration statement filed pursuant to Rule 462(b) under the Act, shall have
become effective not later than 5:30 P.M., New York time, on the date of this
Agreement or at such later time and date as shall have been consented to in
writing by you; if the Company shall have elected to rely upon Rule 430A or Rule
434 of the Regulations, the Prospectus shall have been filed with the Commission
in a timely fashion in accordance with Section 4(a) hereof; and, at or prior to
the Closing Date and Additional Closing Date, as the case may be, no stop order
suspending the effectiveness of the Registration Statement or any post-effective
amendment thereof shall have been issued and no proceedings therefor shall have
been initiated or threatened by the Commission.

                  (b)  At the Closing Date and each Additional Closing Date, you
shall have received the opinion of Thompson & Knight, a Professional
Corporation, counsel for the Company,

                                       18
<PAGE>   19




dated the Closing Date or the Additional Closing Date, as the case may be,
addressed to the Underwriters and in form and substance satisfactory to
Underwriters' Counsel, to the effect that:

                           (i) Each of the Company and its Subsidiaries has been
                  duly organized and is validly existing as a corporation,
                  limited partnership or limited liability company in good
                  standing under the laws of its jurisdiction of incorporation
                  or formation. Each of the Company and its Subsidiaries is duly
                  qualified and in good standing as a foreign corporation,
                  limited partnership or limited liability company in each
                  jurisdiction in which the character or location of its
                  properties (owned, leased or licensed) or the nature or
                  conduct of its business makes such qualification necessary,
                  except for those failures to be so qualified or in good
                  standing which will not in the aggregate have a material
                  adverse effect on the Company and its Subsidiaries taken as a
                  whole. Each of the Company and its Subsidiaries has all
                  requisite power and authority to own, lease and license its
                  respective properties and conduct its business as now being
                  conducted and as described in the Registration Statement and
                  the Prospectus. All of the issued and outstanding capital
                  stock of each corporate subsidiary of the Company has been
                  duly and validly issued and is fully paid and nonassessable
                  and, to such counsel's knowledge, was not issued in violation
                  of, and is free of, preemptive rights and is owned directly or
                  indirectly by the Company, free and clear of any lien,
                  encumbrance, claim, security interest, restriction on
                  transfer, stockholders' agreement, voting trust or other
                  defect of title whatsoever. All of the partnership interests
                  of each partnership subsidiary of the Company have been duly
                  and validly authorized and issued in accordance with the terms
                  of the governing partnership agreement, and, to such counsel's
                  knowledge, are owned by the Company, directly or through its
                  Subsidiaries, free and clear of any lien, encumbrance, claim,
                  security interest, restriction on transfer, voting agreement,
                  voting trust or other defect of title whatsoever. All of the
                  membership interests of each limited liability company
                  subsidiary of the Company have been duly and validly
                  authorized and issued in accordance with the terms of the
                  governing limited liability company agreement (or
                  regulations), and, to such counsel's knowledge, are owned by
                  the Company, directly or through its Subsidiaries, free and
                  clear of any lien, encumbrance, claim, security interest,
                  restriction on transfer, voting agreement, voting trust or
                  other defect of title whatsoever, with the exception of (i)
                  Quest Resources, L.L.C., in which the Company holds a 99.55%
                  interest in all profits and losses and General Atlantic
                  Partners III, L.P. holds a 0.45% interest and (ii) Venture
                  Acquisition, L.P., in which Quest Resources, L.L.C. shares
                  profits and losses with RIMCO Energy, Inc., RIMCO Production
                  Company, Inc.,


                                       19
<PAGE>   20




         RIMCO Exploration Partners, L.P. I and RIMCO Exploration Partners, L.P.
         II.

                           (ii)  The Company has authorized capital stock as set
                  forth under the caption "Capitalization" in the Registration
                  Statement and the Prospectus. All of the outstanding shares of
                  Common Stock are duly and validly authorized and issued, are
                  fully paid and nonassessable and were not issued in violation
                  of or subject to any preemptive rights. The Shares to be
                  delivered by the Company on the Closing Date or Additional
                  Closing Date, as the case may be, have been duly and validly
                  authorized and, when delivered in accordance with this
                  Agreement, will be duly and validly issued, fully paid and
                  nonassessable and will not have been issued in violation of or
                  subject to any preemptive rights. Each of the Underwriters
                  will receive good, valid and marketable title to the Firm
                  Shares and the Additional Shares being sold by the Company
                  hereunder, free and clear of all liens, encumbrances, claims,
                  security interests, restrictions on transfer, stockholders'
                  agreements, voting trusts and other defects of title
                  whatsoever. The Common Stock, the Firm Shares and the
                  Additional Shares conform to the descriptions thereof
                  contained in the Registration Statement and the Prospectus
                  under the caption "Description of Capital Stock," and,
                  assuming the certificates for the Common Stock are in the form
                  filed with the Commission, are in due and proper form and
                  comply with the requirements of Delaware law, the Company's
                  certificate of incorporation and by-laws, and the requirements
                  of the NASDAQ.

                           (iii) Except as described in or contemplated by the
                  Prospectus, to the knowledge of such counsel, there are no
                  outstanding securities of the Company or any Subsidiary
                  convertible or exchangeable into or evidencing the right to
                  purchase or subscribe for any shares of Common Stock of the
                  Company or shares of capital stock, partnership interests or
                  membership interests of any Subsidiary, respectively, and
                  there are no outstanding options, warrants, or rights of any
                  character obligating the Company or any Subsidiary to issue
                  any shares of its capital stock, any partnership interests or
                  any membership interests, as applicable, or any securities
                  convertible or exchangeable or evidencing the right to
                  purchase or subscribe therefor; and except as described in the
                  Prospectus, to the knowledge of counsel, no holder of
                  securities of the Company or any Subsidiary or any other
                  person has the right, contractual or otherwise, which has not
                  been satisfied or effectively waived, to cause the Company to
                  sell or otherwise issue to them, or to permit them to
                  underwrite the sale of, any of the Shares.


                                       20
<PAGE>   21




                           (iv)  This Agreement has been duly and validly
         authorized, executed and delivered by the Company.

                           (v)   To such counsel's knowledge, there is no
         litigation or governmental or other action, suit, proceeding or
         investigation before any court or before or by any public, regulatory
         or governmental agency or body pending or threatened against, or
         involving the properties or business of, the Company or any of its
         Subsidiaries, which, if resolved against the Company or such
         Subsidiary, individually or, to the extent involving related claims or
         issues, in the aggregate, is of a character required to be disclosed in
         the Registration Statement and the Prospectus which has not been
         properly disclosed therein.

                           (vi)  The execution, delivery, and performance of 
         this Agreement and the consummation of the transactions contemplated
         hereby do not and will not (A) to such counsel's knowledge, conflict
         with or result in a breach of any of the terms and provisions of, or
         constitute a default (or an event which with notice or lapse of time,
         or both, would constitute a default) or require consent under, or
         result in the creation or imposition of any lien, charge or encumbrance
         upon any property or assets of the Company or any of its Subsidiaries
         pursuant to the terms of any agreement, instrument, franchise, license
         or permit known to such counsel to which the Company or any of its
         Subsidiaries is a party or by which any of such corporations or their
         respective properties or assets may be bound or (B) violate or conflict
         with any provision of the organizational documents of the Company or
         any of its Subsidiaries, or, to the knowledge of such counsel, any
         judgment, decree, order, statute, rule or regulation of any court or
         any public, governmental or regulatory agency or body having
         jurisdiction over the Company or any of its Subsidiaries or any of
         their respective properties or assets. To such counsel's knowledge, no
         consent, approval, authorization, order, registration, filing,
         qualification, license or permit of or with any court or any public,
         governmental, or regulatory agency or body having jurisdiction over the
         Company or any of its Subsidiaries or any of their respective
         properties or assets is required for the execution, delivery and
         performance of this Agreement or the consummation of the transactions
         contemplated hereby, except for (1) such as may be required under
         foreign securities laws or state securities or Blue Sky laws in
         connection with the purchase and distribution of the Shares by the
         Underwriters (as to which such counsel need express no opinion) and (2)
         such as have been made or obtained under the Act.


                                       21
<PAGE>   22




                           (vii)  The Registration Statement and the Prospectus
                  and any amendments thereof or supplements thereto (other than
                  the financial statements and schedules and other financial and
                  petroleum engineering data included therein, as to which no
                  opinion need be rendered) comply as to form in all material
                  respects with the requirements of the Act and the Regulations.

                           (viii) The Registration Statement is effective under
                  the Act, and, to the best knowledge of such counsel, no stop
                  order suspending the effectiveness of the Registration
                  Statement or any post-effective amendment thereof has been
                  issued and no proceedings therefor have been initiated or
                  threatened by the Commission, and all filings required by Rule
                  424(b) of the Regulations have been made.

                           (ix)   Except as disclosed in the Prospectus, there 
                  are no contracts, agreements or understandings known to such
                  counsel between the Company and any person granting such
                  person the right to require the Company to file a registration
                  statement under the Act with respect to any securities of the
                  Company owned or to be owned by such person or to require the
                  Company to include such securities in the securities
                  registered pursuant to the Registration Statement or in any
                  securities being registered pursuant to any other registration
                  statement filed by the Company under the Act; and all rights
                  to require registration of any securities under that agreement
                  have been waived with respect to the offering contemplated
                  hereby and for 90 days after the date of the public offering
                  of the Shares.

                           (x)    In addition, such opinion shall also contain a
                  statement that such counsel has participated in conferences
                  with officers and representatives of the Company,
                  representatives of the independent public accountants for the
                  Company and the Underwriters at which the contents and the
                  Prospectus and related matters were discussed, and no facts
                  have come to the attention of such counsel which would lead
                  such counsel to believe that either the Registration Statement
                  at the time it became effective (including the information
                  deemed to be part of the Registration Statement at the time of
                  effectiveness pursuant to Rule 430A or Rule 434, if
                  applicable), or any amendment thereof made prior to the
                  Closing Date or Additional Closing Date, as the case may be,
                  as of the date of such amendment, contained an untrue
                  statement of a material fact or omitted to state any material
                  fact required to be stated therein or necessary to make the
                  statements therein not misleading or that the Prospectus as of
                  its date (or any amendment thereof or supplement thereto made
                  prior to the Closing Date or the Additional Closing

                                       22
<PAGE>   23




                  Date, as the case may be, as of the date of such amendment or
                  supplement) contained or contains an untrue statement of a
                  material fact or omitted or omits to state any material fact
                  required to be stated therein or necessary to make the
                  statements therein, in light of the circumstances under which
                  they were made, not misleading (it being understood that such
                  counsel need express no belief or opinion with respect to the
                  financial statements and schedules and other financial and
                  petroleum engineering data included therein).

                           (xi)  The Common Stock is quoted and the Shares have
                  been approved for quotation on the NASDAQ.

                           (xii) Based on current law, the holding periods for
                  the holders of the Company's unregistered securities for
                  purposes of Rule 144 of the Act are as stated under the
                  caption "Shares Eligible for Future Sale" in the Prospectus.

                  In rendering such opinion, such counsel may rely (A) as to
         matters involving the application of laws other than the laws of the
         United States and jurisdictions in which they are admitted, to the
         extent such counsel deems proper and to the extent specified in such
         opinion, if at all, upon an opinion or opinions, (in form and substance
         reasonably satisfactory to Underwriters' Counsel) of other counsel
         reasonably acceptable to Underwriters' Counsel, familiar with the
         applicable laws; (B) as to matters of fact, to the extent they deem
         proper, on certificates of responsible officers of the Company and
         certificates or other written statements of officers of departments of
         various jurisdictions having custody of documents respecting the
         corporate existence or good standing of the Company and its
         Subsidiaries, provided that copies of any such statements or
         certificates shall be delivered to Underwriters' Counsel. The opinion
         of such counsel for the Company shall state that the opinion of any
         such other counsel is in form satisfactory to such counsel and, in
         their opinion, you and they are justified in relying thereon.

                  (c) At the Closing Date you shall have received the favorable
         opinions of Thompson & Knight, P.C., counsel for the Selling
         Stockholders, dated the Closing Date, addressed to the Underwriters and
         in form and substance satisfactory to Underwriters' Counsel, with
         respect to each Selling Stockholder, to the effect that:

                           (i)   Each of this Agreement and the Custodian
                  Agreement has been duly and validly authorized, executed and
                  delivered by or on behalf of that Selling Stockholder. The
                  Custodian Agreement is a valid and binding

                                       23
<PAGE>   24




                  obligation of that Selling Stockholder, enforceable against
                  such Selling Stockholder in accordance with its terms.

                           (ii)   To the knowledge of such counsel, each Selling
                  Stockholder has all requisite power and authority, and all
                  necessary consents, approvals, authorizations, orders,
                  registrations, filings, qualifications, licenses and permits
                  of and from all courts and all public, governmental or
                  regulatory agencies and bodies as are required for the
                  execution, delivery and performance of this Agreement and the
                  Custodian Agreement and the consummation of the transactions
                  contemplated hereby and thereby except for (A) such as may be
                  required under state securities or Blue Sky Laws in connection
                  with the purchase and distribution of the Shares by the
                  Underwriters (as to which such counsel need express no
                  opinion) and (B) such as have been made or obtained under the
                  Act.

                           (iii)  Upon the delivery of and payment for the
                  Additional Securities as contemplated hereby, each of the
                  Underwriters who has acquired Additional Securities from the
                  Selling Stockholder in good faith and without notice of any
                  adverse claim within the meaning of the Uniform Commercial
                  Code will acquire the Additional Securities being sold by each
                  Selling Stockholder on the Closing Date, free of any adverse
                  claim. The owner of such Additional Securities, if other than
                  the Selling Stockholder, is precluded from asserting against
                  the Underwriters the ineffectiveness of any authorized
                  endorsement or instruction, assuming the Underwriters
                  purchased such Additional Securities for value in good faith
                  and without notice of any adverse claim.

                           (iv)   The execution, delivery and performance of 
                  this Agreement and the Custodian Agreement by that Selling
                  Stockholder and the consummation of the transactions
                  contemplated hereby and thereby will not violate or conflict
                  with, to the best knowledge of such counsel, any judgment,
                  decree, order, statute, rule or regulation of any court or any
                  public, governmental or regulatory agency or body having
                  jurisdiction over any of that Selling Stockholder or any of
                  its properties or assets.

                           (v)    The statements in the Prospectus under the
                  caption "Principal and Selling Stockholders," insofar as such
                  statements relate to the Selling Stockholders, fairly present
                  the information called for with respect to such matters.


                                       24
<PAGE>   25




                  In rendering such opinion, such counsel may rely (A) as to
         matters involving the application of laws other than the laws of the
         United States and jurisdictions in which they are admitted, to the
         extent such counsel deems proper and to the extent specified in such
         opinion, if at all, upon an opinion or opinions (in form and substance
         reasonably satisfactory to Underwriters' Counsel) of other counsel
         reasonably acceptable to Underwriters' Counsel, familiar with the
         applicable laws; (B) as to matters of fact, to the extent they deem
         proper, on certificates of the Selling Stockholders, provided that
         copies of any such Statements or certificates shall be delivered to
         Underwriters' Counsel. The opinions of such counsel for the Selling
         Stockholders shall state that the opinion of any such other counsel is
         in form satisfactory to such counsel and, in their opinion, you and
         they are justified in relying thereon.

                  (d) At the Closing Date and Additional Closing Date, you shall
         have received a certificate of the Chief Executive Officer and the
         Chief Financial Officer of the Company, dated the Closing Date or
         Additional Closing Date, as the case may be, to the effect that (i) the
         condition set forth in subsection (a) of this Section 6 has been
         satisfied, (ii) as of the date hereof and as of the Closing Date or
         Additional Closing Date, as the case may be, the representations and
         warranties of the Company set forth in Section 1 hereof are accurate,
         (iii) as of the Closing Date or the Additional Closing Date, as the
         case may be, the obligations of the Company to be performed hereunder
         on or prior thereto have been duly performed, and (iv) subsequent to
         the respective dates as of which information is given in the
         Registration Statement and the Prospectus, (A) the Company and its
         Subsidiaries have not sustained any material loss or interference with
         their respective businesses or properties from fire, flood, hurricane,
         accident or other calamity, whether or not covered by insurance, or
         from any labor dispute or any legal or governmental proceeding, and (B)
         there has not been any material adverse change, or any development
         involving a material adverse change, in the business prospects,
         properties, operations, condition (financial or otherwise), or results
         of operations of the Company and its Subsidiaries taken as a whole,
         except in each case as described in or contemplated by the Prospectus.

                  (e) At the Closing Date, you shall have received a certificate
         executed by or on behalf of each Selling Stockholder, dated the Closing
         Date, to the effect that the representations and warranties of such
         Selling Stockholder set forth in Section 1 hereof are accurate, and
         that as of the Closing Date, the obligations of such Selling
         Stockholder to be performed hereunder on or prior thereto have been
         duly performed.


                                       25
<PAGE>   26




                  (f) At the time this Agreement is executed and at the Closing
         Date (and Additional Closing Date), you shall have received a letter,
         from Price Waterhouse LLP, independent accountants for the Company,
         dated, respectively, as of the date of this Agreement and as of the
         Closing Date or Additional Closing Date, as the case may be, addressed
         to the Underwriters and in form and substance satisfactory to you, to
         the effect that: (i) they are independent accountants with respect to
         the Partnership and Company within the meaning of the Act and the
         Regulations; (ii) stating that, in their opinion, the financial
         statements of the Partnership and the Company audited by them and
         included in the Registration Statement and the Prospectus comply as to
         form in all material respects with the applicable accounting
         requirements of the Act and the Regulations with respect to
         registration statements on Form S-1; (iii) on the basis of procedures
         (but not an audit in accordance with generally accepted auditing
         standards) consisting of a reading of the minutes of meetings of the
         management committee of the Partnership subsequent to December 31, 1997
         and of the minutes of meetings and consents of the stockholders and
         boards of directors of the Company and its Subsidiaries and the
         committees of such boards subsequent to December 31, 1997 as set forth
         in the minutes books through a specified date not more than five
         business days prior to the date of delivery of such letter, inquiries
         of officers and other employees of the Company and its Subsidiaries who
         have responsibility for financial and accounting matters of the Company
         and its Subsidiaries with respect to transactions and events subsequent
         to December 31, 1997 to a date not more than five days prior to the
         date of such letter, nothing has come to their attention that would
         cause them to believe that: (A) with respect to the period subsequent
         to December 31, 1997, there were, as of a specified date not more than
         five days prior to the date of such letter, any changes in long-term
         indebtedness of the Partnership or the Company or any decrease,
         excluding net losses, of the Partnership or the Company, partners'
         capital, capital stock of the Company, or stockholders' equity of the
         Company, in each case as compared with the amounts shown in the most
         recent balance sheet of the Partnership or the Company, as applicable,
         included in the Registration Statement and the Prospectus, except for
         changes or decreases which the Registration Statement and the
         Prospectus disclose have occurred or may occur or which are set forth
         in such letter, or (B) that during the period from January 1, 1998 to a
         specified date not more than five days prior to the date of such
         letter, there was any decrease, as compared with the corresponding
         period in the prior fiscal year, in total revenues, except for
         decreases which the Registration Statement and the Prospectus disclose
         have occurred or may occur or which are set forth in such letter; (iv)
         they have read the unaudited pro forma financial statements included in
         the Registration Statement and inquired of officials of the Company
         about the basis for their determination of the pro forma adjustments,
         and whether the unaudited pro forma financial statements included in
         the Registration Statement comply as to form

                                       26
<PAGE>   27




         in all material respects with the applicable accounting requirements of
         rule 11-02 of Regulation S-X; (v) they have proved the arithmetic
         accuracy of the application of the pro forma adjustments to the
         historical amounts in the unaudited pro forma financial statements;
         (vi) on the basis of the review referred to in (iv) and (v) above,
         nothing came to their attention that caused them to believe that the
         unaudited pro forma financial statements included in the Registration
         Statement do not comply as to form in all material respects with the
         applicable accounting requirements of rule 11-02 of Regulation S-X and
         that the pro forma adjustments have not been properly applied to the
         historical amounts in the compilation of those statements; and (vii)
         stating that they have compared specific dollar amounts, numbers of
         shares, percentages of revenues and earnings, and other financial
         information pertaining to the Partnership and the Company and its
         Subsidiaries set forth in the Registration Statement and the
         Prospectus, which have been specified by you prior to the date of this
         Agreement, and they (Price Waterhouse LLP) are willing to perform to
         the extent that such amounts, numbers, percentages, and information may
         be derived from the general accounting and financial records of the
         Company and its Subsidiaries which are subject to the internal controls
         of the Company's accounting system, and excluding any questions
         requiring an interpretation by legal counsel, with the results obtained
         from the application of specified readings, inquiries, and other
         appropriate procedures specified by you (which procedures do not
         constitute an examination in accordance with generally accepted
         auditing standards) set forth in such letter.

                  (g) All proceedings taken in connection with the sale of the
         Firm Shares and the Additional Shares as herein contemplated shall be
         satisfactory in form and substance to you and to Underwriters' Counsel,
         and the Underwriters shall have received from Underwriters' Counsel a
         favorable opinion, dated as of the Closing Date and the Additional
         Closing Date, as the case may be, with respect to the issuance and sale
         of the Shares, the Registration Statement and the Prospectus and such
         other related matters, as you may reasonably require, and the Company
         and the Selling Stockholders shall have furnished to Underwriters'
         Counsel such documents as they reasonably request for the purpose of
         enabling them to pass upon such matters.

                  (h) You shall have received from each person who is a director
         or officer of the Company, all of whom are listed on Schedule III
         hereto, and from General Atlantic Partners, L.L.C. and Resource
         Investors Management Company, an agreement to the effect that such
         person will not, directly or indirectly, without your prior written
         consent, offer, sell, offer or agree to sell, grant any option to
         purchase or otherwise dispose (or announce any offer, sale, grant of an
         option to purchase or

                                       27
<PAGE>   28




         other disposition) of any shares of Common Stock (or any securities
         convertible into, exercisable for or exchangeable or exercisable for
         shares of Common Stock) for a period of 90 days after the date of the
         Prospectus.

                  (i)    At the Closing Date, the Common Stock is quoted and the
         Shares have been approved for quotation on the NASDAQ.

                  (j)    At the time of execution of this Agreement, the Closing
         Date and the Additional Closing Date, you shall have received a letter
         of Cawley, Gillespie, dated respectively the date hereof, the Closing
         Date or the Additional Closing Date, substantially in the forms
         heretofore approved by the Representatives.

                  (k)    Prior to the Closing Date and the Additional Closing 
         Date, the Company and the Selling Stockholders shall have furnished to
         you such further information, certificates and documents as you may
         reasonably request.

                  If any of the conditions specified in this Section 6 shall not
have been fulfilled when and as required by this Agreement, or if any of the
certificates, opinions, written statements or letters furnished to you or to
Underwriters' Counsel pursuant to this Section 6 shall not be in all material
respects reasonably satisfactory in form and substance to you and to
Underwriters' Counsel, all obligations of the Underwriters hereunder may be
canceled by you at, or at any time prior to, the Closing Date and the
obligations of the Underwriters to purchase the Additional Shares may be
canceled by you at, or at any time prior to, the Additional Closing Date. Notice
of such cancellation shall be given to the Company and the Selling Stockholders
in writing, or by telephone, telex or telegraph, confirmed in writing.

                  7.     Indemnification.

                  (a)    The Company agrees to indemnify and hold harmless each
         Underwriter and each person, if any, who controls any Underwriter
         within the meaning of Section 15 of the Act or Section 20(a) of the
         Securities Exchange Act of 1934 (the "Exchange Act"), against any and
         all losses, liabilities, claims, damages and expenses whatsoever as
         incurred (including but not limited to reasonable attorneys' fees and
         any and all reasonable expenses whatsoever incurred in investigating,
         preparing or defending against any litigation, commenced or threatened,
         or any claim whatsoever, and any and all amounts paid in settlement of
         any claim or litigation), joint or several, to which they or any of
         them may become subject under the Act, the Exchange Act or otherwise,
         insofar as such losses, liabilities, claims, damages or expenses (or
         actions in respect thereof) arise out of or

                                       28
<PAGE>   29




         are based upon any untrue statement or alleged untrue statement of a
         material fact contained in the registration statement for the
         registration of the Shares, as originally filed or any amendment
         thereof (including any registration statement filed pursuant to Rule
         462(b)), or any related preliminary prospectus or the Prospectus, or in
         any supplement thereto or amendment thereof, or arise out of or are
         based upon the omission or alleged omission to state therein a material
         fact required to be stated therein or necessary to make the statements
         therein not misleading; provided, however, that the Company will not be
         liable in any such case to the extent but only to the extent that any
         such loss, liability, claim, damage or expense arises out of or is
         based upon any such untrue statement or alleged untrue statement or
         omission or alleged omission made therein in reliance upon and in
         conformity with written information furnished to the Company by or on
         behalf of any Underwriter through you, in each case expressly for use
         therein. This indemnity agreement will be in addition to any liability
         which the Company may otherwise have including under this Agreement.

                  (b) Each Selling Stockholder, severally and not jointly,
         agrees to indemnify and hold harmless each Underwriter and each person,
         if any, who controls any Underwriter within the meaning of Section 15
         of the Act or Section 20(a) of the Exchange Act, against any and all
         losses, liabilities, claims, damages and expenses whatsoever as
         incurred (including but not limited to reasonable attorneys' fees and
         any and all reasonable expenses incurred in investigating, preparing or
         defending against any litigation, commenced or threatened, or any claim
         whatsoever, and any and all amounts paid in settlement of any claim or
         litigation), joint or several, to which they or any of them may become
         subject under the Act, the Exchange Act or otherwise, insofar as such
         losses, liabilities, claims, damages or expenses (or actions in respect
         thereof) arise out of or are based upon any untrue statement or alleged
         untrue statement of a material fact contained in the registration
         statement for the registration of the Shares, as originally filed or
         any amendment thereof (including any registration statement filed
         pursuant to Rule 462(b)), or any related preliminary prospectus or the
         Prospectus, or in any supplement thereto or amendment thereof, or arise
         out of or are based upon the omission or alleged omission to state
         therein a material fact required to be stated therein or necessary to
         make the statements therein not misleading; provided however, that the
         Selling Stockholders will not be liable in any such case to the extent
         but only to the extent that any such loss, liability, claim, damage or
         expense arises out of or is based upon any such untrue statement or
         alleged untrue statement or omission or alleged omission made therein
         in reliance upon and in conformity with written information furnished
         to the Company by or on behalf of any Underwriter through you, in each
         case expressly for use therein. Notwithstanding any other provision of
         this Agreement, the aggregate liability of any

                                       29
<PAGE>   30




         Selling Stockholder pursuant to all provisions of this Agreement shall
         be limited to an amount equal to the aggregate public offering price of
         the shares sold by such Selling Stockholder, less commissions received
         by the Underwriters. This indemnity agreement will be in addition to
         any liability which the Selling Stockholder may otherwise have
         including under this Agreement.

                  Notwithstanding the foregoing, the Underwriters agree that, in
         the case of any loss, liability, claim, damage or expense for which
         they may claim indemnification hereunder, they will first make demand
         for indemnification from the Company, and will not seek to enforce any
         right or remedy granted under this Section 7 against the Selling
         Stockholders, unless and until (i) the Underwriters shall have
         delivered a written demand for indemnification hereunder to the Company
         and (ii) the Company shall have failed to observe or comply in all
         materials respects with any of its obligations hereunder in respect of
         such loss, liability, claim, damage or expense for a period of at least
         30 days following the delivery of such written demand. In the event
         that the Company and the Selling Stockholders shall have failed to
         comply with their obligations in respect of any loss, liability, claim,
         damage or expense, the Underwriters further agree that (x) they will
         not commence any legal proceeding against the Selling Stockholders to
         recover such loss, claim, damage, liability or expenses unless, prior
         to or concurrently therewith, they shall have commenced a legal
         proceeding against the Company to recover the same, (y) they will
         diligently and in good faith prosecute any such legal proceeding
         against the Company for as long as the Selling Stockholders are a party
         thereto, and (z) in the event that judgments are entered in favor of
         the Underwriters against both the Company and the Selling Stockholders
         in any such legal proceeding, (1) during the period of 15 days
         following the date on which the judgment against the Company becomes
         final and is not subject to appeal, the Underwriters will take
         commercially reasonable steps to enforce the judgment entered against
         the Company and will not seek to enforce the judgment entered against
         the Selling Stockholders, and (2) after the expiration of such period,
         the Underwriters may seek to enforce the judgment entered against the
         Selling Stockholders, but will continue to take commercially reasonable
         steps to enforce the judgment entered against the Company for so long
         as they are seeking to enforce the judgment entered against the Selling
         Stockholders.

                  (c) Each Underwriter severally, and not jointly, agrees to
         indemnify and hold harmless the Company, each Selling Stockholder, each
         of the directors of the Company, each of the officers of the Company
         who shall have signed the Registration Statement, and each other
         person, if any, who controls the Company within the meaning of Section
         15 of the Act or Section 20(a) of the Exchange Act, against any losses,
         liabilities, claims, damages and expenses whatsoever as incurred

                                       30
<PAGE>   31




         (including but not limited to attorneys' fees and any and all expenses
         whatsoever incurred in investigating, preparing or defending against
         any litigation, commenced or threatened, or any claim whatsoever, and
         any and all amounts paid in settlement of any claim or litigation),
         joint or several, to which they or any of them may become subject under
         the Act, the Exchange Act or otherwise, insofar as such losses,
         liabilities, claims, damages or expenses (or actions in respect
         thereof) arise out of or are based upon any untrue statement or alleged
         untrue statement of a material fact contained in the Registration
         Statement for the registration of the Shares, as originally filed or
         any amendment thereof, or any related preliminary prospectus or the
         Prospectus, or in any amendment thereof or supplement thereto, or arise
         out of or are based upon the omission or alleged omission to state
         therein a material fact required to be stated therein or necessary to
         make the statements therein not misleading, in each case to the extent,
         but only to the extent, that any such loss, liability, claim, damage or
         expense arises out of or is based upon any such untrue statement or
         alleged untrue statement or omission or alleged omission made therein
         in reliance upon and in conformity with written information furnished
         to the Company by or on behalf of any Underwriter through you expressly
         for use therein; provided, however, that in no event shall any
         Underwriter be liable or responsible for any amount in excess of the
         underwriting discount applicable to the Shares purchased by such
         Underwriter hereunder. This indemnity will be in addition to any
         liability which any Underwriter may otherwise have including under this
         Agreement. The Company and each Selling Stockholder acknowledge that
         the statements set forth in the last paragraph of the cover page and in
         the [THIRD, FIFTH AND NINTH] paragraphs under the caption
         "Underwriting" in the Prospectus constitute the only information
         furnished in writing by or on behalf of any Underwriter expressly for
         use in the registration statement relating to the Shares as originally
         filed or in any amendment thereof, any related preliminary prospectus
         or the Prospectus or in any amendment thereof or supplement thereto, as
         the case may be.

                  (d) Promptly after receipt by an indemnified party under
         subsection (a), (b) or (c) above of notice of the commencement of any
         action, such indemnified party shall, if a claim in respect thereof is
         to be made against the indemnifying party under such subsection, notify
         each party against whom indemnification is to be sought in writing of
         the commencement thereof (but the failure so to notify an indemnifying
         party shall not relieve it from any liability which it may have under
         this Section 7 except to the extent that it has been prejudiced in any
         material respect by such failure or from any liability which it may
         have otherwise). In case any such action is brought against any
         indemnified party, and it notifies an indemnifying party of the
         commencement thereof, the indemnifying party will be entitled to
         participate therein, and to the extent it may elect by written notice
         delivered to the indemnified party

                                       31
<PAGE>   32




         promptly after receiving the aforesaid notice from such indemnified
         party, to assume the defense thereof with counsel satisfactory to such
         indemnified party. Notwithstanding the foregoing, the indemnified party
         or parties shall have the right to employ its or their own counsel in
         any such case, but the fees and expenses of such counsel shall be at
         the expense of such indemnified party or parties unless (i) the
         employment of such counsel shall have been authorized in writing by one
         of the indemnifying parties in connection with the defense of such
         action, (ii) the indemnifying parties shall not have employed counsel
         to have charge of the defense of such action within a reasonable time
         after notice of commencement of the action, or (iii) such indemnified
         party or parties shall have reasonably concluded that there may be
         defenses available to it or them which are different from or additional
         to those available to one or all of the indemnifying parties (in which
         case the indemnifying parties shall not have the right to direct the
         defense of such action on behalf of the indemnified party or parties,
         it being understood, however, that the Company and the Stockholders
         shall not, in connection with any one such action or separate but
         substantially similar or related actions in the same jurisdiction
         arising out of the same general allegations or circumstances, be liable
         for the fees and expenses of more than one separate firm of attorneys
         (in addition to any local counsel) for all the Underwriters and their
         controlling persons, which firm shall be designated in writing by Bear,
         Stearns & Co. Inc. and that the reasonable fees and expenses of such
         counsel shall be reimbursed as they are incurred), in any of which
         events such fees and expenses shall be borne by the indemnifying
         parties. No indemnifying party shall, without the prior written consent
         of the indemnified parties, settle or compromise or consent to the
         entry of any judgment with respect to any litigation, or any
         investigation or proceeding by any governmental agency or body,
         commenced or threatened, or any claim whatsoever in respect of which
         indemnification or contribution could be sought under this Section 6 or
         Section 7 hereof (whether or not the indemnified parties are actual or
         potential parties thereto), unless such settlement, compromise or
         consent (i) includes an unconditional release of each indemnified party
         from all liability arising out of such litigation, investigation,
         proceeding or claim and (ii) does not include a statement as to or an
         admission of fault, culpability or a failure to act by or on behalf of
         any indemnified party.

                  (e) If at any time an indemnified party shall have requested
         an indemnifying party to reimburse the indemnified party for fees and
         expenses of counsel, such indemnifying party agrees that it shall be
         liable for any settlement of the nature contemplated by Section 7(a) or
         (b) effected without its written consent if (i) such settlement is
         entered into more than 45 days after receipt by such indemnifying party
         of the aforesaid request, (ii) such indemnifying party shall have

                                       32
<PAGE>   33




         received notice of the terms of such settlement at least 30 days prior
         to such settlement being entered into, and (iii) such indemnifying
         party shall neither (a) have reimbursed such indemnified party in
         accordance with such request for fees and expenses of counsel prior to
         the date of such settlement nor (b) no later than ten days prior to
         such settlement being entered into, have both given written notice to
         such indemnified party of the amount of such fees and expenses that it
         believes are unreasonable and the basis (which must be reasonable) for
         that view and reimbursed such indemnified party for all other such fees
         and expenses.

                  (f) The provisions of this Section shall not affect any
         agreement among the Company and the Selling Shareholder(s) with respect
         to indemnification.

                  8. Contribution. In order to provide for contribution in
circumstances in which the indemnification provided for in Section 7(a) and (b)
hereof is for any reason held to be unavailable from the Company or any Selling
Stockholder or is insufficient to hold harmless a party indemnified thereunder,
the Company, the Selling Stockholders and the Underwriters shall contribute to
the aggregate losses, claims, damages, liabilities and expenses of the nature
contemplated by such indemnification provisions (including any investigation,
legal and other expenses incurred in connection with, and any amount paid in
settlement of, any action, suit or proceeding or any claims asserted, but after
deducting in the case of losses, claims, damages, liabilities and expenses
suffered by the Company and any Selling Stockholder any contribution received by
the Company or such Selling Stockholder from persons, other than the
Underwriters, who may also be liable for contribution, including persons who
control the Company within the meaning of Section 15 of the Act or Section 20(a)
of the Exchange Act, officers of the Company who signed the Registration
Statement and directors of the Company) as incurred to which the Company, one or
more of the Selling Stockholders and one or more of the Underwriters may be
subject, in such proportions as is appropriate to reflect the relative benefits
received by the Company, the Selling Stockholders and the Underwriters from the
offering of the Shares or, if such allocation is not permitted by applicable law
or indemnification is not available as a result of the indemnifying party not
having received notice as provided in Section 7 hereof, in such proportion as is
appropriate to reflect not only the relative benefits referred to above but also
the relative fault of the Company, the Selling Stockholders and the Underwriters
in connection with the statements or omissions which resulted in such losses,
claims, damages, liabilities or expenses, as well as any other relevant
equitable considerations. The relative benefits received by the Company, the
Selling Stockholders and the Underwriters shall be deemed to be in the same
proportion as (x) the total proceeds from the offering (net of underwriting
discounts and commissions but before deducting expenses) received by the Company
and (y) the total proceeds from the offering (net of underwriting discounts and
commissions but before deducting expenses) received by the Selling Stockholders
and (z) the underwriting discounts and commissions received by the Underwriters,
respectively, in each case as set forth in the table on the cover page of the
Prospectus (and as each such amount may be

                                       33
<PAGE>   34




similarly determined to give effect to the sale of the Additional Shares, if
any). The relative fault of the Company, the Selling Stockholders and of the
Underwriters shall be determined by reference to, among other things, whether
the untrue or alleged untrue statement of a material fact or the omission or
alleged omission to state a material fact relates to information supplied by the
Company, the Selling Stockholders or the Underwriters and the parties' relative
intent, knowledge, access to information and opportunity to correct or prevent
such statement or omission. The Company, the Selling Stockholders and the
Underwriters agree that it would not be just and equitable if contribution
pursuant to this Section 8 were determined by pro rata allocation (even if the
Underwriters were treated as one entity for such purpose) or by any other method
of allocation which does not take account of the equitable considerations
referred to above. The Company and each Selling Stockholder shall be jointly and
severally liable for the amounts to be contributed by any of them pursuant to
the provisions of this Section 8. Notwithstanding the provisions of this Section
8, (i) in no case shall any Underwriter (except as may be provided in the
Agreement Among Underwriters) be liable or responsible for any amount in excess
of the underwriting discount applicable to the Shares purchased by such
Underwriter hereunder, and (ii) no person guilty of fraudulent misrepresentation
(within the meaning of Section 11(f) of the Act) shall be entitled to
contribution from any person who was not guilty of such fraudulent
misrepresentation. Notwithstanding the provisions of this Section 8, no
Underwriter shall be required to contribute any amount in excess of the amount
by which the total price at which the Shares underwritten by it and distributed
to the public were offered to the public exceeds the amount of any damages that
such Underwriter has otherwise been required to pay by reason of such untrue or
alleged untrue statement or omission or alleged omission. For purposes of this
Section 8, each person, if any, who controls an Underwriter within the meaning
of Section 15 of the Act or Section 20(a) of the Exchange Act shall have the
same rights to contribution as such Underwriter, each person, if any, who
controls a Selling Stockholder within the meaning of Section 15 of the Act or
Section 20(a) of the Exchange Act shall have the same rights to contribution as
such Selling Stockholder, and each person, if any, who controls the Company
within the meaning of Section 15 of the Act or Section 20(a) of the Exchange
Act, each officer of the Company who shall have signed the Registration
Statement and each director of the Company shall have the same rights to
contribution as the Company, subject in each case to clauses (i) and (ii) of
this Section 8. Any party entitled to contribution will, promptly after receipt
of notice of commencement of any action, suit or proceeding against such party
in respect of which a claim for contribution may be made against another party
or parties under this Section 8, notify such party or parties from whom
contribution may be sought, but the omission to so notify such party or parties
shall not relieve the party or parties from whom contribution may be sought from
any obligation it or they may have under this Section 8 or otherwise.

         The obligations of the Selling Stockholders to contribute to this
Section 8 shall be subject to the limitation contained in paragraph 7(b) above
with respect to the maximum aggregate liability of the Selling Stockholders
under or in connection with this Agreement.

                                       34
<PAGE>   35


                  9.  Default by an Underwriter.

                  (a) If any Underwriter or Underwriters shall default in its or
         their obligation to purchase Firm Shares or Additional Shares
         hereunder, and if the Firm Shares or Additional Shares with respect to
         which such default relates do not (after giving effect to arrangements,
         if any, made by you pursuant to subsection (b) below) exceed in the
         aggregate 10% of the number of shares of Firm Shares or Additional
         Shares, as the case may be, which all Underwriters have agreed to
         purchase hereunder, then such Firm Shares or Additional Shares to which
         the default relates shall be purchased by the non-defaulting
         Underwriters in proportion to the respective proportions which the
         numbers of Firm Shares set forth opposite their respective names in
         Schedule I hereto bear to the aggregate number of Firm Shares set forth
         opposite the names of the non-defaulting Underwriters.

                  (b) In the event that such default relates to more than 10% of
         the Firm Shares or Additional Shares, as the case may be, you may in
         your discretion arrange for yourself or for another party or parties
         (including any non-defaulting Underwriter or Underwriters who so agree)
         to purchase such Firm Shares or Additional Shares, as the case may be,
         to which such default relates on the terms contained herein. In the
         event that within five calendar days after such a default you do not
         arrange for the purchase of the Firm Shares or Additional Shares, as
         the case may be, to which such default relates as provided in this
         Section 9, this Agreement or, in the case of a default with respect to
         the Additional Shares, the obligations of the Underwriters to purchase
         and of the Company to sell the Additional Shares shall thereupon
         terminate, without liability on the part of the Company or the Selling
         Stockholders with respect thereto (except in each case as provided in
         Sections 5, 7(a) and (b) and 8 hereof) or the several Underwriters, but
         nothing in this Agreement shall relieve a defaulting Underwriter or
         Underwriters of its or their liability, if any, to the other several
         Underwriters, the Company and the Selling Stockholders for damages
         occasioned by its or their default hereunder.

                  (c) In the event that the Firm Shares or Additional Shares to
         which the default relates are to be purchased by the non-defaulting
         Underwriters, or are to be purchased by another party or parties as
         aforesaid, you or the Company shall have the right to postpone the
         Closing Date or Additional Closing Date, as the case may be, for a
         period, not exceeding five business days, in order to effect whatever
         changes may thereby be made necessary in the Registration Statement or
         the Prospectus or in any other documents and arrangements, and the
         Company agrees to file promptly any amendment or supplement to the
         Registration Statement or the Prospectus which, in the opinion of
         Underwriters' Counsel, may thereby be made necessary or advisable.

                                       35
<PAGE>   36




         The term "Underwriter" as used in this Agreement shall include any
         party substituted under this Section 9 with like effect as if it had
         originally been a party to this Agreement with respect to such Firm
         Shares and Additional Shares.

                  10. Survival of Representations and Agreements. All
representations and warranties, covenants and agreements of the Underwriters,
the Selling Stockholders and the Company contained in this Agreement, including
the agreements contained in Section 5, the indemnity agreements contained in
Section 7 and the contribution agreements contained in Section 8, shall remain
operative and in full force and effect regardless of any investigation made by
or on behalf of any Underwriter or any controlling person thereof or by or on
behalf of the Company, any of its officers and directors or any Selling
Stockholder or any controlling person thereof, and shall survive delivery of and
payment for the Shares to and by the several Underwriters. The representations
contained in Section 1 and the agreements contained in Sections 5, 7, 8 and
11(d) hereof shall survive the termination of this Agreement including pursuant
to Sections 9 or 11 hereof.

                  11. Effective Date of Agreement; Termination.

                  (a) This Agreement shall become effective upon the later of
         (i) when you and the Company shall have received notification of the
         effectiveness of the Registration Statement, or (ii) the execution of
         this Agreement. Until this Agreement becomes effective as aforesaid, it
         may be terminated by the Company by notifying you and the Selling
         Stockholders or by you by notifying the Company and the
         Attorney-in-Fact. Notwithstanding the foregoing, the provisions of this
         Section 11 and of Sections 1, 5, 7 and 8 hereof shall at all times be
         in full force and effect.

                  (b) You shall have the right to terminate this Agreement at
         any time prior to the Closing Date or the obligations of the
         Underwriters to purchase the Additional Shares at any time prior to the
         Additional Closing Date, as the case may be, if (A) any domestic or
         international event or act or occurrence has materially disrupted, or
         in your opinion will in the immediate future materially disrupt, the
         market for the Company's securities or securities in general; or (B) if
         trading on the New York Stock Exchange or on the NASDAQ generally or
         with respect to securities of the Company shall have been suspended, or
         minimum or maximum prices for trading shall have been fixed, or maximum
         ranges for prices for securities shall have been required, on the New
         York Stock Exchange or on the NASDAQ by order of the New York Stock
         Exchange or the NASDAQ or by order of the Commission or any other
         governmental authority having jurisdiction; or (C) if a banking
         moratorium has been declared by a state or federal authority or if any
         new restriction materially adversely affecting the distribution of the
         Firm Shares or the Additional Shares, as the case may be, shall have
         become effective; or (D) if a moratorium in foreign exchange trading

                                       36
<PAGE>   37




         by major international banks or persons has been declared; or (E) if
         the United States becomes engaged in hostilities or there is an
         escalation of hostilities involving the United States or there is a
         declaration of a national emergency or war by the United States; or (F)
         if there shall have been such change in the market for the Company's
         securities or securities in general or in political, financial or
         economic conditions, if the effect of any such event as in your
         judgment makes it inadvisable to proceed with the offering, sale and
         delivery of the Firm Shares or the Additional Shares, as the case may
         be, on the terms contemplated by the Prospectus.

                  (c) Any notice of termination pursuant to this Section 11
         shall be by telephone, telex, or telegraph, confirmed in writing by
         letter.

                  (d) If this Agreement shall be terminated pursuant to any of
         the provisions hereof (otherwise than pursuant to (i) notification by
         you as provided in Section 11(a) hereof or (ii) Sections 9(b) or 11(b)
         hereof), or if the sale of the Shares provided for herein is not
         consummated because any condition to the obligations of the several
         Underwriters set forth herein is not satisfied or because of any
         refusal, inability or failure on the part of the Company or any Selling
         Stockholder to perform any agreement herein or comply with any
         provision hereof, the Company agrees subject to demand by you, to
         reimburse the Underwriters for all out-of-pocket expenses (including
         the fees and expenses of their counsel), incurred by the several
         Underwriters in connection herewith.

                  12. Notice. All communications hereunder, except as may be
otherwise specifically provided herein, shall be in writing and, if sent to any
Underwriter, shall be mailed, delivered, or telexed or telegraphed and confirmed
in writing, to such Underwriter c/o Bear, Stearns & Co., 245 Park Avenue, New
York, N.Y. 10167, Attention: David F. Huff; if sent to the Company or any
Selling Stockholder, shall be mailed, delivered, or telegraphed and confirmed in
writing, in the case of the Company, to the Company, to 6300 Bridge Point
Parkway, Building 2, Suite 500, Austin, Texas 78730, Attention: Ben M. Brigham,
and, in the case of any Selling Stockholder, to 6300 Bridge Point Parkway,
Building 2, Suite 500, Austin, Texas 78730.

                  13. Parties. You represent that you are authorized to act on
behalf of the several Underwriters named in Schedule I hereto, and the Company
and the Selling Stockholders shall be entitled to act and rely on any request,
notice, consent, waiver or agreement purportedly given on behalf of the
Underwriters when the same shall have been given by you on such behalf. This
Agreement shall inure solely to the benefit of, and shall be binding upon, the
several Underwriters, the Selling Stockholders and the Company and the
controlling persons, directors, officers, employees and agents referred to in
Sections 7 and 8, and their respective successors and assigns, and no other
person shall have or be construed to have any legal or equitable right, remedy
or claim under or in

                                       37
<PAGE>   38




respect of or by virtue of this Agreement or any provision herein contained. The
term "successors and assigns" shall not include a purchaser, in its capacity as
such, of Shares from any of the Underwriters.

                  14. Governing Law. This Agreement shall be governed by and
construed in accordance with the laws of the State of New York, but without
regard to principles of conflict of law.

                  15. Counterparts. This Agreement may be executed in any number
of counterparts, each of which shall be deemed to be an original, but all such
counterparts shall together constitute one and the same Agreement.

                  16. Jurisdiction of Disputes. The Company and the Selling
Stockholders hereby submit to the non-exclusive jurisdiction of the Federal and
state courts in the Borough of Manhattan in The City of New York in any suit or
proceeding arising out of or relating to this Agreement or the transactions
contemplated hereby.



                                       38
<PAGE>   39




                  If the foregoing correctly sets forth the understanding among
you, the Company and the Selling Stockholders, please so indicate in the space
provided below for that purpose, whereupon this letter shall constitute a
binding agreement among us.

                                               Very truly yours,

                                               THE COMPANY:

                                               BRIGHAM EXPLORATION COMPANY, a
                                               Delaware corporation

                                               By:
                                                  -----------------------------
                                                        Ben M. Brigham,
                                                        President

                                               SELLING STOCKHOLDERS:

                                               GENERAL ATLANTIC PARTNERS, L.L.C.

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


                                               RESOURCE INVESTORS MANAGEMENT
                                               COMPANY

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


Accepted as of the date first above written.

BEAR, STEARNS & CO. INC.,
DAIN RAUSCHER WESSELS
HOWARD, WEIL, LABOUISSE,
    FRIEDRICHS INCORPORATED

BY BEAR, STEARNS & CO. INC.



By 
  ------------------------------------        

On behalf of themselves and the other several
Underwriters named in Schedule I hereto.


<PAGE>   40




                                   SCHEDULE I

<TABLE>
<CAPTION>


                                                                                     Number of Firm
                                                                                      Shares to be
Name of Underwriter                                                                     Purchased
--------------------                    -------------------------                    --------------
<S>                                                                                     <C>      
Bear, Stearns & Co. Inc
Dain Rauscher Wessels
Howard, Weil, Labouisse, Friedrichs Incorporated


Total....................................................                               3,400,000
</TABLE>






<PAGE>   41

                                   SCHEDULE II


                       Additional Shares to be sold by the
                      Company and the Selling Stockholders

<TABLE>
<CAPTION>

                                                                                            Percentage of
                                              Number of Additional                            Additional
                                               Shares to be Sold                          Shares to be Sold
                                               -----------------                          ------------------   

<S>                                            <C>                                        <C>
General Atlantic Partners, L.L.C.
Resource Investors Management
  Company
</TABLE>







<PAGE>   42



                                  SCHEDULE III

                           Lockup List of Stockholders

Ben M. Brigham
Anne L. Brigham
Jon L. Glass
Craig M. Fleming
David T. Brigham
A. Lance Langford
Karen E. Lynch
Harold D. Carter
Alexis M. Cranberg
Gary J. Milavec
Stephen P. Reynolds
General Atlantic Partners, L.L.C.
Resource Investors Management Company