BRIGHAM EXPLORATION CO
S-1/A, 1997-04-22
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>   1
 
   
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON APRIL 22, 1997
    
 
   
                                                      REGISTRATION NO. 333-22491
    
================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------
   
                                AMENDMENT NO. 1
    
   
                                       TO
    
                                    FORM S-1
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                             ---------------------
                          BRIGHAM EXPLORATION COMPANY
             (Exact name of Registrant as specified in its charter)
 
<TABLE>
<C>                             <C>                             <C>
           DELAWARE
 (State or other jurisdiction                1311                         75-2692967
      of incorporation or        (Primary Standard Industrial          (I.R.S. Employer
          organization)           Classification Code Number)         Identification No.)
</TABLE>
 
                          5949 SHERRY LANE, SUITE 1616
                              DALLAS, TEXAS 75225
                                 (214) 360-9182
  (Address, including zip code, and telephone number, including area code, of
                   Registrant's principal executive offices)
 
                             ---------------------
 
                                 BEN M. BRIGHAM
                       PRESIDENT, CHIEF EXECUTIVE OFFICER
                           AND CHAIRMAN OF THE BOARD
                          BRIGHAM EXPLORATION COMPANY
                          5949 SHERRY LANE, SUITE 1616
                              DALLAS, TEXAS 75225
                                 (214) 360-9182
 (Name, address, including zip code, and telephone number, including area code,
                       of Registrant's agent for service)
 
                             ---------------------
 
                          Copies of Communication to:
 
<TABLE>
<C>                                            <C>
               JOE DANNENMAIER                               ROBERT L. KIMBALL
           THOMPSON & KNIGHT, P.C.                         VINSON & ELKINS L.L.P.
       1700 PACIFIC AVENUE, SUITE 3300                  2001 ROSS AVENUE, SUITE 3700
             DALLAS, TEXAS 75201                            DALLAS, TEXAS 75201
</TABLE>
 
                             ---------------------
 
     APPROXIMATE DATE OF COMMENCEMENT OF PROPOSED SALE TO THE PUBLIC: As soon as
practicable after this Registration Statement.
 
     If any of the securities being registered on this Form are to be offered on
a delayed or continuous basis pursuant to Rule 415 under the Securities Act of
1933, check the following box.  [ ]
 
     If this Form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, please check the following box
and list the Securities Act registration statement number of the earlier
effective registration statement for the same offering.  [ ]
 
     If this Form is a post-effective amendment filed pursuant to Rule 462(c)
under the Securities Act, check the following box and list the Securities Act
registration statement number of the earlier effective registration statement
for the same offering.  [ ]
 
     If delivery of the Prospectus is expected to be made pursuant to Rule 434,
please check the following box.  [X]
 
     THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT SHALL
FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS REGISTRATION
STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH SECTION 8(A) OF
THE SECURITIES ACT OF 1933 OR UNTIL THE REGISTRATION STATEMENT SHALL BECOME
EFFECTIVE ON SUCH DATE AS THE SECURITIES AND EXCHANGE COMMISSION, ACTING
PURSUANT TO SAID SECTION 8(A), MAY DETERMINE.
================================================================================
<PAGE>   2
 
     Information contained herein is subject to completion or amendment. A
     registration statement relating to these securities has been filed with the
     Securities and Exchange Commission. These securities may not be sold nor
     may offers to buy be accepted prior to the time the registration statement
     becomes effective. This prospectus shall not constitute an offer to sell or
     the solicitation of an offer to buy nor shall there be any sale of these
     securities in any State in which such offer, solicitation or sale would be
     unlawful prior to registration or qualification under the securities laws
     of any such State.
 
   
                  SUBJECT TO COMPLETION, DATED APRIL 22, 1997
    
PROSPECTUS
 
   
                                3,000,000 SHARES
    
                       [BRIGHAM EXPLORATION COMPANY LOGO]
   
                                  COMMON STOCK
    
 
   
     The 3,000,000 shares of common stock, par value $.01 per share (the "Common
Stock"), offered hereby are being sold by Brigham Exploration Company ("Brigham"
or the "Company"). Prior to the offering made hereby (the "Offering"), there has
been no public market for the Common Stock. It is currently estimated that the
initial public offering price will be between $9.50 and $11.50 per share. See
"Underwriting" for information relating to the factors to be considered in
determining the initial public offering price. The Common Stock has been
approved for listing on the Nasdaq National Market under the symbol "BEXP."
    
 
                         ------------------------------
 
   
     ANY INVESTMENT IN THE SECURITIES OFFERED HEREIN INVOLVES A HIGH DEGREE OF
RISK. SEE "RISK FACTORS" BEGINNING ON PAGE 10.
    
 
                         ------------------------------
 
  THESE SECURITIES HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE SECURITIES AND
 EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION NOR HAS THE SECURITIES
   AND EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION PASSED UPON THE
ACCURACY OR ADEQUACY OF THIS PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A
                               CRIMINAL OFFENSE.
 
   
<TABLE>
<CAPTION>
==============================================================================================================
                                                                         UNDERWRITING
                                                      PRICE TO          DISCOUNTS AND         PROCEEDS TO
                                                       PUBLIC           COMMISSIONS(1)         COMPANY(2)
- --------------------------------------------------------------------------------------------------------------
<S>                                             <C>                  <C>                  <C>
Per Share......................................          $                    $                    $
- --------------------------------------------------------------------------------------------------------------
Total(3).......................................          $                    $                    $
==============================================================================================================
</TABLE>
    
 
   
(1) The Company and the Selling Stockholders named herein have agreed to
    indemnify the Underwriters against certain liabilities, including
    liabilities under the Securities Act of 1933. See "Underwriting."
    
 
   
(2) Before deducting expenses of the Offering payable by the Company estimated
    at $750,000.
    
 
   
(3) The Company and the Selling Stockholders have granted the Underwriters a
    30-day option to purchase up to 450,000 additional shares of Common Stock on
    the same terms and conditions as set forth above to cover over-allotments,
    if any. If the Underwriters exercise this option in full, the total Price to
    Public will be $          , the total Underwriting Discounts and Commissions
    will be $          , the total Proceeds to Company will be $          and
    the total Proceeds to Selling Stockholders will be $          . See
    "Underwriting."
    
 
                         ------------------------------
 
     The shares of Common Stock are offered, subject to prior sale, when, as and
if delivered to and accepted by the Underwriters and subject certain other
conditions. The Underwriters reserve the right to withdraw, cancel or modify
such offer and to reject orders in whole or in part. It is expected that
delivery of the shares of Common Stock will be made against payment therefor, on
or about             , 1997 at the offices of Bear, Stearns & Co. Inc., 245 Park
Avenue, New York, New York 10167.
 
                         ------------------------------
 
BEAR, STEARNS & CO. INC.
 
                      HOWARD, WEIL, LABOUISSE, FRIEDRICHS
                                     INCORPORATED
 
   
                                                   RAUSCHER PIERCE REFSNES, INC.
    
 
   
                 THE DATE OF THIS PROSPECTUS IS APRIL   , 1997
    
<PAGE>   3
 
   
     [MAP DEPICTING BRIGHAM'S AREAS OF CORE ACTIVITY. The omitted map is
captioned "Core Exploration Provinces" and depicts Texas, Louisiana and
Oklahoma, with three areas marked to indicate the Anadarko Basin, the West Texas
Region and the Gulf Coast. Relating to the area marked Anadarko Basin, the
following information is provided: 1,043 Sq. Miles of 3-D Acquired, 942 Sq.
Miles of 3-D Interpreted, 24 Projects, 325 Potential 3-D Drilling Locations.
Relating to the area marked West Texas Region, the following information is
provided: 1,552 Sq. Miles of 3-D Acquired, 1,552 Sq. Miles of 3-D Interpreted,
73 Projects, 508 Potential 3-D Drilling Locations. Relating to the area marked
Gulf Coast, the following information is provided: 533 Sq. Miles of 3-D
Acquired, 154 Sq. Miles of 3-D Interpreted, 6 Projects, 31 Potential 3-D
Drilling Locations. Under the caption "Other", the following information, set
apart from the three-state map, is provided: 215 Sq. Miles of 3-D Acquired, 189
Sq. Miles of 3-D Interpreted, 22 Projects, 30 Potential 3-D Drilling Locations.
Beneath the map and under the caption "TOTAL," the following information is
provided: 3,343 Sq. Miles of 3-D Acquired, 2,837 Sq. Miles of 3-D Interpreted,
125 Projects, 894 Potential 3-D Drilling Locations.]
    
 
                         ------------------------------
 
   
     CERTAIN PERSONS PARTICIPATING IN THIS OFFERING MAY ENGAGE IN TRANSACTIONS
THAT STABILIZE, MAINTAIN OR OTHERWISE AFFECT THE PRICE OF THE COMMON STOCK,
INCLUDING OVER-ALLOTMENT, STABILIZING AND SHORT-COVERING TRANSACTIONS IN SUCH
COMMON STOCK, AND THE IMPOSITION OF A PENALTY BID, DURING AND AFTER THE
OFFERING. FOR A DESCRIPTION OF THESE ACTIVITIES, SEE "UNDERWRITING."
    
 
                                        2
<PAGE>   4
 
                               PROSPECTUS SUMMARY
 
   
     The following summary should be read in conjunction with, and is qualified
in its entirety by, the detailed information and the Financial Statements and
notes thereto included elsewhere in this Prospectus. All references in this
Prospectus to "Brigham" or the "Company" include Brigham Exploration Company,
its predecessors and their subsidiaries. Unless otherwise indicated, the
information in this Prospectus assumes no exercise of the Underwriters'
over-allotment option. Certain terms relating to the oil and gas industry are
defined in "Glossary of Certain Oil and Gas Terms."
    
 
                                  THE COMPANY
 
   
     Brigham is an independent exploration and production company that applies
3-D seismic imaging and other advanced technologies to systematically explore
and develop onshore domestic natural gas and oil provinces. With this focus,
Brigham has achieved rapid growth in reserves, potential drilling locations and
3-D seismic data.
    
 
   
     Since inception in 1990, Brigham has drilled over 265 exploratory and 35
development wells on its 3-D generated prospects with an aggregate 63% success
rate. Through December 31, 1996, the Company had discovered total estimated
proved reserves of 70.1 Bcf of natural gas and 22.4 MMBbls of oil, or an
aggregate of 204.7 Bcfe, 14% of which is attributable to the Company's interest.
The Company's estimated proved reserves as of December 31, 1996 were 21.9 Bcfe
having an aggregate Present Value of Future Net Revenues of $44.5 million,
compared to estimated proved reserves as of December 31, 1993 of 2.2 Bcfe having
an aggregate Present Value of Future Net Revenues of $3.2 million.
    
 
     The Company pioneered the acquisition of large scale onshore 3-D seismic
surveys for exploration, obtaining extensive 3-D seismic data and experience in
capturing undiscovered natural gas and oil reserves. Brigham has acquired over
3,300 square miles (2,112,000 acres) of 3-D seismic data and, from the 2,837
square miles interpreted to date, has identified approximately 1,200 potential
drilling locations. Brigham has drilled over 300 of these locations with an
average working interest of 21%. The Company generates most of its exploratory
projects and, therefore, has the ability to retain a sizeable working interest
to the extent that it decides not to place interests with industry participants.
In the projects in which it is currently acquiring 3-D seismic data, the Company
may retain an average working interest in the drilling and leasing phases in
excess of 60%.
 
                               BUSINESS STRATEGY
 
   
     Brigham was founded in 1990 with the core belief that systematic
exploration applying 3-D seismic imaging and other advanced technologies could
reduce drilling risks and finding costs. Brigham's business strategy is to
continue to increase shareholder value by focusing on this core belief.
    
 
     Brigham's exploration activities are concentrated primarily in three
provinces: the Anadarko Basin, the Gulf Coast and the West Texas region. The
Company is accelerating its 3-D seismic activity in the Anadarko Basin and the
Gulf Coast and will continue such activity in those geologic trends of the West
Texas region where it has achieved its best results historically. Brigham is
focusing its 3-D seismic activity in provinces where it believes 3-D technology
may be effectively applied and that it believes offer large potential reserve
volumes per well and per field, high potential production rates and multiple
producing objectives.
 
     The Company's growth will be driven by drilling and developing its
potential drilling locations, as well as adding new locations through its
systematic 3-D seismic exploration effort. Using the proceeds of the Offering,
Brigham plans to accelerate growth by (i) increasing the working interest it
retains in drilling locations in order to capture a greater share of the
reserves the Company discovers, (ii) increasing the rate at which it acquires
3-D seismic data and identifies potential drilling locations, (iii) seeking to
identify higher potential drilling locations, (iv) increasing the rate at which
potential drilling locations are drilled and (v) reducing the time spent
marketing projects to industry participants.
                                        3
<PAGE>   5
 
                             COMPETITIVE ADVANTAGES
 
     Brigham believes that its knowledge base, personnel and technology provide
it with the following competitive advantages to capture undiscovered natural gas
and oil reserves.
 
   
          Pioneering Innovations. In 1990 the Company pioneered the
     assemblage of large scale onshore 3-D seismic projects and the use of
     preseismic lease options for the systematic exploration of proven
     natural gas and oil provinces. Subsequent innovations include the
     Company's 3-D seismic acquisition and processing alliances and
     creative industry trade structures to financially leverage its
     drilling program.
    
 
   
          3-D Seismic Knowledge Base. Since inception, the Company has
     acquired over 3,300 square miles of 3-D seismic data and drilled more
     than 300 wells in over 20 geologic trends in six basins and seven
     states. With the resulting knowledge of the application of 3-D seismic
     to different geologic trends, the Company has refined its exploration
     techniques and identified exploration areas where it believes 3-D
     seismic can reduce risks and enhance returns on its investments.
    
 
   
          Technological Expertise. Brigham's explorationists collectively
     have over 200 years of experience, including over 65 years of
     experience using computer aided exploration ("CAEX") workstations, and
     have expertise in many geologic trends.
    
 
   
          Project Generation and Control. Brigham is not dependent on third
     parties for its project flow, having generated approximately 90% of
     its 3-D exploration projects. With the resulting project control, the
     Company is able to manage the predrilling exploration phases and can
     determine the level of working interest it retains and the extent to
     which it manages drilling and post-drilling operations.
    
 
   
          Numerous Potential Drilling Locations. The Company has identified
     approximately 1,200 3-D defined potential drilling locations in
     historically productive geologic trends, of which over 300 have been
     drilled. The Company anticipates drilling 91 of these locations (23.8
     net) in 1997 at a cost of approximately $16.0 million.
    
 
                         PRIMARY EXPLORATION PROVINCES
 
     Brigham's exploration activities are concentrated primarily in three
provinces: the Anadarko Basin, the Gulf Coast and the West Texas region. Brigham
is accelerating 3-D seismic activity in the Anadarko Basin and the Gulf Coast
and will continue such activity in those geologic trends of the West Texas
region where it has achieved its best results historically. Brigham is focusing
its 3-D seismic exploration efforts in provinces where it believes 3-D
technology may be effectively applied and that it believes offer large potential
reserve volumes per well and per field, high potential production rates and
multiple producing objectives.
 
   
     Although the Company is acquiring 3-D seismic data within the provinces
listed below and has identified approximately 900 potential drilling locations
yet to be drilled in those provinces, there can be no assurance that any of the
seismic data will be acquired or will generate additional drilling locations or
that any potential drilling locations will be drilled at all or within the
expected time frame. The final determination with respect to the drilling of any
well, including those currently budgeted, will depend on a number of factors,
including (i) the results of exploration efforts and the review and analysis of
the seismic data, (ii) the availability of sufficient capital resources by the
Company and other participants for drilling prospects, (iii) economic and
industry conditions at the time of drilling, including prevailing and
anticipated prices for natural gas and oil and the availability of drilling rigs
and crews, (iv) the financial resources and results of the Company and (v) the
availability of leases on reasonable terms and permitting for the potential
drilling location. There can be no assurance that the budgeted wells will, if
drilled, encounter reservoirs of commercial quantities of natural gas or oil.
    
                                        4
<PAGE>   6
 
   
<TABLE>
<CAPTION>
                                                   ADDITIONAL 3-D                                      1997
                                                    SEISMIC DATA                     ADDITIONAL      BUDGETED        ESTIMATED
                                   3-D SEISMIC      BUDGETED FOR     TOTAL GROSS     POTENTIAL        WELLS            1997
                                 DATA ACQUIRED/     ACQUISITION     WELLS DRILLED     DRILLING     ------------       CAPITAL
           PROVINCE              INTERPRETED(1)       IN 1997       THROUGH 1996    LOCATIONS(2)   GROSS   NET    EXPENDITURES(3)
           --------              ---------------   --------------   -------------   ------------   -----   ----   ---------------
                                 (SQUARE MILES)    (SQUARE MILES)                                                  (IN THOUSANDS)
<S>                              <C>               <C>              <C>             <C>            <C>     <C>    <C>
Anadarko Basin.................      1,043/942          493               31            325         41     12.3       $15,000
Gulf Coast.....................        533/154          191                1             31          7      2.2         7,000
West Texas Region..............    1,552/1,552           68              255            508         41      8.2         4,000
Other (4)......................        215/189           60               11             30          2      1.1         1,000
                                   -----------          ---              ---            ---         --     ----       -------
        Total..................    3,343/2,837          812(5)           298            894         91     23.8       $27,000
                                   ===========          ===              ===            ===         ==     ====       =======
</TABLE>
    
 
   
- ---------------
    
 
(1) 3-D seismic data that had been or was being acquired/interpreted on February
    15, 1997.
 
(2) The potential drilling locations that had been identified from the portion
    of the 3-D seismic data that had been interpreted by February 15, 1997.
 
(3) 3-D seismic and land acquisition costs and drilling expenditures.
 
(4) Colorado, Kansas and Montana.
 
(5) The Company has budgeted approximately 1,400 square miles of 3-D seismic
    data for acquisition in 1997, 582 of which had been acquired or were being
    acquired on February 15, 1997.
 
     Anadarko Basin. The Anadarko Basin is a prolific natural gas province that
the Company believes has been relatively under explored, particularly with
regard to deep, high potential objectives. The Anadarko Basin contains numerous
historically elusive stratigraphic targets, such as the Red Fork, Morrow and
Springer channel sands, and structural targets, such as the Hunton and Arbuckle
carbonates, which are well-suited to 3-D seismic imaging. In some cases, these
objectives have produced in excess of 30 Bcf of natural gas from a single well
at rates up to 30 MMcf of natural gas per day.
 
   
     The Company has assembled an extensive digital data base in this province,
including geologic studies, basin wide geologic tops, production data, well
data, geographic data and over 7,400 miles of 2-D seismic data. Working with
consulting regional geologists, the Company's explorationists integrate this
data with their expertise and knowledge base to generate 3-D projects in the
Anadarko Basin.
    
 
   
     As of February 15, 1997, the Company had acquired 1,043 square miles
(667,520 acres) of 3-D seismic data in 24 projects in the Anadarko Basin. As of
December 31, 1996, Brigham had completed 23 wells in 31 attempts (a 74% success
rate) in this province and had found cumulative proved reserves of 53.4 Bcf of
natural gas and 1.7 MMBbls of oil, or an aggregate of 63.4 Bcfe, with 16.3%
attributable to the Company's interest. In 1996, the Company completed 14 wells
in 20 attempts, adding 38.8 Bcfe of proved reserves, with 6.7 Bcfe attributable
to the Company's interest. As of February 15, 1997, the Company had 325 3-D
delineated potential drilling locations in the Anadarko Basin, of which the
Company intends to drill 41 gross (12.3 net) wells in 1997.
    
 
     Gulf Coast. The Gulf Coast is a high potential, multi-pay province that
lends itself to 3-D seismic exploration due to its substantial structural and
stratigraphic complexity. The Company has assembled a digital data base
including geographical, production, geophysical and geological information that
the Company evaluates on its CAEX workstations. Working with consulting regional
geologists the Company's explorationists integrate this data with their
expertise and knowledge base to generate 3-D projects in the Gulf Coast.
Brigham's commitment to this province is evidenced by the Company's staff
additions, the opening of its Houston office and the addition of ten new 3-D
seismic projects in 1996 and 1997.
 
     As of February 15, 1997, the Company had acquired or was acquiring 533
square miles (341,120 acres) of 3-D seismic data in six projects in the onshore
Gulf Coast. The Company anticipates acquiring 191 square miles (122,240 acres)
of additional 3-D seismic data in 1997.
 
     The Company anticipates that its increased project assemblage and 3-D
seismic acquisition activity in the Gulf Coast will generate accelerated
drilling in the province in 1997 and 1998. The Company is currently assembling
projects in the Expanded Wilcox, Expanded Vicksburg and Yegua trends in South
Texas, the
                                        5
<PAGE>   7
 
   
Miocene trend in South Texas and South Louisiana, and the Lower and Middle Frio
trends of the upper Gulf Coast of Texas. The Company has thirty-one 3-D
delineated potential drilling locations in the Gulf Coast and intends to drill 7
gross (2.2 net) wells in 1997.
    
 
   
     West Texas Region. The Company's 3-D seismic and drilling activity in the
West Texas region has been focused in the Horseshoe Atoll, the Midland Basin and
the Eastern Shelf of the Permian Basin and the Hardeman Basin. The Company plans
to continue drilling its locations in these areas. Recently the Company
increased its activity in portions of geologic trends that the Company believes
offer greater potential for lower finding costs and higher returns, including
the Ellenberger and Devonian formations of the Delaware Basin and the Fusselman
formation of the Permian Basin. One area where the Company increased its
activity is in the Midland Basin, where the Company has drilled five recent
Fusselman discoveries and has acquired or intends to acquire 3-D seismic in four
additional projects, in which it expects to retain working interests in excess
of 50%.
    
 
   
     As of February 15, 1997, the Company had acquired 1,552 square miles
(993,280 acres) of 3-D seismic in 73 projects in the West Texas region. As of
December 31, 1996, the Company had completed 164 wells in 255 attempts (a 64%
success rate) and had found cumulative proved reserves of 16.7 Bcf of natural
gas and 20.6 MMBbls of oil, or an aggregate of 139.8 Bcfe, with 13.0%
attributable to the Company's interest. In 1996 the Company completed 28 wells
in 43 attempts in this province, adding 29.8 Bcfe of proved reserves, with 5.7
Bcfe attributable to the Company's interest. The Company has 508 3-D delineated
potential drilling locations in the West Texas region and intends to drill 41
gross (8.2 net) wells in 1997.
    
 
                                  THE OFFERING
 
   
<TABLE>
<S>                                                         <C>
Common Stock Offered by the Company.......................  3,000,000 shares
Common Stock to be Outstanding after the Offering.........  11,928,571 shares(1)
Use of Proceeds...........................................  The net proceeds of the Offering will
                                                            be used for exploration and development
                                                            activities, repayment of all
                                                            outstanding indebtedness of
                                                            approximately $10.9 million, and other
                                                            general corporate purposes. See "Use of
                                                            Proceeds."
Nasdaq National Market Symbol.............................  "BEXP"
</TABLE>
    
 
- ---------------
 
   
(1) Does not include 644,097 shares of Common Stock issuable upon exercise of
    outstanding employee stock options with an average exercise price of $5.00
    per share. See "Management -- Executive Compensation" and Note 3 of Notes to
    Balance Sheet and Note 8 of Notes to Financial Statements.
    
 
                                  RISK FACTORS
 
     Any investment in the Common Stock involves a high degree of risk. For a
discussion of certain risks that a potential investor should carefully evaluate
prior to making an investment in the Common Stock, see "Risk Factors."
                                        6
<PAGE>   8
 
                             SUMMARY FINANCIAL DATA
                    (IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)
 
     The following table sets forth certain summary financial data of the
Company. The information should be read in conjunction with the Management's
Discussion and Analysis of Financial Condition and Results of Operations, the
Unaudited Pro Forma Financial Statements and notes thereto and the Financial
Statements and notes thereto included elsewhere in this Prospectus.
 
   
<TABLE>
<CAPTION>
                                                           YEAR ENDED DECEMBER 31,
                                               ------------------------------------------------
                                               1992(1)    1993      1994      1995       1996
                                               -------   -------   -------   -------   --------
<S>                                            <C>       <C>       <C>       <C>       <C>
STATEMENT OF OPERATIONS DATA:
  Revenues:
     Natural gas and oil sales...............  $   244   $   937   $ 2,565   $ 3,578   $  6,141
     Workstation revenue.....................      252       467       815       635        627
                                               -------   -------   -------   -------   --------
          Total revenues.....................      496     1,404     3,380     4,213      6,768
  Costs and expenses:
     Lease operating.........................       32       111       491       761        726
     Production taxes........................       12        47       126       165        362
     General and administrative..............      462     1,433     1,785     1,897      2,199
     Depletion of natural gas and oil
       properties............................      127     4,371(2)   1,104    1,626      2,323
     Depreciation and amortization...........      224       406       561       533        487
                                               -------   -------   -------   -------   --------
          Total costs and expenses...........      857     6,368     4,067     4,982      6,097
                                               -------   -------   -------   -------   --------
  Operating income (loss)....................     (361)   (4,964)     (687)     (769)       671
  Other income (expense):
     Interest income.........................       12         6        56       128         52
     Interest expense........................      (21)     (105)     (668)     (936)    (1,173)
                                               -------   -------   -------   -------   --------
  Net loss...................................  $  (370)  $(5,063)  $(1,299)  $(1,577)  $   (450)
                                               =======   =======   =======   =======   ========
PRO FORMA STATEMENT OF OPERATIONS DATA:
  Net loss(3)(4).............................                                          $    (56)
  Net loss per share(3)(4)...................                                          $   0.00
  Weighted average shares outstanding(3).....                                             9,266
STATEMENT OF CASH FLOWS DATA:
  Net cash provided by (used in) operating
     activities..............................  $  (172)  $  (730)  $   626   $ 1,383   $  3,710
  Net cash used in investing activities......   (3,931)   (6,983)   (5,463)   (8,005)   (11,796)
  Net cash provided by financing
     activities..............................    4,845     7,839     4,634     7,724      7,731
OTHER FINANCIAL DATA:
  Capital expenditures.......................  $ 4,285   $ 6,632   $ 5,445   $ 7,935   $ 13,612
  EBITDA(5)..................................        2      (181)    1,034     1,518      3,533
  Cash flow from operations(6)...............      (19)     (286)      366       582      2,360
</TABLE>
    
 
   
<TABLE>
<CAPTION>
                                                               AS OF DECEMBER 31, 1996
                                                  --------------------------------------------------
                                                                                     PRO FORMA
                                                  ACTUAL     PRO FORMA(3)(4)    AS ADJUSTED(3)(4)(7)
                                                  -------    ---------------    --------------------
<S>                                               <C>        <C>                <C>
BALANCE SHEET DATA:
  Cash and cash equivalents.....................  $ 1,447        $ 1,447              $21,992
  Natural gas and oil properties, net...........   28,005         28,005               28,005
  Total assets..................................   33,614         33,614               54,159
  Notes payable.................................   24,000          8,000                   --
  Total equity..................................    3,244         14,565               43,110
</TABLE>
    
 
                                        7
<PAGE>   9
 
- ---------------
 
(1) Represents the period from inception (May 1, 1992) of the Partnership, the
    Company's predecessor, through December 31, 1992. Operations of the
    predecessor to the Partnership for the period from January 1, 1992 through
    April 30, 1992 were insignificant. See "The Company."
 
(2) Includes a capitalized ceiling impairment of $3.3 million in 1993.
 
(3) Gives effect to the Exchange (see "The Company") and the issuance of stock
    options to employees under the 1997 Incentive Plan as if they had occurred
    on January 1, 1996 for Statement of Operations Data and as of December 31,
    1996 for Balance Sheet Data. See the Unaudited Pro Forma Financial
    Statements and Note 1 of Notes to Financial Statements.
 
   
(4) Prior to the Exchange, the Company's predecessor was classified as a
    partnership for federal income tax purposes. No provision has been made for
    income taxes since these taxes are the responsibility of the partners. The
    pro forma data reflect an income tax benefit in 1996 of $161,000 and a
    deferred tax liability of $5.1 million at December 31, 1996 which would have
    been recorded if the Company's predecessor had been required to pay federal
    income taxes.
    
 
(5) EBITDA represents net income plus income taxes, interest expense and
    depreciation, depletion and amortization expense. EBITDA should not be
    considered in isolation or as a substitute for net income, cash flows from
    operating activities or any other measure of financial performance prepared
    in accordance with generally accepted accounting principles or as a measure
    of a company's profitability or liquidity.
 
(6) Cash flow from operations represents net income plus non-cash items. Cash
    flow from operations should not be considered in isolation or as a
    substitute for net income, cash flows from operating activities or any other
    measure of financial performance prepared in accordance with generally
    accepted accounting principles or as a measure of a company's profitability
    or liquidity.
 
   
(7) As adjusted for the Offering and the application of the estimated $28.5
    million in net proceeds. See "Use of Proceeds."
    
                                        8
<PAGE>   10


 
                       SUMMARY RESERVE AND OPERATING DATA
                             (DOLLARS IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                           YEAR ENDED DECEMBER 31,
                                              --------------------------------------------------
                                              1992(1)     1993      1994       1995      1996(2)
                                              -------    ------    -------    -------    -------
<S>                                           <C>        <C>       <C>        <C>        <C>
3-D SEISMIC ACQUIRED ANNUALLY:
  Gross square miles........................     288        908        423        311        655
  Average project working interest..........      17%        30%        27%        29%        37%

WELLS DRILLED ANNUALLY:
  Gross wells drilled.......................      19         52         73         78         68
  Net wells drilled.........................     1.5        9.2       16.8       18.5       16.0
  Average drilling working interest.........       8%        18%        23%        24%        24%

ESTIMATED PROVED RESERVES (AT YEAR END)(3):
  Natural gas (MMcf)........................      57        227      3,579      4,257     10,257
  Oil (MBbls)...............................      93        336      1,022      1,672      1,940
  Natural gas equivalent (MMcfe)............     614      2,243      9,710     14,288     21,895
  Proved developed reserves as a percentage
     of proved reserves.....................     100%       100%        76%        80%        67%
  Present Value of Future Net Revenues......  $1,083     $3,158    $10,240    $18,222    $44,506

PRODUCTION VOLUMES:
  Natural gas (MMcf)........................       6         59        165        272        698
  Oil (MBbls)...............................      11         50        140        177        227
  Natural gas equivalent (MMcfe)............      74        359      1,002      1,332      2,060

PERCENTAGE OF RESERVES REPLACED(4)..........     936%       533%       809%       368%       500%

PER MCFE DATA:
  Natural gas and oil sales.................  $ 3.32     $ 2.61    $  2.56    $  2.69    $  2.98
  Workstation revenue.......................    3.43       1.30        .81        .48        .30
  Lease operating expenses..................    (.43)      (.31)      (.49)      (.57)      (.35)
  Production taxes..........................    (.16)      (.13)      (.13)      (.12)      (.18)
  General and administrative expenses.......   (6.28)     (3.99)     (1.78)     (1.42)     (1.07)
                                              ------     ------    -------    -------    -------
     Operating margin.......................  $ (.12)    $ (.52)   $   .97    $  1.06    $  1.68
                                              ======     ======    =======    =======    =======
</TABLE>
 
- ---------------
 
(1) Represents the period from inception (May 1, 1992) of the Partnership, the
    Company's predecessor, through December 31, 1992. Operations of the
    predecessor to the Partnership for the period from January 1, 1992 through
    April 30, 1992 were insignificant. See "The Company."
 
   
(2) Net of a sale by the Company in January 1996 of its interest in certain
    properties that accounted for 303 MMcf of natural gas and 277 MBbls of oil
    (1,962 MMcfe of proved reserves) as of December 31, 1995.
    
 
(3) The estimates of reserve and present value data as of December 31, 1996 have
    been prepared in accordance with the SEC's guidelines by Cawley, Gillespie &
    Associates, Inc., the Company's independent petroleum consultants ("Cawley
    Gillespie"). Cawley Gillespie's letter summarizing its December 31, 1996
    reserve report is Appendix A to this Prospectus.
 
(4) Reserve replacement is calculated as reserve additions divided by the
    Company's production for the period.
                                        9
<PAGE>   11
 
                                  RISK FACTORS
 
     Any investment in the Common Stock involves a high degree of risk.
Prospective purchasers of the Common Stock should carefully consider the risk
factors set forth below, as well as the other information contained in this
Prospectus. This Prospectus contains forward-looking statements. Actual results
may differ materially from those projected in the forward-looking statements as
a result of any number of factors, including risk factors set forth below.
 
DEPENDENCE ON EXPLORATORY DRILLING ACTIVITIES
 
   
     The Company's revenues, operating results and future rate of growth are
highly dependent upon the success of its exploratory drilling program, which
will be funded in part with the proceeds of the Offering. Exploratory drilling
involves numerous risks, including the risk that no commercially productive
natural gas or oil reservoirs will be encountered. The cost of drilling,
completing and operating wells is often uncertain, and drilling operations may
be curtailed, delayed or cancelled as a result of a variety of factors,
including unexpected drilling conditions, pressure or irregularities in
formations, equipment failures or accidents, adverse weather conditions,
compliance with governmental requirements and shortages or delays in the
availability of drilling rigs and the delivery of equipment. Despite the use of
3-D seismic and other advanced technologies, exploratory drilling remains a
speculative activity. Even when fully utilized and properly interpreted, 3-D
seismic data and other advanced technologies only assist geoscientists in
identifying subsurface structures and do not enable the interpreter to know
whether hydrocarbons are in fact present in those structures. In addition, the
use of 3-D seismic data and other advanced technologies requires greater
predrilling expenditures than traditional drilling strategies, and the Company
could incur losses as a result of such expenditures. The Company's future
drilling activities may not be successful. There can be no assurance that the
Company's overall drilling success rate or its drilling success rate for
activity within a particular province will not decline. Unsuccessful drilling
activities could have a material adverse effect on the Company's results of
operations and financial condition. The Company often gathers 3-D seismic data
over large areas. The Company's interpretation of data delineates those portions
of an area desirable for drilling. Therefore, the Company may choose not to
acquire option and lease rights prior to acquiring seismic and, in many cases,
the Company may identify a drilling location before seeking option or lease
rights in the location. Although the Company has identified numerous potential
drilling locations, there can be no assurance that they will ever be leased or
drilled or that natural gas or oil will be produced from these or any other
potential drilling locations.
    
 
VOLATILITY OF NATURAL GAS AND OIL PRICES
 
   
     The Company's revenues, operating results and future rate of growth are
highly dependent upon the prices received for the Company's natural gas and oil.
Historically, the markets for natural gas and oil have been volatile and are
likely to continue to be volatile in the future. Various factors beyond the
control of the Company will affect prices of its natural gas and oil, including
worldwide and domestic supplies of natural gas and oil, the ability of the
members of the Organization of Petroleum Exporting Countries to agree to and
maintain oil price and production controls, political instability or armed
conflict in oil-producing regions, the price and level of foreign imports, the
level of consumer demand, the price and availability of alternative fuels, the
availability of pipeline capacity, weather conditions, domestic and foreign
governmental regulations and taxes, and the overall economic environment. During
1996, the high and low prices for oil on the NYMEX were $26.57 per Bbl and
$17.45 per Bbl, and the high and low prices for natural gas on the NYMEX were
$4.57 per MMBtu and $1.76 per MMBtu. It is impossible to predict future natural
gas and oil price movements with certainty. Declines in natural gas and oil
prices may materially adversely affect the Company's financial condition,
liquidity, ability to finance planned capital expenditures and results of
operations. Lower natural gas and oil prices also may reduce the amount of
natural gas and oil that the Company can produce economically. Any significant
decline in the price of oil or natural gas would adversely affect the Company's
revenues and operating income and may require a reduction in the carrying value
of the Company's natural gas and oil properties. See "Risk Factors-Uncertainty
of Reserve Information and Future Net Revenue Estimates" and "Business and
Properties -- Competition."
    
 
                                       10
<PAGE>   12
 
RISKS ASSOCIATED WITH MANAGEMENT OF GROWTH AND IMPLEMENTATION OF GROWTH STRATEGY
 
     The Company's rapid growth has placed, and is expected to continue to
place, a significant strain on the Company's financial, technical, operational
and administrative resources. As the Company increases the number of projects it
is evaluating or in which it is participating, there will be additional demands
on the Company's financial, technical and administrative resources. In addition,
the Company has only limited experience operating and managing field operations,
including drilling, and there can be no assurances that the Company will be
successful in doing so. Any increase in the Company's activities as an operator
will increase its exposure to operating hazards. See "Risk Factors -- Operating
Hazards and Uninsured Risks." The failure to continue to upgrade the Company's
technical, administrative, operating and financial control systems or the
occurrence of unexpected expansion difficulties, including difficulties in
recruiting and retaining geophysicists, geologists, engineers and sufficient
numbers of qualified personnel to enable the Company to expand its role in the
drilling and production phase, or the reduced availability of seismic gathering,
drilling or other services in the face of growing demand, could have a material
adverse effect on the Company's business, financial condition and results of
operations.
 
SUBSTANTIAL CAPITAL REQUIREMENTS
 
     The Company makes and will continue to make substantial capital
expenditures in its exploration and development projects. The Company intends to
finance these capital expenditures with the net proceeds from the Offering, cash
flow from operations and its existing financing arrangements. Additional
financing may be required in the future to fund the Company's developmental and
exploratory drilling and 3-D seismic acquisition activities. No assurance can be
given as to the availability or terms of any such additional financing that may
be required or that financing will continue to be available under the existing
or new financing arrangements. If additional capital resources are not available
to the Company, its drilling and other activities may be curtailed and its
business, financial condition and results of operations could be materially
adversely affected. See "Use of Proceeds" and "Management's Discussion and
Analysis of Financial Condition and Results of Operations -- Liquidity and
Capital Resources."
 
HISTORICAL OPERATING LOSSES AND VARIABILITY OF OPERATING RESULTS
 
   
     The Company had net losses of approximately $370,000 in 1992, $5.1 million
in 1993, $1.3 million in 1994, $1.6 million in 1995 and $450,000 in 1996. The
Company has incurred net losses in each year of operation, and there can be no
assurance that the Company will be profitable in the future. At December 31,
1996, the Company's pro forma accumulated deficit was $5.1 million, as a result
of recording deferred federal income tax expense as if the Company's partnership
predecessor was a taxable entity, and its pro forma total stockholders' equity
was $14.6 million. In addition, the Company's future operating results may
fluctuate significantly depending upon a number of factors, including industry
conditions, prices of natural gas and oil, rates of drilling success, rates of
production from completed wells and the timing of capital expenditures. This
variability could have a material adverse effect on the Company's business,
financial condition and results of operations. In addition, any failure or delay
in the realization of expected cash flows from operating activities could limit
the Company's ability to invest and participate in economically attractive
projects. See "Selected Financial Data" and "Management's Discussion and
Analysis of Financial Condition and Results of Operations."
    
 
RESERVE REPLACEMENT RISK
 
     In general, production from natural gas and oil properties declines as
reserves are depleted, with the rate of decline depending on reservoir
characteristics. Except to the extent the Company conducts successful
exploration and development activities or acquires properties containing proved
reserves, or both, the proved reserves of the Company will decline as reserves
are produced. The Company's future natural gas and oil production is highly
dependent upon its ability to economically find, develop or acquire reserves in
commercial quantities. The business of exploring for or developing reserves is
capital intensive. To the extent cash flow from operations is reduced and
external sources of capital become limited or unavailable, the Company's ability
to make the necessary capital investment to maintain or expand its asset base of
natural gas and oil
 
                                       11
<PAGE>   13
 
reserves would be impaired. The Company participates in a substantial percentage
of its wells as non-operator. The failure of an operator of the Company's wells
to adequately perform operations, or an operator's breach of the applicable
agreements, could adversely impact the Company. In addition, there can be no
assurance that the Company's future exploration and development activities will
result in additional proved reserves or that the Company will be able to drill
productive wells at acceptable costs. Furthermore, although the Company's
revenues could increase if prevailing prices for natural gas and oil increase
significantly, the Company's finding and development costs could also increase.
See "Management's Discussion and Analysis of Financial Condition and Results of
Operations."
 
OPERATING HAZARDS AND UNINSURED RISKS
 
   
     The Company's operations are subject to hazards and risks inherent in
drilling for and producing and transporting natural gas and oil, such as fires,
natural disasters, explosions, encountering formations with abnormal pressures,
blowouts, cratering, pipeline ruptures and spills, any of which can result in
the loss of hydrocarbons, environmental pollution, personal injury claims and
other damage to properties of the Company and others. As protection against
operating hazards, the Company maintains insurance coverage against some, but
not all, potential losses. The Company may elect to self-insure if management
believes that the cost of insurance, although available, is excessive relative
to the risks presented. The Company generally maintains insurance for the
hazards and risks inherent in drilling for and producing and transporting
natural gas and oil and believes this insurance is adequate. Nevertheless, the
occurrence of an event that is not covered, or not fully covered, by insurance
could have a material adverse effect on the Company's financial condition and
results of operations. In addition, pollution and environmental risks generally
are not fully insurable. See "Business and Properties -- Operating Hazards and
Uninsured Risks."
    
 
UNCERTAINTY OF RESERVE INFORMATION AND FUTURE NET REVENUE ESTIMATES
 
     Numerous uncertainties are inherent in estimating quantities of proved
reserves and their values, including many factors beyond the Company's control.
The reserve information in this Prospectus is an estimate only. Although the
Company believes these estimates are reasonable, reserve estimates are imprecise
and are expected to change as additional information becomes available.
 
     Estimates of natural gas and oil reserves by necessity are projections
based on engineering data, and uncertainties are inherent in the interpretation
of this data, the projection of future rates of production and the timing of
development expenditures. Reserve engineering is a subjective process of
estimating underground accumulations of natural gas and oil that are difficult
to measure. The accuracy of any reserve estimate is a function of the quality of
available data, engineering and geologic interpretation, and judgment. Estimates
of economically recoverable natural gas and oil reserves and of future net cash
flows depend upon a number of variable factors and assumptions, such as
historical production from the area compared with production from other
producing areas, the assumed effects of regulations by governmental agencies,
and assumptions concerning future natural gas and oil prices, future operating
costs, severance and excise taxes, development costs and workover and remedial
costs, all of which may in fact vary considerably from actual results. For these
reasons, estimates of the economically recoverable quantities of natural gas and
oil attributable to any particular group of properties, classifications of
reserves based on risk of recovery, and estimates of the future net cash flows
may vary substantially. Moreover, there can be no assurance that the Company's
reserves will ultimately be produced or that the Company's proved undeveloped
reserves will be developed within the periods anticipated. Any significant
variance in the assumptions could materially affect the estimated quantity and
value of the Company's reserves. Actual production, revenues and expenditures
with respect to the Company's reserves will likely vary from estimates, and such
variances may be material. See "Business and Properties -- Natural Gas and Oil
Reserves."
 
   
     The Present Value of Future Net Revenues referred to in this Prospectus
should not be construed as the current market value of the estimated natural gas
and oil reserves attributable to the Company's properties. In accordance with
applicable requirements of the SEC, the estimated discounted future net cash
flows from proved reserves are generally based on prices and costs as of the
date of the estimate, whereas actual future prices and costs may be materially
higher or lower. At December 31, 1996, the date Cawley Gillespie
    
 
                                       12
<PAGE>   14
 
   
estimated the Company's reserves and present value data, the prices of natural
gas and oil on the NYMEX were $2.76 per MMBtu and $25.92 per Bbl, respectively.
At March 31, 1997, the prices were $1.93 per MMBtu and $20.41 per Bbl,
respectively. Actual future net cash flows also will be affected by factors such
as the amount and timing of actual production, supply and demand for natural gas
and oil, curtailments or increases in consumption by gas purchasers, and changes
in governmental regulations or taxation. The timing of actual future net cash
flows from proved reserves, and thus their actual present value, will be
affected by the timing of both the production and the incurrence of expenses in
connection with development and production of natural gas and oil properties. In
addition, the 10% discount factor, which must be used to calculate discounted
future net cash flows for reporting purposes, is not necessarily the most
appropriate discount factor based on interest rates in effect from time to time
and risks associated with the Company or the oil and gas industry in general.
    
 
COMPETITION
 
     The Company operates in the highly competitive areas of natural gas and oil
exploration, exploitation, acquisition and production with other companies. In
seeking to acquire desirable producing properties or new leases for future
exploration and in marketing its natural gas and oil production, as well as in
seeking to acquire the equipment and expertise necessary to operate and develop
those properties, the Company faces intense competition from a large number of
independent, technology-driven companies as well as both major and other
independent natural gas and oil companies. Many of these competitors have
financial and other resources substantially in excess of those available to the
Company. See "Business and Properties -- Competition." The effects of this
highly competitive environment could have a material adverse effect on the
Company.
 
COMPLIANCE WITH GOVERNMENT REGULATIONS
 
     The Company's business is subject to federal, state and local laws and
regulations relating to the exploration for, and the development, production and
transportation of, natural gas and oil, as well as safety matters. Although the
Company believes it is in substantial compliance with all applicable laws and
regulations, legal requirements are frequently changed and subject to
interpretation, and the Company is unable to predict the ultimate cost of
compliance with these requirements or their effect on its operations.
Significant expenditures may be required to comply with governmental laws and
regulations. See "Business and Properties -- Governmental Regulation."
 
COMPLIANCE WITH ENVIRONMENTAL REGULATIONS
 
     The Company's operations are subject to complex environmental laws and
regulations adopted by federal, state and local governmental authorities.
Environmental laws and regulations are frequently changed. The implementation of
new, or the modification of existing, laws or regulations could have a material
adverse effect on the Company. The discharge of natural gas, oil, or other
pollutants into the air, soil or water may give rise to significant liabilities
on the part of the Company to the government and third parties and may require
the Company to incur substantial costs of remediation. No assurance can be given
that existing environmental laws or regulations, as currently interpreted or
reinterpreted in the future, or future laws or regulations will not materially
adversely affect the Company's results of operations and financial condition.
See "Business and Properties -- Environmental Matters."
 
RISK OF HEDGING ACTIVITIES
 
   
     In an attempt to reduce its sensitivity to energy price volatility, the
Company uses swap arrangements that generally result in a fixed price over a
period of six months. If the Company's reserves are not produced at rates
equivalent to the hedged position, the Company would be required to satisfy its
obligations under hedging contracts on potentially unfavorable terms without the
ability to hedge that risk through sales of comparable quantities of its own
production. Further, the terms under which the Company enters into hedging
contracts are based on assumptions and estimates of numerous factors such as
cost of production and pipeline and other transportation costs to delivery
points. Substantial variations between the assumptions and estimates
    
 
                                       13
<PAGE>   15
 
   
used by the Company and actual results experienced could materially adversely
affect the Company's anticipated profit margins and its ability to manage the
risk associated with fluctuations in natural gas and oil prices. Additionally,
hedging contracts limit the benefits the Company will realize if actual prices
rise above the contract prices. In addition, hedging contracts are subject to
the risk that the other party may prove unable or unwilling to perform its
obligations under such contracts. Any significant nonperformance could have a
material adverse financial effect on the Company. As of December 31, 1996, the
Company had approximately 37.1% of its average monthly oil production (based on
fourth quarter production) committed to hedging contracts through May 1997.
These arrangements provide for the Company to exchange a floating market price
for a fixed contract price. Payments are made by the Company when the floating
price exceeds the fixed price for a contract month and payments are received
when the fixed price exceeds the floating price. Settlements on these swaps are
based on the difference between the average daily closing NYMEX price for a
contract month and the fixed contract price for the same month. In 1996 the
Company did not hedge any of its natural gas production. For the year ended
December 31, 1996, the Company realized a reduction in revenues attributable to
oil hedges of $301,280. See "Management's Discussion and Analysis of Financial
Condition and Results of Operations -- Other Matters."
    
 
MARKETABILITY OF PRODUCTION
 
     The marketability of the Company's production depends in part upon the
availability, proximity and capacity of natural gas gathering systems, pipelines
and processing facilities. The Company delivers natural gas through gas
gathering systems and gas pipelines that it does not own. Federal and state
regulation of natural gas and oil production and transportation, tax and energy
policies, changes in supply and demand and general economic conditions all could
adversely affect the Company's ability to produce and market its natural gas and
oil. Any dramatic change in market factors could have a material adverse effect
on the Company.
 
DEPENDENCE ON KEY PERSONNEL
 
     The Company has assembled a team of geologists, geophysicists and engineers
having considerable experience applying 3-D imaging technology. The Company is
dependent upon the knowledge, skills and experience of these experts to provide
3-D imaging and assist the Company in reducing the risks associated with its
participation in natural gas and oil exploration projects. In addition, the
success of the Company's business also depends to a significant extent upon the
abilities and continued efforts of its management, particularly Ben M. Brigham,
the Company's President, Chief Executive Officer and Chairman of the Board. The
Company has an employment agreement with Ben M. Brigham, but does not have an
employment agreement with any of its other employees. The Company has key man
life insurance on Mr. Brigham in the amount of $2.0 million. The loss of
services of key management personnel or the Company's technical experts, or the
inability to attract additional qualified personnel, could have a material
adverse effect on the Company's business, financial condition, results of
operations, development efforts and ability to grow. There can be no assurance
that the Company will be successful in attracting and retaining such executives,
geophysicists, geologists and engineers. See "Management -- Directors and
Executive Officers" and "Business and Properties -- Exploration Staff."
 
CONTROL BY EXISTING STOCKHOLDERS
 
   
     Upon completion of the Offering, directors, executive officers and
principal stockholders of the Company, and certain of their affiliates, will
beneficially own approximately 74.7% of the Company's outstanding Common Stock
(approximately 71.8% if the Underwriters exercise the over-allotment option in
full). Accordingly, these stockholders, as a group, will be able to control the
outcome of stockholder votes, including votes concerning the election of
directors, the adoption or amendment of provisions in the Company's Certificate
of Incorporation or Bylaws and the approval of mergers and other significant
corporate transactions. The existence of these levels of ownership concentrated
in a few persons make it unlikely that any other holder of Common Stock will be
able to affect the management or direction of the Company. These factors may
also have the effect of delaying or preventing a change in the management or
voting control of the Company. See "Principal Stockholders."
    
 
                                       14
<PAGE>   16
 
CERTAIN ANTITAKEOVER CONSIDERATIONS
 
     The Company's Certificate of Incorporation authorizes the Board of
Directors of the Company to issue up to 10.0 million shares of preferred stock
without stockholder approval and to set the rights, preferences and other
designations, including voting rights, of those shares as the Board of Directors
may determine. These provisions, alone or in combination with the matters
described in "Risk Factors -- Control by Existing Stockholders," may discourage
transactions involving actual or potential changes of control of the Company,
including transactions that otherwise could involve payment of a premium over
prevailing market prices to holders of Common Stock. The Company also is subject
to provisions of the Delaware General Corporation Law that may make some
business combinations more difficult. See "Description of Capital Stock --
Delaware Law Provisions."
 
SHARES ELIGIBLE FOR FUTURE SALE; REGISTRATION RIGHTS
 
   
     Sales of a substantial number of shares of Common Stock in the public
market following the Offering could adversely affect the market price for the
Common Stock. The Company believes all of the shares of Common Stock currently
outstanding, 8,928,571 shares, will be eligible for sale under Rule 144 on
February 27, 1998, subject to compliance with the volume and other limitations
of Rule 144. Investors holding 8,421,428 shares have the right to require the
Company to register the public resale of their shares before that time. Holders
of approximately 8,928,571 shares are entitled to "piggyback" registration
rights. Approximately 8,908,571 shares are subject to "lock-up" agreements from
which they will be released 180 days after the date of this Prospectus. Options
covering 644,097 shares of Common Stock have been issued, with an exercise price
of $5.00 per share, subject to vesting. See "Shares Eligible for Future Sale"
and "Description of Capital Stock -- Registration Rights."
    
 
IMMEDIATE AND SUBSTANTIAL DILUTION
 
     Purchasers of the Common Stock in the Offering will experience an immediate
and substantial dilution in pro forma net tangible book value per share. See
"Dilution."
 
NO PRIOR PUBLIC MARKET; POSSIBLE STOCK PRICE VOLATILITY
 
     Before the Offering, there has been no public market for the Common Stock,
and an active public market for the Common Stock may not develop or be
sustained. The initial public offering price will be determined through
negotiation between the Company and the Representatives of the Underwriters
based on several factors that may not be indicative of future market prices. See
"Underwriting" for a discussion of the factors to be considered in determining
the initial public offering price. The trading price of the Common Stock and the
price at which the Company may sell securities in the future could be subject to
large fluctuations in response to changes in government regulations, quarterly
variations in operating results, litigation, general market conditions, the
prices of natural gas and oil, announcements by the Company and its competitors,
the liquidity of the Company, the Company's ability to raise additional funds
and other events.
 
                                       15
<PAGE>   17
 
                                  THE COMPANY
 
   
     Brigham was formed in February 1997 and is the holding company for Brigham
Oil & Gas, L.P. (the "Partnership"), a Texas limited partnership. Brigham, Inc.
was formed as a Texas corporation in September 1990 to pursue natural gas and
oil exploration using 3-D seismic technology. The Partnership was formed in May
1992 by contribution of assets of Brigham, Inc., and its general partners were
General Atlantic Partners III, L.P., a Delaware limited partnership ("GAP III"),
and Brigham, Inc. Under the Exchange Agreement (the "Exchange Agreement"),
effective February 27, 1997, the following transactions occurred: (i) GAP III
and the limited partners of the Partnership transferred all their partnership
interests to the Company in exchange for an aggregate of 3,314,286 shares of
Common Stock, (ii) the stockholders of Brigham, Inc. transferred all the issued
and outstanding stock of Brigham, Inc. to the Company in exchange for an
aggregate of 3,859,821 shares of Common Stock and (iii) Resource Investors
Management Company ("RIMCO") exchanged all of the 5% Convertible Unsecured
Subordinated Notes of the Partnership for 1,754,464 shares of Common Stock.
These transactions are referred to in this Prospectus as the "Exchange."
Following the Exchange, the Company owns all the general and limited partnership
interests in the Partnership and no instruments, agreements or rights exist
which may be converted, exchanged into, or otherwise become interests in the
Partnership. The stockholders of Brigham, Inc. were Ben M. Brigham, President,
Chief Executive Officer and Chairman of the Board of the Company, and Anne L.
Brigham, Executive Vice President and a Director of the Company. The limited
partners of the Partnership included the following officers and/or directors of
the Company, who received shares of Common Stock as indicated: Jon L. Glass,
Vice President -- Exploration and a Director (66,964 shares); Craig M. Fleming,
Chief Financial Officer (44,643 shares); David T. Brigham, Vice
President -- Legal (44,643 shares); and Harold D. Carter, a Director (350,893
shares). As a result of the Exchange, Brigham Exploration Company owns, directly
or indirectly, all the partnership interests in the Partnership and conducts its
active business operations through the Partnership. References to the "Company"
or to "Brigham" are to Brigham Exploration Company and its predecessors and
subsidiaries, including the Partnership and Brigham, Inc.
    
 
     Brigham's principal executive offices are located at 5949 Sherry Lane,
Suite 1616, Dallas, Texas 75225, and its telephone number is (214) 360-9182. In
July 1997, the Company intends to relocate its principal executive offices to
6300 Bridgepoint Parkway, Building 2, Suite 500, Austin, Texas 78730.
 
                                USE OF PROCEEDS
 
   
     The net proceeds to the Company from the sale of the shares of Common Stock
offered by the Company are estimated to be approximately $28.5 million ($32.0
million if the Underwriters exercise their over-allotment option in full), based
on an assumed initial public offering price of $10.50 per share and after
deducting the estimated underwriting discounts and commissions and estimated
offering expenses.
    
 
   
     The Company intends to use the net proceeds for exploration and development
activities (including 3-D seismic and land acquisition and drilling for which
the Company had budgeted approximately $27 million in 1997), repayment of all
outstanding indebtedness under the Revolving Credit Facility ($10.9 million at
March 31, 1997), and other general corporate purposes. While the Company
believes that the net proceeds from the Offering, cash flow from operations and
borrowings under the Revolving Credit Facility should allow the Company to
finance its operations at least through 1998 based on current conditions,
additional financing may be required in the future to fund the Company's 3-D
seismic acquisition and drilling programs. The interest rate for borrowings
under the Revolving Credit Facility is either the lender's base rate or LIBOR
plus from 1.75% to 2.25% depending on the amount outstanding under the facility.
At March 31, 1997 the current rate paid by the Company was 8.0%. See
"Management's Discussion and Analysis of Financial Condition and Results of
Operations -- Liquidity and Capital Resources -- Revolving Credit Facility" for
a description of the Revolving Credit Facility. Pending application of the net
proceeds of the Offering as described above, they will be invested in
short-term, interest-bearing instruments. The Company will not receive any of
the proceeds from the sale of Common Stock by the Selling Stockholders, which
will occur only if the Underwriters exercise their over-allotment option.
    
 
                                       16
<PAGE>   18
 
                                DIVIDEND POLICY
 
     The Company has never declared or paid cash dividends on its Common Stock
and anticipates that all future earnings will be retained for use in its
business. In addition, the Revolving Credit Facility prohibits the payment of
cash dividends on Common Stock. The Board of Directors of the Company may review
the Company's dividend policy from time to time in light of, among other things,
the Company's earning and financial position. See "Management's Discussion and
Analysis of Financial Condition and Results of Operation -- Liquidity and
Capital Resources" and Note 4 of Notes to Financial Statements.
 
                                    DILUTION
 
   
     The Company's pro forma net tangible book value at December 31, 1996 was
$14.6 million, or approximately $1.63 per share of Common Stock. Pro forma net
tangible book value per share represents the amount of total tangible assets of
the Company reduced by the amount of the Company's total liabilities, divided by
the number of shares of Common Stock outstanding. All amounts below give effect
to the Exchange. After giving effect to the sale by the Company of shares of
Common Stock in the Offering at an assumed initial public offering price of
$10.50 per share and the application of the estimated net proceeds as described
under "Use of Proceeds," the Company's pro forma as adjusted net tangible book
value as of December 31, 1996 would have been $43.1 million, or $3.61 per share.
This represents an immediate increase in pro forma net tangible book value of
$1.98 per share to the Company's existing stockholders and an immediate dilution
in pro forma net tangible book value of $6.89 per share to new investors
purchasing shares of Common Stock in the Offering. The following tables
illustrates the per share dilution in pro forma net tangible book value to new
investors:
    
 
   
<TABLE>
<CAPTION>
                                                                           AMOUNT
                                                      COMMON     --------------------------
                                                      SHARES         TOTAL        PER SHARE
                                                    ----------   --------------   ---------
                                                                 (IN THOUSANDS)
<S>                                                 <C>          <C>              <C>
Actual net tangible book value at December 31,
  1996...........................................           --      $ 3,244
Pro forma adjustments:
  Exchange of common stock for Partnership
     interest....................................    7,174,107           --
  Conversion of subordinated notes...............    1,754,464       16,433
  Deferred tax liability.........................           --       (5,112)
                                                    ----------      -------
Pro forma net tangible book value at December 31,
  1996...........................................    8,928,571       14,565        $ 1.63
Net offering proceeds............................    3,000,000       28,545
                                                    ----------      -------
Pro forma as adjusted net tangible book value at
  December 31, 1996..............................   11,928,571      $43,110        $ 3.61
                                                    ==========      =======



Assumed Initial public offering price per share.............                       $10.50
  Pro forma net tangible book value per share
     of Common Stock at December 31, 1996...................  $     1.63
  Increase per share attributable to new investors..........        1.98
                                                              ----------
Pro forma as adjusted net tangible book value per share.....                         3.61
                                                                                   ------
Pro forma dilution per share to new investors...............                       $ 6.89
                                                                                   ======
</TABLE>
    
 
                                       17
<PAGE>   19
 
     The following table sets forth the number of shares of Common Stock
purchased from the Company, the total consideration paid, and the average price
per share paid by the existing stockholders and new investors (based on the
assumed initial public offering price before deducting estimated underwriting
discounts and commissions and estimated offering expenses):
 
   
<TABLE>
<CAPTION>
                                       SHARES PURCHASED           TOTAL CONSIDERATION       AVERAGE
                                  ---------------------------   ------------------------     PRICE
                                      NUMBER       PERCENTAGE     AMOUNT      PERCENTAGE   PER SHARE
                                  --------------   ----------   -----------   ----------   ---------
<S>                               <C>              <C>          <C>           <C>          <C>
Existing stockholders...........     8,928,571        74.9%     $28,433,100      47.0%      $ 3.18
New investors...................     3,000,000        25.1       31,500,000      53.0        10.50
                                    ----------       -----      -----------     -----
     Total......................    11,928,571       100.0%     $59,933,100     100.0%
                                    ==========       =====      ===========     =====
</TABLE>
    
 
   
     The Company has reserved 1,588,169 shares for future issuance under the
Company's 1997 Incentive Plan. The preceding table excludes options that have
been granted to purchase 644,097 shares with an exercise price of $5.00 per
share, all of which have been granted since December 31, 1996. See
"Management -- Employee Benefit Plans -- 1997 Incentive Plan," Note 3 of Notes
to Balance Sheet and Note 8 of Notes to Financial Statements.
    
 
                                       18
<PAGE>   20
 
                                 CAPITALIZATION
 
   
     The following table sets forth the capitalization of the Company (i) as of
December 31, 1996, (ii) pro forma to give effect to the Exchange and (iii) pro
forma as adjusted for the Offering and the application of the estimated $28.5
million in net proceeds described under "Use of Proceeds." The table should be
read with "Management's Discussion and Analysis of Financial Condition and
Results of Operations," the Unaudited Pro Forma Financial Statements, and the
Financial Statements and notes thereto in this Prospectus.
    
 
   
<TABLE>
<CAPTION>
                                                           AS OF DECEMBER 31, 1996
                                                   ---------------------------------------
                                                                              PRO FORMA
                                                   ACTUAL    PRO FORMA(3)   AS ADJUSTED(4)
                                                   -------   ------------   --------------
                                                               (IN THOUSANDS)
<S>                                                <C>       <C>            <C>
Total debt(1):
  Notes payable..................................  $ 8,000     $ 8,000         $    --
  Subordinated notes payable.....................   16,000          --              --
                                                   -------     -------         -------
                                                    24,000       8,000              --
Partners' capital and stockholders' equity:
  Partners' capital..............................    3,244          --              --
  Preferred Stock, $.01 par value, 10,000,000
     shares authorized; no shares outstanding
     actual, pro forma and pro forma as
     adjusted....................................       --          --              --
  Common Stock, $.01 par value, 30,000,000 shares
     authorized; no shares issued and outstanding
     actual; 8,928,571 shares issued and
     outstanding pro forma; and 11,928,571 shares
     issued and outstanding pro forma as
     adjusted(2).................................       --          89             119
  Additional paid-in capital.....................       --      22,486          51,001
  Unearned stock compensation....................       --      (2,898)         (2,898)
  Accumulated deficit............................       --      (5,112)         (5,112)
                                                   -------     -------         -------
  Total partners' capital and stockholders'
     equity......................................    3,244      14,565          43,110
                                                   -------     -------         -------
Total capitalization.............................  $27,244     $22,565         $43,110
                                                   =======     =======         =======
</TABLE>
    
 
- ---------------
 
(1) See Note 4 of Notes to Financial Statements.
 
   
(2) Excludes 1,588,169 shares of Common Stock the Company has reserved for
    future issuance under the Company's 1997 Incentive Plan, of which options
    have been granted since December 31, 1996 to purchase 644,097 shares with an
    exercise price equal to $5.00 per share. See "Management -- Employee Benefit
    Plans 1997 Incentive Plan," Note 3 of Notes to Balance Sheet and Note 8 of
    Notes to Financial Statements.
    
 
   
(3) Pro forma adjustments include the (i) exchange of 7,174,107 shares of Common
    Stock for all of the Partnership interests, (ii) exchange of 1,754,464
    shares of Common Stock for the Partnership's subordinated notes payable of
    $16 million and $.4 million of deferred interest, (iii) recording of
    unearned compensation of $2.9 million relative to the granting of 644,097
    options to employees for the purchases of the Common Stock, and (iv) the
    recording of deferred federal income tax expense of $5.1 million as if the
    Partnership had been a taxable entity.
    
 
   
(4) Pro forma as adjusted reflects the issuance of 3,000,000 shares of common
    stock at the assumed initial public offering price of $10.50 per share for
    estimated proceeds of $28,545,000, net of estimated underwriting discounts
    and expenses of the Offering.
    
 
                                       19
<PAGE>   21
 
                            SELECTED FINANCIAL DATA
 
     The following selected financial data should be read in conjunction with
"Management's Discussion and Analysis of Financial Condition and Results of
Operations," the Unaudited Pro Forma Financial Statements and notes thereto, and
the Financial Statements and notes thereto included elsewhere in this
Prospectus. All financial data presented, other than pro forma data, below are
derived from audited financial statements.
 
   
<TABLE>
<CAPTION>
                                                                          YEAR ENDED DECEMBER 31,
                                                              ------------------------------------------------
                                                              1992(1)    1993      1994      1995       1996
                                                              -------   -------   -------   -------   --------
<S>                                                           <C>       <C>       <C>       <C>       <C>
STATEMENT OF OPERATIONS DATA:
  Revenues:
    Natural gas and oil sales...............................  $   244   $   937   $ 2,565   $ 3,578   $  6,141
    Workstation revenue.....................................      252       467       815       635        627
                                                              -------   -------   -------   -------   --------
        Total revenues......................................      496     1,404     3,380     4,213      6,768
  Costs and expenses:
    Lease operating.........................................       32       111       491       761        726
    Production taxes........................................       12        47       126       165        362
    General and administrative..............................      462     1,433     1,785     1,897      2,199
    Depletion of natural gas and oil properties.............      127     4,371(2)   1,104    1,626      2,323
    Depreciation and amortization...........................      224       406       561       533        487
                                                              -------   -------   -------   -------   --------
        Total costs and expenses............................      857     6,368     4,067     4,982      6,097
                                                              -------   -------   -------   -------   --------
  Operating income (loss)...................................     (361)   (4,964)     (687)     (769)       671
  Other income (expense):
    Interest income.........................................       12         6        56       128         52
    Interest expense........................................      (21)     (105)     (668)     (936)    (1,173)
                                                              -------   -------   -------   -------   --------
  Net loss..................................................  $  (370)  $(5,063)  $(1,299)  $(1,577)  $   (450)
                                                              =======   =======   =======   =======   ========
 
PRO FORMA STATEMENT OF OPERATIONS DATA:
  Net loss(3)(4)............................................                                          $    (56)
  Net loss per share(3)(4)..................................                                          $   0.00
  Weighted average shares outstanding(3)....................                                             9,266
 
STATEMENT OF CASH FLOWS DATA:
  Net cash provided by (used in) operating activities.......  $  (172)  $  (730)  $   626   $ 1,383   $  3,710
  Net cash used in investing activities.....................   (3,931)   (6,983)   (5,463)   (8,005)   (11,796)
  Net cash provided by financing activities.................    4,845     7,839     4,634     7,724      7,731
 
OTHER FINANCIAL DATA:
  Capital expenditures......................................  $ 4,285   $ 6,632   $ 5,445   $ 7,935   $ 13,612
  EBITDA(5).................................................        2      (181)    1,034     1,518      3,533
  Cash flow from operations(6)..............................      (19)     (286)      366       582      2,360
</TABLE>
    
 
   
<TABLE>
<CAPTION>
                                                                   AS OF DECEMBER 31,
                                  ------------------------------------------------------------------------------------
                                                                                             1996
                                                                         ---------------------------------------------
                                                                                                       PRO FORMA AS
                                   1992     1993      1994      1995     ACTUAL    PRO FORMA(3)(4)   ADJUSTED(3)(4)(7)
                                  ------   -------   -------   -------   -------   ---------------   -----------------
<S>                               <C>      <C>       <C>       <C>       <C>       <C>               <C>
BALANCE SHEET DATA:
  Cash and cash equivalents.....  $  777   $   903   $   700   $ 1,802   $ 1,447       $ 1,447            $21,992
  Natural gas and oil
    properties, net.............   5,541     7,803    11,970    18,538    28,005        28,005             28,005
  Total assets..................   8,056    14,003    15,781    22,916    33,614        33,614             54,159
  Notes payable.................      --     3,000     7,950    16,000    24,000         8,000                 --
  Total equity..................   6,632     6,570     5,271     3,694     3,244        14,565             43,110
</TABLE>
    
 
- ---------------
 
(1) Represents the period from inception (May 1, 1992) of the Partnership, the
    Company's predecessor, through December 31, 1992. Operations of the
    predecessor to the Partnership for the period from January 1, 1992 through
    April 30, 1992 were insignificant. See "The Company."
 
(2) Includes a capitalized ceiling impairment of $3.3 million in 1993.
 
(3) Gives effect to the Exchange (see "The Company") and the issuance of stock
    options to employees under the 1997 Incentive Plan as if they had occurred
    on January 1, 1996 for Statement of Operations
 
                                       20
<PAGE>   22
 
    Data and as of December 31, 1996 for Balance Sheet Data. See the Unaudited
    Pro Forma Financial Statements and Note 1 of Notes to Financial Statements.
 
   
(4) Prior to the Exchange, the Company's predecessor was classified as a
    partnership for federal income tax purposes. No provision has been made for
    income taxes since these taxes are the responsibility of the partners. The
    pro forma data reflect an income tax benefit in 1996 of $161,000 and a
    deferred tax liability of $5.1 million at December 31, 1996 which would have
    been recorded if the Company's predecessor had been required to pay federal
    income taxes.
    
 
(5) EBITDA represents net income plus income taxes, interest expense and
    depreciation, depletion and amortization expense. EBITDA should not be
    considered in isolation or as a substitute for net income, cash flows from
    operating activities or any other measure of financial performance prepared
    in accordance with generally accepted accounting principles or as a measure
    of a company's profitability or liquidity.
 
(6) Cash flow from operations represents net income plus non-cash items. Cash
    flow from operations should not be considered in isolation or as a
    substitute for net income, cash flows from operating activities or any other
    measure of financial performance prepared in accordance with generally
    accepted accounting principles or as a measure of a company's profitability
    or liquidity.
 
   
(7) As adjusted for the Offering and the application of the estimated $28.5
    million in net proceeds. See "Use of Proceeds."
    
 
                                       21
<PAGE>   23
 
                    MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITION AND RESULTS OF OPERATIONS
 
OVERVIEW
 
   
     The Company is an independent exploration and production company that
applies 3-D seismic imaging and other advanced technologies to systematically
explore and develop onshore domestic natural gas and oil provinces. Brigham has
acquired over 3,300 square miles of 3-D seismic, identified approximately 1,200
potential drilling locations and drilled over 300 wells. The Company believes
this performance demonstrates a systematic methodology for finding natural gas
and oil in onshore domestic natural gas and oil provinces.
    
 
   
     Combining its geologic and geophysical expertise with a sophisticated land
effort, the Company manages the majority of its projects from conception through
3-D acquisition, processing and interpretation and leasing. Because it generates
most of its projects, the Company can control the size of the working interest
that it retains as well as the selection of the operator and the non-operating
participants. Additionally, the Company manages the negotiation and drafting of
most of its geophysical exploration agreements, resulting in reduced contract
risk and more consistent deal terms. In 1995, the Company began to manage
operations, on a limited basis, through the drilling and production phases. The
Company had discovered an aggregate of 204.7 Bcfe of proved reserves as of
December 31, 1996. However, primarily due to capital constraints the Company
retained an interest in only approximately 14% of the reserves discovered, or
28.7 Bcfe. Brigham is endeavoring to increase its working interest in its
projects, based on capital availability and perceived risk, and plans to use a
portion of the proceeds of the Offering to retain a larger portion of the value
it creates.
    
 
     Expenditures made in natural gas and oil exploration vary from project to
project depending primarily on the costs related to land, seismic acquisition,
drilling costs and the working interest retained by the Company. Typically, the
Company's participants bear a disproportionate share of the costs of optioning
available acreage and acquiring, processing and interpreting the 3-D seismic
data, and the Company and its participants each bear leasing, drilling and
completion costs in proportion to their ownership interests.
 
   
     From inception through 1993, the Company acquired 1,373 square miles of 3-D
seismic in 63 projects. The majority of the Company's 3-D seismic acquisitions
were concentrated in the Horseshoe Atoll and Eastern Shelf of the Permian Basin
and the Hardeman Basin of West Texas. The Company drilled seventy-nine 3-D
delineated wells during this period, increasing its revenues from natural gas
and oil production to $936,634 in 1993. The Company's production volumes
consisted of 85% oil on an equivalent basis. The Company's average working
interest in these wells was 14%. In 1992, the Company increased its capacity to
finance its project generation and drilling activities through a $10.0 million
private placement of equity. This financing partially funded the Company's
acquisition of 908 square miles of 3-D seismic data in 32 projects in 1993,
which contributed to the Company's reserve growth in subsequent years. The
Company also issued $3.0 million of 10% Senior Secured General Obligation Notes
(the "10% Notes") in 1993.
    
 
   
     During 1994, the Company acquired 423 square miles of 3-D seismic in 16
projects, primarily in the Horseshoe Atoll and Eastern Shelf areas of the
Permian Basin, the Hardeman Basin and the Anadarko Basin. The Company drilled
seventy-three 3-D delineated wells, increasing its revenues from natural gas and
oil production to $2.6 million. The Company's production volumes consisted of
84% oil on an equivalent basis. The Company's average working interest in wells
drilled in 1994 was 23%. To finance its project generation and drilling
activities, the Company supplemented cash flow from operations with capital from
the issuance of $4.9 million of its 10% Notes and the placement of working
interests in projects to industry participants. The Company's acquisition of
seismic data declined in 1994 compared to previous years as the Company
allocated a greater portion of its capital expenditure budget to drilling 3-D
delineated locations.
    
 
     During 1995, the Company significantly expanded its efforts in the Anadarko
Basin of Texas and Oklahoma by acquiring 195 square miles of 3-D seismic in four
projects in this basin, and initiated its exploration program in the Gulf Coast
with the Esperson Dome Project (39 square miles of 3-D seismic). The Company
also continued its efforts in the Horseshoe Atoll and Eastern Shelf areas of the
Permian Basin and the Hardeman Basin by acquiring 77 square miles of 3-D
seismic. The Company drilled seventy-eight 3-D delineated wells, increasing its
revenues from natural gas and oil production to $3.6 million. The Company's
 
                                       22
<PAGE>   24
 
production volumes consisted of 80% oil on an equivalent basis. The Company's
average working interest in wells drilled in 1995 was 24%. To finance its
project generation and drilling activities the Company supplemented cash flow
from operations with capital from the issuance of $2.6 million of the 10% Notes,
the issuance of $16.0 million principal amount of its 5% Convertible Unsecured
Subordinated Notes (the "5% Notes") and the placement of working interests in
projects to industry participants. The Company used $10.5 million of the
proceeds from the issuance of the 5% Notes to retire the then outstanding
balance of the 10% Notes.
 
   
     During 1996, the Company acquired 655 square miles of 3-D seismic data and
continued to focus the majority of its 3-D exploration efforts in the Anadarko
Basin and the Gulf Coast. The Company acquired 457 square miles (70%) of the 3-D
seismic data in eight projects in the Anadarko Basin, making this basin the most
active 3-D acquisition province for the Company in 1996. Brigham also
significantly increased its Gulf Coast activity, adding eight 3-D projects, and
continued to expand its operations through staff additions and opening a Houston
office in January 1997. While an increasing portion of the Company's capital was
dedicated to 3-D seismic and land acquisition and subsequent drilling in the
Anadarko Basin and the Gulf Coast, the Company continued to allocate a
significant amount of capital to the drilling of its potential drilling
locations in the West Texas region. The Company expects that its change in
geographic focus will result in a larger percentage of its reserves consisting
of natural gas. During 1996, the Company drilled sixty-eight 3-D delineated
wells, increasing its revenues from natural gas and oil production to $6.1
million. The Company's production volumes consisted of 66% oil on an equivalent
basis. The Company's average working interest in wells drilled in 1996 was 24%.
The Company's fourth quarter 1996 revenue from natural gas and oil production
increased to $1.9 million from $955,000 in the fourth quarter of 1995. The
Company supplemented cash flow from operations with borrowings under its
Revolving Credit Facility, the sale of producing properties and the placement of
working interests in projects to industry participants to finance its project
generation and drilling activities.
    
 
   
     The Company uses the full-cost method of accounting for its natural gas and
oil properties. Under this method, all acquisition, exploration and development
costs, including certain internal costs that are directly attributable to the
Company's acquisition, exploration and development activities, are capitalized
in the amortizable base of the "full-cost pool" as incurred. Upon the
interpretation by the Company of the 3-D seismic data associated with unproved
properties, the geological and geophysical costs of acreage that is not
specifically identified as prospective are transferred to the amortizable base.
Geological and geophysical costs associated with prospective acreage, as well as
leasehold costs, are transferred to the amortizable base when the prospects are
drilled. The Company records depletion of its full-cost pool using the unit of
production method. To the extent that the costs capitalized in the full-cost
pool (net of depreciation, depletion and amortization and related deferred
taxes) exceed the present value (using a 10% discount rate) of estimated future
net after-tax cash flows from proved natural gas and oil reserves plus the
capitalized cost of unproved properties, such costs are charged to operations.
Once incurred, a write-down of natural gas and oil properties is not reversed at
a later date. See Note 2 of Notes to Financial Statements.
    
 
   
     In connection with the Exchange, the Company issued options to purchase
644,097 shares of Common Stock to certain of its officers and employees. The
Company recorded an unearned stock compensation balance of $2.9 million, of
which approximately one-half will be added to the amortizable base of the
full-cost pool over the vesting period of the options and the balance will be
recorded as a noncash compensation expense of approximately $516,000 in 1997,
$374,000 in 1998 and an aggregate of $457,000 in the five years thereafter.
    
 
   
     The Company's predecessor was classified as a partnership for federal
income tax purposes. Therefore, no income taxes were paid or provided for by the
Company prior to the Exchange. The Company is a taxable entity. Assuming the
Exchange had occurred on December 31, 1996, the Company would have incurred an
estimated charge of $5.1 million to record a deferred tax liability primarily
reflecting the difference between the tax bases and financial statement bases of
the Partnership's natural gas and oil properties. Accordingly, the Company
anticipates that a charge approximating this amount will be recorded in the
first quarter of 1997, when the Exchange occurred.
    
 
                                       23
<PAGE>   25
 
RESULTS OF OPERATIONS
 
     The following table sets forth certain operating data for the periods
presented.
 
<TABLE>
<CAPTION>
                                                            YEAR ENDED DECEMBER 31,
                                                           --------------------------
                                                            1994      1995      1996
                                                           ------    ------    ------
<S>                                                        <C>       <C>       <C>
Production:
  Natural gas (MMcf).....................................     165       272       698
  Oil (MBbls)............................................     140       177       227
  Natural gas equivalent (MMcfe).........................   1,002     1,332     2,060
Average sales prices per unit(1):
  Natural gas (per Mcf)..................................  $ 1.76    $ 1.62    $ 2.30
  Oil (per Bbl)..........................................   16.30     17.76     19.98
  Natural gas equivalent (per Mcfe)......................    2.56      2.69      2.98
Costs and expenses per Mcfe:
  Lease operating........................................  $  .49    $  .57    $  .35
  General and administrative.............................    1.78      1.42      1.07
  Depletion of natural gas and oil properties............    1.10      1.22      1.13
</TABLE>
 
- ---------------
 
(1) Reflects the effects of the Company's hedging activities. See "Management's
    Discussion and Analysis of Financial Condition and Results of
    Operations -- Other Matters -- Hedging Activities."
 
  Year Ended December 31, 1996 Compared to Year Ended December 31, 1995
 
   
     Natural gas and oil sales. Natural gas and oil sales increased 72% from
$3.6 million in 1995 to $6.1 million in 1996. Of this increase, $2.0 million or
76% was attributable to an increase in production, and $607,894 or 24% was
attributable to an increase in the average sales price received for natural gas
and oil. Production volumes for natural gas increased 157% from 271,707 Mcf in
1995 to 698,036 Mcf in 1996. The average price received for natural gas
increased 42% from $1.62 per Mcf in 1995 to $2.30 per Mcf in 1996. Production
volumes for oil increased 28% from 176,693 Bbls in 1995 to 226,925 Bbls in 1996.
The average price received for oil increased 13% from $17.76 per Bbl in 1995 to
$19.98 per Bbl in 1996. Natural gas and oil sales were increased by production
from 43 wells completed in 1996, which was partially offset by the sale of
certain producing properties in January 1996 and the natural decline of existing
production. Hedging activities in 1996 reduced the amount by which oil revenues
increased by $301,280, compared to an increase in oil revenues of $40,849 as a
result of hedging activities in 1995.
    
 
     Workstation revenue. Workstation revenue decreased 1% from $635,401 in 1995
to $627,255 in 1996, primarily as a result of a decrease in the rate at which
3-D seismic data were acquired in 1995 and interpreted in 1996. Workstation
revenue is recognized by Brigham as industry participants in the Company's
seismic programs are charged an hourly rate for the work performed by the
Company on its 3-D seismic interpretation workstations. The Company expects an
increase in workstation revenues in 1997 due to the increase in square miles of
3-D seismic acquired in 1996. Workstation revenue is expected to decline after
1997 due to the Company's increasing its interest in the square miles of 3-D
seismic acquired beginning in 1997, reducing the net hours billed to its
participants.
 
     Lease operating expenses. Lease operating expenses decreased 5% from
$760,784 ($.57 per Mcfe) in 1995 to $725,785 ($.35 per Mcfe) in 1996. The
decrease is primarily due to the sale of certain producing properties in January
1996 partially offset by an increase in producing wells. The decrease in the per
unit rate was a result of the sale of higher cost oil wells in January 1996 and
an increase in the percentage of production from natural gas wells.
 
   
     General and administrative expenses. General and administrative expenses
increased 16% from $1.9 million ($1.42 per Mcfe) in 1995 to $2.2 million ($1.07
per Mcfe) in 1996. Approximately $110,000 of the increase in 1996 resulted from
salary increases for employees, and the rest is primarily attributable to an
increase in third-party consulting fees. The decrease in the per unit rate was a
result of the increase in natural gas and oil production from 1995 to 1996. The
Company expects general and administrative expenses to
    
 
                                       24
<PAGE>   26
 
   
increase in 1997, primarily as a result of a nonrecurring expense related to
relocating its principal executive office to Austin, Texas and the hiring of
additional personnel as the Company's operations grow.
    
 
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 43% from $1.6 million ($1.22 per Mcfe) in 1995 to $2.3
million ($1.13 per Mcfe) in 1996 as a result of higher production volumes.
 
     Interest expense. Interest expense increased 25% from $936,266 in 1995 to
$1.2 million in 1996. This increase was due to a higher average outstanding debt
balance in 1996, which was partially offset by a lower effective interest rate.
The weighted average outstanding debt balance increased 71% from approximately
$11.5 million in 1995 to $19.7 million in 1996. The effective interest rate
decreased 25% from 7.6% in 1995 to 5.7% in 1996. The increase in the weighted
average outstanding debt balance and decrease in the effective interest rate
resulted primarily from the retirement of the 10% Notes and the issuance of
$16.0 million in principal amount of the 5% Notes in August 1995. The Company
entered into the Revolving Credit Facility in April 1996, which had an effective
interest rate of 7.9% at December 31, 1996.
 
  Year Ended December 31, 1995 Compared to Year Ended December 31, 1994
 
     Natural gas and oil sales. Natural gas and oil sales increased 39% from
$2.6 million in 1994 to $3.6 million in 1995. Of this increase, $843,635 or 83%
was attributable to an increase in production and $168,785 or 17% was
attributable to an increase in the average sales price received for natural gas
and oil. Production volumes for natural gas increased 65% from 164,893 Mcf in
1994 to 271,707 Mcf in 1995. The average price received for natural gas
decreased 8% from $1.76 per Mcf in 1994 to $1.62 per Mcf in 1995. Production
volumes for oil increased 27% from 139,560 Bbls in 1994 to 176,693 Bbls in 1995.
The average price received for oil increased 9% from $16.30 per Bbl in 1994 to
$17.76 per Bbl in 1995. Natural gas and oil sales were increased by the
completion of 46 wells in 1995, which was partially offset by the natural
decline of existing production.
 
     Workstation revenue. Workstation revenue decreased 22% from $814,841 in
1994 to $635,401 in 1995, primarily as a result of a decrease in the rate at
which 3-D seismic data were acquired in 1994 and interpreted in 1995.
 
     Lease operating expenses. Lease operating expenses increased 55% from
$491,047 ($.49 per Mcfe) in 1994 to $760,784 ($.57 per Mcfe) in 1995. The
increase was primarily due to an increase in production from new wells and an
increase in the per unit rate. The per unit rate increase was due to natural
production decline in existing wells relative to the cost of operating the
wells.
 
     General and administrative expenses. General and administrative expenses
increased 6% from $1.8 million ($1.78 per Mcfe) in 1994 to $1.9 million ($1.42
per Mcfe) in 1995. The increase was related to salary increases for existing
employees. The decrease in the per unit rate was the result of the increase in
natural gas and oil production from 1994 to 1995.
 
     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 47% from $1.1 million ($1.10 per Mcfe) in 1994 to $1.6
million ($1.22 per Mcfe) in 1995, as a result of higher production volumes and
per unit rates.
 
     Interest expense. Interest expense increased 40% from $667,418 in 1994 to
$936,266 in 1995. This increase was due to a higher average outstanding debt
balance partially offset by a lower effective interest rate in 1995. The
weighted average outstanding debt balance increased 95% from approximately $5.9
million in 1994 to $11.5 million in 1995. The effective interest rate decreased
24% from 10.0% in 1994 to 7.6% in 1995. The increase in the weighted average
outstanding debt balance and decrease in the effective interest rate resulted
from the retirement of the 10% Notes and the issuance of $16.0 million in
principal amount of the 5% Notes in August 1995.
 
                                       25
<PAGE>   27
 
LIQUIDITY AND CAPITAL RESOURCES
 
     The Company's primary sources of capital have been borrowings (primarily
the 10% Notes, the 5% Notes and the Revolving Credit Facility), equity capital
from private sources, the sale of interests in projects and funds generated by
operations. The Company's primary capital requirements are 3-D seismic and land
acquisition costs and drilling expenditures.
 
   
     Revolving Credit Facility. In April 1996, the Company entered into the
Revolving Credit Facility with Bank One, Texas, NA ("Bank One"). This facility
has a three-year term and provides for a maximum borrowing base of $25.0
million, subject to certain borrowing base limitations. Principal outstanding is
due at maturity on March 31, 1999 with interest due monthly. On March 31, 1997,
the borrowing base was $13.7 million and borrowings outstanding under the
Revolving Credit Facility were $10.9 million. The Company intends to repay the
balance then outstanding under the Revolving Credit Facility with a portion of
the net proceeds from the Offering. The Revolving Credit Facility will remain in
place, although the Company intends to reduce the borrowing base in the future.
    
 
     The borrowing base is determined semiannually, in March and September,
based upon the Company's proved natural gas and oil reserves. The interest rate
for borrowings under the Revolving Credit Facility is either the lender's base
rate or LIBOR plus from 1.75% to 2.25%, depending on the amounts outstanding.
The Company is subject to typical covenants and restrictions under the terms of
the Revolving Credit Facility. The Company's obligations under the Revolving
Credit Facility are secured by substantially all of the natural gas and oil
properties of the Company. See Note 4 of Notes to Financial Statements.
 
     5% Notes. In August 1995, the Company entered into a note purchase
agreement with RIMCO under which RIMCO purchased $16.0 million in convertible
subordinated notes due September 1, 2002. These notes were unsecured and bore
interest at 5% per annum, of which 3% was currently payable and 2% was deferred
and payable at the maturity date. The balance outstanding under the 10% Notes
was retired with a portion of the proceeds from the issuance of the $16.0
million in principal amount of the 5% Notes. RIMCO converted these notes and the
deferred interest thereon into a 19.65% equity interest in the Company in
February 1997. The Company will pay RIMCO an amount equal to the interest the
Company would have paid on the 5% Notes through the earlier to occur of the
closing of the Offering or September 30, 1997. See Note 4 of Notes to Financial
Statements.
 
  Cash Flow Analysis
 
     Cash Flows from Operating Activities. Cash flows provided by operating
activities were $3.7 million in 1996, $1.4 million in 1995 and $626,205 in 1994.
Increase in cash flows for 1996 compared to 1995 was due primarily to an
increase in natural gas and oil revenues, net of lease operating expenses,
production taxes and general and administrative expenses. The increase in cash
flows for 1995 compared to 1994 was due primarily to an increase in natural gas
and oil revenues, net of lease operating expenses, production taxes and general
and administrative expenses, and changes in balance sheet items.
 
   
     Cash Flows from Investing Activities. Cash flows used in investing
activities increased to $11.8 million in 1996 compared to $8.0 million in 1995
and $5.5 million in 1994. These increases are directly related to an increase in
capital expenditures. Capital expenditures were $13.6 million in 1996, $7.9
million in 1995 and $5.5 million in 1994. The Company acquired 655 square miles
of 3-D seismic data in 1996, 311 square miles in 1995 and 423 square miles in
1994. The Company's drilling efforts resulted in the successful completion of 42
wells (8.5 net) in 1996, 46 wells (9.9 net) in 1995 and 45 wells (10.3 net) in
1994, which resulted in aggregate increases in PV-10 of $30.8 million in 1996,
$8.7 million in 1995 and $8.2 million in 1994. In 1996, the Company sold
producing properties for $2.1 million.
    
 
     Cash Flows from Financing Activities. Cash flows from financing activities
for 1996 were $7.7 million, primarily as a result of borrowings under the
Revolving Credit Facility. Cash flows from financing activities for 1995 were
$7.7 million, primarily a result of the issuance of the 5% Notes offset by the
net repayment of the $7.9 million outstanding balance on the 10% Notes. Cash
flows from financing activities for 1994 were $4.6 million, primarily a result
of issuances of the 10% Notes.
 
                                       26
<PAGE>   28
 
  Capital Expenditures
 
     The Company estimates capital expenditures in 1997 will be at least $27
million. The Company expects to incur these capital expenditures primarily to
drill 91 gross (23.8 net) planned wells, acquire approximately 1,400 square
miles of 3-D seismic data and continue to add to and upgrade its 3-D seismic
interpretation hardware and software. The actual number of wells drilled and
square miles acquired may differ significantly from these estimates. See
"Business and Properties -- Primary Exploration Provinces."
 
     Due to the Company's active 3-D seismic acquisition and drilling programs,
the Company has experienced and expects to continue to experience substantial
working capital requirements. While the Company believes that the net proceeds
from the Offering, cash flow from operations and borrowings under the Revolving
Credit Facility should allow the Company to finance its operations at least
through 1998 based on current conditions, additional financing may be required
in the future to fund the Company's 3-D seismic acquisition and drilling
programs. In the event additional financing is not available, the Company may be
required to curtail these activities.
 
OTHER MATTERS
 
  Hedging Activities
 
   
     In 1995 the Company, in an attempt to reduce its sensitivity to volatile
commodity prices, began using swap arrangements resulting in a fixed price over
a period of six months. The Company believes that hedging, although not free of
risk, allows the Company to achieve a more predictable cash flow and to reduce
exposure to price fluctuations. However, hedging arrangements, when utilized,
limit the benefit to the Company of increases in the prices of the hedged
commodity. Moreover, the Company's present hedging arrangements apply only to a
portion of its oil production and provide only partial price protection against
declines in oil prices. As of December 31, 1996, the Company had approximately
37.1% of its average monthly oil production (based on fourth quarter production)
committed to hedging contracts through May 1997. These arrangements provide for
the Company to exchange a floating market price for a fixed contract price.
Payments are made by the Company when the floating price exceeds the fixed price
for a contract month and payments are received when the fixed price exceeds the
floating price. Settlements on these swaps are based on the difference between
the average daily closing NYMEX price for a contract month and the fixed
contract price for the same month. Such hedging arrangements may expose the
Company to risk of financial loss in certain circumstances. See "Risk
Factors -- Risk of Hedging Activities." Total oil purchased and sold subject to
the swap arrangements was 118,150 Bbls in 1996 and 54,900 Bbls in 1995. The
Company accounts for all these transactions as hedging activities and,
accordingly, adjusts the price received for oil and gas production during the
period the hedged transactions occur. Adjustments to the price received for oil
under the swap arrangement resulted in an increase in oil revenues of $40,849 in
1995 and a decrease in oil revenues of $301,280 in 1996. There was no hedging in
1994. The Company expects that the amount of its hedges will vary from time to
time. Outstanding hedges at December 31, 1996 were 37,750 Bbls.
    
 
  Effects of Inflation and Changes in Prices
 
     The Company's results of operations and cash flows are affected by changing
natural gas and oil prices. If the price of natural gas and oil increases
(decreases), there could be a corresponding increase (decrease) in revenues as
well as the operating costs that the Company is required to bear for operations.
Inflation has had a minimal effect on the Company.
 
  Environmental and other Regulatory Matters
 
     The Company's business is subject to certain federal, state and local laws
and regulations relating to the exploration for and the development, production
and transportation of, natural gas and oil, as well as environmental and safety
matters. Many of these laws and regulations have become more stringent in recent
years, often imposing greater liability on a larger number of potentially
responsible parties. Although the Company believes it is in substantial
compliance with all applicable laws and regulations, the requirements imposed by
laws and regulations are frequently changed and subject to interpretation, and
the Company is
 
                                       27
<PAGE>   29
 
unable to predict the ultimate cost of compliance with these requirements or
their effect on its operations. Any suspensions, terminations or inability to
meet applicable bonding requirements could materially adversely affect the
Company's financial condition and operations. Although significant expenditures
may be required to comply with governmental laws and regulations applicable to
the Company, compliance has not had a material adverse effect on the earnings or
competitive position of the Company. Future regulations may add to the cost of,
or significantly limit, drilling activity. See "Risk Factors -- Compliance with
Environmental Regulations," "Business and Properties -- Governmental Regulation"
and "Business and Properties -- Environmental Matters."
 
                            BUSINESS AND PROPERTIES
 
   
     Brigham is an independent exploration and production company that applies
3-D seismic imaging and other advanced technologies to systematically explore
and develop onshore domestic natural gas and oil provinces. With this focus,
Brigham has achieved rapid growth in reserves, potential drilling locations and
3-D seismic data.
    
 
   
     Since inception in 1990, Brigham has drilled over 265 exploratory and 35
development wells on its 3-D generated prospects with an aggregate 63% success
rate. From January 1, 1994 through December 31, 1996, the Company had achieved
finding and development costs of $1.05 per Mcfe. These costs included 3-D
seismic and land costs for all of the Company's 3-D delineated locations, of
which it had only drilled a portion. For the same period, the Company achieved a
drilling cost of $.68 per Mcfe of reserves discovered and, in 1996, achieved a
drilling cost of $.37 per Mcfe of reserves discovered.
    
 
   
     Through December 31, 1996, the Company had discovered total estimated
proved reserves of 70.1 Bcf of natural gas and 22.4 MMBbls of oil, or an
aggregate of 204.7 Bcfe, 14% of which is attributable to the Company's interest.
The Company's estimated proved reserves as of December 31, 1996 were 21.9 Bcfe
having an aggregate Present Value of Future Net Revenues of $44.5 million,
compared to estimated proved reserves as of December 31, 1993 of 2.2 Bcfe having
an aggregate Present Value of Future Net Revenues of $3.2 million.
    
 
   
     The Company pioneered the acquisition of large scale onshore 3-D seismic
surveys for exploration, obtaining extensive 3-D seismic data and experience in
capturing undiscovered natural gas and oil reserves. Brigham has acquired over
3,300 square miles (2,112,000 acres) of 3-D seismic data and, from the 2,837
square miles interpreted to date, has identified approximately 1,200 potential
drilling locations. Brigham has drilled over 300 of these locations with an
average working interest of 21%. The Company generates most of its exploratory
projects and, therefore, has the ability to retain a sizeable working interest
to the extent that it decides not to place interests with industry participants.
In the projects in which it is currently acquiring 3-D seismic data, the Company
may retain an average working interest in the drilling and leasing phases in
excess of 60%.
    
 
BUSINESS STRATEGY
 
   
     Brigham was founded in 1990 with the core belief that systematic
exploration applying 3-D seismic imaging and other advanced technologies could
reduce drilling risks and finding costs. Brigham's business strategy is to
continue to increase shareholder value by focusing on this core belief.
    
 
     Brigham's exploration activities are concentrated primarily in three
provinces: the Anadarko Basin, the Gulf Coast and the West Texas region. The
Company is accelerating 3-D seismic activity in the Anadarko Basin and the Gulf
Coast and will continue such activity in those geologic trends of the West Texas
region where it has achieved its best results historically. Brigham is focusing
its 3-D seismic activity in provinces where it believes 3-D technology may be
effectively applied and the Company believes offer large potential reserve
volumes per well and per field, high potential production rates and multiple
producing objectives.
 
     The Company's growth will be driven by drilling and developing its
potential drilling locations, as well as adding new locations through its
systematic 3-D seismic exploration effort. Using the proceeds of the Offering,
Brigham plans to accelerate growth by (i) increasing the working interest it
retains in drilling locations in
 
                                       28
<PAGE>   30
 
order to capture a greater share of the reserves the Company discovers, (ii)
increasing the rate at which it acquires 3-D seismic data and identifies
potential drilling locations, (iii) seeking to identify higher potential
drilling locations, (iv) increasing the rate at which potential drilling
locations are drilled and (v) reducing the time spent marketing projects to
industry participants.
 
COMPETITIVE ADVANTAGES
 
     Brigham believes that its knowledge base, personnel and technology provide
it with the following competitive advantages to capture undiscovered natural gas
and oil reserves.
 
   
          Pioneering Innovations. In 1990 the Company pioneered the
     assemblage of large scale onshore 3-D seismic projects and the use of
     preseismic lease options for the systematic exploration of proven
     natural gas and oil provinces. The Company believes it was one of the
     first to form alliances and joint participation arrangements with
     companies and individuals possessing extensive local geologic or
     operating expertise to complement its 3-D exploration expertise.
     Subsequent innovations include the Company's 3-D seismic acquisition
     and processing alliances and its creative industry trade structures to
     financially leverage its drilling program.
    
 
          3-D Seismic Knowledge Base. The Company began acquiring 3-D
     seismic in 1990 and drilled its first 3-D delineated well, which was a
     discovery, in February 1991. Since inception, the Company has acquired
     over 3,300 square miles of 3-D seismic data and drilled more than 300
     wells in over 20 geologic trends in six basins and seven states. As a
     result, the Company has gained extensive technological and economic
     knowledge relating to the application of 3-D seismic to different
     geologic trends. This experience and knowledge enable the Company to
     refine its exploration techniques and identify exploration areas where
     Brigham believes 3-D seismic can be applied to reduce risks and
     enhance returns on its investments.
 
   
          Technological Expertise. Led by its CEO, who is an experienced,
     practicing geophysicist, the Company has built an exploration staff
     that includes nine other geophysicists and six geologists. Brigham's
     explorationists collectively have over 200 years of experience,
     including over 65 years of experience using CAEX workstations, and
     have expertise in many geologic trends. The Company makes extensive
     use of advanced technologies, including 3-D seismic imaging and CAEX
     and in-house analytical and processing capabilities, to define
     drilling prospects. To support the efforts of its explorationists,
     Brigham has invested in advanced hardware and software, including
     twelve UNIX-based CAEX workstations.
    
 
          Project Generation and Control. Brigham is not dependent on third
     parties for its project flow, having generated approximately 90% of
     its 3-D exploration projects. Therefore, the Company is able to manage
     the predrilling exploration phases, from project conception and
     assemblage through 3-D data acquisition, processing and interpretation
     and subsequent leasing. Brigham believes that its management of the
     exploration process enhances project quality and compresses the cycle
     time, contributing to lower finding and development costs and an
     enhanced project rate of return. Furthermore, the Company can
     determine the level of working interest it retains and the extent to
     which it manages drilling and post-drilling operations and continues
     to expand its efforts in these areas.
 
   
          Numerous Potential Drilling Locations. The Company has identified
     approximately 1,200 3-D defined potential drilling locations in
     historically productive geologic trends, of which over 300 have been
     drilled. The Company anticipates drilling 91 of these locations (23.8
     net) in 1997 at a cost of approximately $16 million. The Company also
     anticipates acquiring approximately 1,400 square miles of 3-D seismic
     data in 1997 at a net cost to the Company of approximately $5.6
     million. The Company continually evaluates and prioritizes potential
     drilling locations to determine whether to drill them, farm them out
     or replace them with higher quality locations.
    
 
                                       29
<PAGE>   31
 
EXPLORATION AND OPERATING APPROACH
 
   
     The Company has acquired 3-D seismic data in approximately 110 projects
covering over 3,300 square miles (2,112,000 acres) in 20 geologic trends in six
basins and seven states. Through this activity, the Company has developed
expertise in the selection of geologic trends that are suitable for 3-D seismic
exploration. Brigham uses experience that it gains within a trend to enhance the
quality of subsequent projects in the same trend and other analogous trends,
contributing to lower finding and development costs, compressing project cycle
times and increasing project rates of return.
    
 
   
     The Company typically acquires 3-D seismic data in and around existing
production where the Company can benefit from the mapping of producing analogs.
These 3-D defined analogs, combined with the Company's experience in drilling
over 300 wells, provide the Company a knowledge base to evaluate other potential
geologic trends, 3-D seismic projects within trends and delineated potential
drilling locations. The Company believes that this experience is a major factor
in the Company's success to date and that this knowledge base differentiates the
Company from its competitors. The Company's knowledge base assists in
identifying geologic trends where Brigham believes it can find and develop large
volumes of natural gas and oil at a low relative cost.
    
 
     The Company has experience in a wide range of reservoir types and geologic
trapping styles, both stratigraphic and structural (including reefs, salt domes,
channel sands, complex faulted and fractured reservoirs and pinchout plays). The
Company seeks to supplement its knowledge base with the best local geologic
expertise available for a particular geologic trend by hiring new
explorationists, engaging consultants and entering into joint ventures with
industry participants. In addition, if the targeted geologic trend is extensive,
the Company typically acquires a digital data base for integration on the
Company's CAEX workstations, including digital land grids, well information, log
curves, production information, geologic studies, geologic top data bases and
existing 2-D seismic data.
 
     The Company uses its knowledge base, local geological expertise and
acquired digital data bases to create 3-D maps of producing reservoirs. The
Company believes its maps are more accurate than previous reservoir maps (which
generally were based on subsurface geological information and surface surveys),
enabling the Company to more precisely evaluate recoverable reserves and the
economic feasibility of projects and drilling locations.
 
   
     Brigham acquires most of its raw 3-D seismic data on a proprietary basis
using vendors. Additionally, the Company acquires data through alliances
affording it the exclusive right to interpret and use data. Occasionally the
Company participates in non-proprietary group shoots of 3-D data. In its
proprietary acquisitions and alliances, Brigham selects the sites of projects,
primarily guided by its knowledge and experience in the core provinces it
explores; establishes and monitors the seismic parameters of each project for
which data is shot; and typically selects the equipment that will be used. Data
is generally priced on the basis of square miles shot. See "Business and
Properties -- Industry Alliances."
    
 
PRIMARY EXPLORATION PROVINCES
 
     Brigham's exploration activities are concentrated primarily in three
provinces: the Anadarko Basin, the Gulf Coast and the West Texas region. Brigham
is accelerating 3-D seismic activity in the Anadarko Basin and the Gulf Coast
and will continue such activity in those geologic trends of the West Texas
region where it has achieved its best results historically. Brigham is focusing
its 3-D seismic exploration efforts in provinces where it believes 3-D
technology may be effectively applied and the Company believes offer large
potential reserve volumes per well and per field, high potential production
rates and multiple producing objectives.
 
     Although the Company is acquiring 3-D seismic data within the provinces
listed below and has identified approximately 900 potential drilling locations
yet to be drilled in those provinces, there can be no assurance that any of the
seismic data will be acquired or will generate additional drilling locations or
that any potential drilling locations will be drilled at all or within the
expected time frame. The final determination with respect to the drilling of any
well, including those currently budgeted, will depend on a number of factors,
including (i) the results of exploration efforts and the review and analysis of
the seismic data, (ii) the availability of
 
                                       30
<PAGE>   32
 
sufficient capital resources by the Company and other participants for drilling
prospects, (iii) economic and industry conditions at the time of drilling,
including prevailing and anticipated prices for natural gas and oil and the
availability of drilling rigs and crews, (iv) the financial resources and
results of the Company and (v) the availability of leases on reasonable terms
and permitting for the potential drilling location. There can be no assurance
that the budgeted wells will, if drilled, encounter reservoirs of commercial
quantities of natural gas or oil.
 
<TABLE>
<CAPTION>
                                         ADDITIONAL 3-D                                      1997
                                          SEISMIC DATA                     ADDITIONAL      BUDGETED        ESTIMATED
                         3-D SEISMIC      BUDGETED FOR     TOTAL GROSS     POTENTIAL        WELLS            1997
                        DATA ACQUIRED/    ACQUISITION     WELLS DRILLED     DRILLING     ------------       CAPITAL
       PROVINCE         INTERPRETED(1)      IN 1997       THROUGH 1996    LOCATIONS(2)   GROSS   NET    EXPENDITURES(3)
       --------         --------------   --------------   -------------   ------------   -----   ----   ---------------
                        (SQUARE MILES)   (SQUARE MILES)                                                 (IN THOUSANDS)
<S>                     <C>              <C>              <C>             <C>            <C>     <C>    <C>
Anadarko Basin........     1,043/942          493               31            325         41     12.3       $15,000
Gulf Coast............       533/154          191                1             31          7      2.2         7,000
West Texas Region.....   1,552/1,552           68              255            508         41      8.2         4,000
Other(4)..............       215/189           60               11             30          2      1.1         1,000
                         -----------          ---              ---            ---         --     ----       -------
Total.................   3,343/2,837          812(5)           298            894         91     23.8       $27,000
                         ===========          ===              ===            ===         ==     ====       =======
</TABLE>
 
- ---------------
 
(1) 3-D seismic data that had been or was being acquired/interpreted on February
    15, 1997.
 
(2) The potential drilling locations that had been identified from the portion
    of the 3-D seismic data that had been interpreted by February 15, 1997.
 
(3) 3-D seismic and land acquisition costs and drilling expenditures.
 
(4) Colorado, Kansas and Montana.
 
(5) The Company has budgeted approximately 1,400 square miles of 3-D seismic
    data for acquisition in 1997, 582 of which had been acquired or were being
    acquired on February 15, 1997.
 
     Anadarko Basin. The Anadarko Basin is a prolific natural gas province that
the Company believes has been relatively under explored, particularly with
regard to deep, high potential objectives. The Anadarko Basin contains numerous
historically elusive stratigraphic targets, such as the Red Fork, Morrow and
Springer channel sands, and structural targets, such as the Hunton and Arbuckle
carbonates, which are well-suited to 3-D seismic imaging. In some cases, these
objectives have produced in excess of 30 Bcf of natural gas from a single well
at rates up to 30 MMcf of natural gas per day.
 
     The Company has assembled an extensive digital data base in this province,
including geologic studies, basin wide geologic tops, production data, well
data, geographic data and over 7,400 miles of 2-D seismic data. Working with
consulting regional geologists, the Company's explorationists integrate this
data with their extensive expertise and knowledge base to generate 3-D projects
in the Anadarko Basin.
 
     Following its initial 3-D seismic acquisition in the province in 1991 (12.5
square miles), the Company acquired 51 square miles of 3-D seismic in 1993. Over
the last several years the Company has accelerated its activity in the Anadarko
Basin, acquiring 151 square miles of 3-D seismic in 1994, 195 square miles in
1995 and 457 square miles in 1996. The Company retained a 33% average working
interest in the 3-D seismic data it acquired in this province in 1996. The
Company believes its increased level of activity in the Anadarko Basin will be a
significant factor in the Company's growth. On February 15, 1997, the Company
had acquired or was acquiring 1,043 square miles (667,520 acres) of 3-D seismic
data in 24 projects in the Anadarko Basin.
 
   
     An example of the Company's success in the Anadarko Basin is the Foster
well, drilled late in 1996 in Lipscomb County, Texas. Identified through the
Company's interpretation of its 34 square mile 3-D program, the Foster well was
drilled to a depth of 10,550 feet, where it encountered 54 feet of gross pay, 33
feet net. The well, in which Brigham has a 22.5% working interest, is currently
producing approximately 3.0 MMcf of gas per day. The field in which the well is
producing is estimated to have total recoverable reserves of 13.2 Bcf of natural
gas from the Foster well and two proved undeveloped locations that the Company
plans to drill in 1997. Brigham is currently completing an exploratory test well
on an analogous prospect in the same project and plans to test other analogous
prospects in 1997. The Company is currently processing a 43 square mile 3-D
project, in which it currently has retained a 37.5% project working interest,
adjacent to the Foster well.
    
 
                                       31
<PAGE>   33
 
     In 1997, the Company plans to drill at least three exploratory wells to
test 3-D delineated Hunton structural prospects in which the Company's working
interest currently ranges from 25% to 42%. These prospects are adjacent to
prolific production from the Hunton formation in fields such as Buffalo Wallow
(approximately 350 Bcfe), Mathers Ranch (approximately 186 Bcfe) and Wheeler Pan
(approximately 130 Bcfe).
 
     As of February 15, 1997, the Company had acquired 1,043 square miles
(667,520 acres) in 24 projects in the Anadarko Basin. As of December 31, 1996,
Brigham had completed 23 wells in 31 attempts (a 74% success rate) in this
province and had found cumulative proved reserves of 53.4 Bcf of natural gas and
1.7 MMBbls of oil, or an aggregate of 63.4 Bcfe, with 16.3% attributable to the
Company's interest. From inception to December 31, 1996, the Company incurred
drilling costs in this province of $.48 per Mcfe. In 1996, the Company completed
14 wells in 20 attempts, adding 38.8 Bcfe of proved reserves, with 6.7 Bcfe
attributable to the Company's interest, at a drilling cost of $.27 per Mcfe. As
of February 15, 1997, the Company had 325 3-D delineated potential drilling
locations in the Anadarko Basin, of which the Company intends to drill 41 gross
(12.3 net) wells in 1997.
 
     Gulf Coast. The Gulf Coast is a high potential, multi-pay province that
lends itself to 3-D seismic exploration due to its substantial structural and
stratigraphic complexity. The Company has assembled a digital data base
including geographical, production, geophysical and geological information that
the Company evaluates on its CAEX workstations. Working with consulting regional
geologists the Company's explorationists integrate this data with their
extensive expertise and knowledge base to generate 3-D projects in the Gulf
Coast. Brigham's commitment to this province is evidenced by the Company's staff
additions, the opening of its Houston office and the addition of ten new 3-D
seismic projects in 1996 and 1997.
 
   
     Brigham initiated its Gulf Coast effort in 1995 with the Esperson Dome
Project in Liberty County, Texas where the Company and its partners currently
control approximately 9,600 gross acres (7,500 net) through leases and farmouts
and have acquired 39 square miles of seismic data. Brigham is not required to
invest capital for its interest until payout, when it earns a variable back-in
working interest of 12% to 20%. Because payout has not yet occurred, no reserves
or production are attributed to this project. The Esperson Dome Field has
produced in excess of 59 MMBbl of oil and 60 Bcf of natural gas to date from a
section of sands in the Miocene, Vicksburg and Yegua/Cook Mountain series
ranging in depth from 1,200 feet to 10,000 feet. The Company has drilled six
wells in the project to date (one Yegua/Cook Mountain and five Vicksburg)
yielding three discoveries. The most significant of these discoveries was
drilled and completed in January 1997 and found over 70 feet of gross pay (65
feet net pay) in a Vicksburg sand at a depth of 5,300 feet. This well tested for
352 Bbls of oil and 400 Mcf of natural gas per day from approximately 20 feet of
perforations. Gross reserves attributed to this discovery and one development
well (plus an additional undrilled development location) are approximately 1.5
MMBbls of oil with associated natural gas. An additional three Vicksburg
prospects have been identified in the project. Brigham also plans to drill
additional wells testing potential prospects in the shallower Miocene sands and
the deeper Yegua/Cook Mountain Sands in the Esperson Dome Project.
    
 
   
     In 1996 the Company initiated the Welder Ranch Project in the South Texas
Expanded Wilcox geologic trend where the Company currently controls 18,000 gross
acres (17,950 net). In and immediately adjacent to the project area production
has been established from prospective pay zones ranging in depth from 1,600 feet
in the Queen City sands to over 15,500 feet in the Lower Wilcox sands. The East
Seven Sisters Field located on the north end of the project area is producing
from the Lower Wilcox and has cumulative production exceeding 360 Bcf of natural
gas. Recent exploration by Sonat, Inc. on a 1,000 acre block located in the
interior of the Company's acreage block has yielded two Lower Wilcox wells.
Brigham is currently in the process of acquiring a 50 square mile 3-D survey
over the Welder Ranch Project that it expects to begin processing in the second
quarter of 1997 and in which the Company currently holds at least a 70% working
interest. In addition to the extensive exploration potential associated with
this project, Brigham also expects to delineate several development locations
adjacent to the recent Sonat activity. The Company is also participating in a
356 square mile 3-D seismic program immediately adjacent to the Welder Ranch
Project.
    
 
                                       32
<PAGE>   34
 
   
     The Company is also undertaking exploratory projects in the prolific
Miocene trend in South Louisiana. The Company's Tigre Point Project is located
immediately south of the developing Freshwater Bayou Field where Unocal and
others have seven wells currently producing over 245 MMcf of natural gas per day
(an average of over 35 MMcf of natural gas per day from each well) from a lower
Miocene sand. This project also offers several shallower objectives as
attractive secondary targets.
    
 
     As of February 15, 1997, the Company had acquired or was acquiring 533
square miles (341,120 acres) of 3-D seismic data in six projects in the onshore
Gulf Coast. The Company anticipates acquiring 191 square miles (122,240 acres)
of additional 3-D seismic data in 1997.
 
     The Company anticipates that its increased project assemblage and 3-D
seismic acquisition activity in the Gulf Coast will generate accelerated
drilling in the province in 1997 and 1998. The Company is currently assembling
projects in the Expanded Wilcox, Expanded Vicksburg and Yegua trends in South
Texas, the Miocene trend in South Texas and South Louisiana, the Lower and
Middle Frio trends of the upper Gulf Coast of Texas. The Company has thirty-one
3-D delineated potential drilling locations in the Gulf Coast and intends to
drill 7 gross (2.2 net) wells in 1997.
 
   
     West Texas Region. The Company's 3-D seismic drilling activity in the West
Texas region has been focused in the Horseshoe Atoll, the Midland Basin and the
Eastern Shelf of the Permian Basin and the Hardeman Basin. The Company plans to
continue drilling its locations in these areas. Recently the Company initiated
an exploration program in the Delaware Basin and increased its activity in
portions of geologic trends that the Company believes offer greater potential
for lower finding costs and higher returns, including the Ellenberger and
Devonian formations of the Delaware Basin and the Fusselman formation of the
Midland Basin.
    
 
   
     One area in which the Company increased its activity is the Midland Basin,
where the Company has drilled five Fusselman discoveries and has acquired or
intends to acquire 3-D seismic in four additional projects, in which it expects
to retain working interests in excess of 50%. Currently the most significant of
these discoveries is the Elizabeth Rose Field, with gross proved reserves
estimated by Cawley Gillespie at December 31, 1996 at 2.1 MMBbls of oil. The
Company has drilled three wells in this Fusselman field that are producing a
total of approximately 500 Bbls of oil per day. Brigham's working interest in
the five Fusselman discoveries ranges from 18.75% to 38.5%. In addition, the
Company owns a 25% to 100% working interest in an additional fifty 3-D defined
potential drilling locations in the adjoining four projects. In 1997 the Company
also plans to acquire 26 square miles of 3-D seismic data in three additional
3-D projects adjacent to the Elizabeth Rose Field and to retain working
interests of 75% to 100% in these projects.
    
 
   
     Among Brigham's higher potential West Texas Region projects is the Longhorn
Project, located in the Delaware Basin, in which the Company owns a 25% working
interest. From its 40 square mile 3-D program acquired in the third quarter of
1996, the Company has identified twenty-three 3-D potential drilling locations
and has leased 6,400 gross acres (1,600 net). The project is surrounded by
prolific production from the Devonian and Ellenberger formations at depths of
15,000 feet to 21,000 feet, in fields such as Evetts (approximately 600 Bcf of
natural gas to date from 16 wells) and War Wink South (approximately 295 Bcf of
natural gas to date from eight wells). The Company plans to spud its first deep
test in the second quarter of 1997.
    
 
   
     As of February 15, 1997, the Company had acquired 1,552 square miles
(993,280 acres) of 3-D seismic in 73 projects in the West Texas region. As of
December 31, 1996, the Company had completed 164 wells in 255 attempts (a 64%
success rate) and had found cumulative proved reserves of 16.7 Bcf of natural
gas and 20.6 MMBbls of oil, or an aggregate of 139.8 Bcfe, with 13.0%
attributable to the Company's interest. From inception to December 31, 1996, the
Company incurred drilling costs in this province of $.76 per Mcfe. In 1996 the
Company completed 28 wells in 43 attempts in this province, adding 29.8 Bcfe of
proved reserves, with 5.7 Bcfe attributable to the Company's interest, at a
drilling cost of $.42 per Mcfe. The Company has 508 3-D delineated potential
drilling locations in the West Texas region and intends to drill 41 gross (8.2
net) wells in 1997.
    
 
                                       33
<PAGE>   35
 
NATURAL GAS AND OIL RESERVES
 
     The Company's estimated total proved reserves of natural gas and oil as of
December 31, 1994, 1995 and 1996 and the present values attributable to these
reserves as of those dates were as follows:
 
<TABLE>
<CAPTION>
                                                              AS OF DECEMBER 31,
                                                         -----------------------------
                                                          1994       1995      1996(1)
                                                         -------    -------    -------
<S>                                                      <C>        <C>        <C>
Estimated proved reserves
  Natural gas (MMcf)...................................    3,579      4,257     10,257
  Oil (MBbls)..........................................    1,022      1,672      1,940
  Natural gas equivalent (MMcfe).......................    9,710     14,288     21,895
Proved developed reserves as a percentage of proved
  reserves.............................................      76%        80%        67%
Present Value of Future Net Revenues(2)
  (in thousands).......................................  $10,240    $18,222    $44,506
</TABLE>
 
- ---------------
 
   
(1) Net of a sale by the Company in January 1996 of its interest in certain
    properties that accounted for 299 MMcf of natural gas and 272 MBbls of oil
    (1,931 MMcfe of proved reserves) as of December 31, 1995.
    
 
   
(2) The Present Value of Future Net Revenues attributable to the Company's
    reserves was prepared using prices in effect at the end of the respective
    periods presented discounted at 10% per annum on a pre-tax basis. The
    estimated pro forma income taxes, discounted at 10% per annum, are
    approximately $12.1 million, resulting in pro forma discounted net cash
    flows of approximately $32.4 million as of December 31, 1996. The effects of
    the Company's hedging activities were immaterial.
    
 
   
     The average prices for the Company's reserves were $1.83 per Mcf of natural
gas and $16.19 per Bbl of oil as of December 31, 1994, $1.85 per Mcf of natural
gas and $18.22 per Bbl of oil as of December 31, 1995, and $3.62 per Mcf of
natural gas and $24.66 per Bbl of oil as of December 31, 1996. The reserve
estimates reflected above for 1996 were prepared by Cawley Gillespie, the
Company's petroleum consultants, and are part of a report on the Company's
natural gas and oil properties prepared by Cawley Gillespie, a summary of which
is Appendix A to this Prospectus.
    
 
   
     In accordance with applicable requirements of the SEC, estimates of the
Company's proved reserves and future net revenues are made using sales prices
estimated to be in effect as of the date of such reserve estimates and are held
constant throughout the life of the properties (except to the extent a contract
specifically provides for escalation). Estimated quantities of proved reserves
and future net revenues therefrom are affected by natural gas and oil prices,
which have fluctuated widely in recent years. At December 31, 1996, the date
Cawley Gillespie estimated the Company's reserves and present value data, the
prices of natural gas and oil on the NYMEX were $2.76 per MMBtu and $25.92 per
Bbl, respectively. At March 31, 1997, the prices were $1.93 per MMBtu and $20.41
per Bbl, respectively. There are numerous uncertainties inherent in estimating
natural gas and oil reserves and their estimated values, including many factors
beyond the control of the Company. The reserve data set forth in this Prospectus
represents only estimates. Reservoir engineering is a subjective process of
estimating underground accumulations of natural gas and oil that cannot be
measured in an exact manner. The accuracy of any reserve estimate is a function
of the quality of available data and of engineering and geologic interpretation
and judgment. As a result, estimates of different engineers, including those
used by the Company, may vary. In addition, estimates of reserves are subject to
revision based upon actual production, results of future development and
exploration activities, prevailing natural gas and oil prices, operating costs
and other factors. The revisions may be material. Accordingly, reserve estimates
are often different from the quantities of natural gas and oil that are
ultimately recovered and are highly dependent upon the accuracy of the
assumptions upon which they are based. The Company's estimated proved reserves
have not been filed with or included in reports to any federal agency. See "Risk
Factors -- Uncertainty of Reserve Information and Future Net Revenue Estimates."
    
 
     Estimates with respect to proved reserves that may be developed and
produced in the future are often based upon volumetric calculations and upon
analogy to similar types of reserves rather than actual production history.
Estimates based on these methods are generally less reliable than those based on
actual production
 
                                       34
<PAGE>   36
 
history. Subsequent evaluation of the same reserves based upon production
history will result in variations in the estimated reserves that may be
substantial.
 
DRILLING ACTIVITIES
 
     The Company drilled, or participated in the drilling of, the following
number of wells during the periods indicated.
 
<TABLE>
<CAPTION>
                                                         YEAR ENDED DECEMBER 31,
                                                ------------------------------------------
                                                    1994           1995           1996
                                                ------------   ------------   ------------
                                                GROSS   NET    GROSS   NET    GROSS   NET
                                                -----   ----   -----   ----   -----   ----
<S>                                             <C>     <C>    <C>     <C>    <C>     <C>
Exploratory Wells:
  Natural gas.................................    6      1.8     5      1.2     4       .9
  Oil.........................................   34      8.3    37      8.1    24      5.4
  Non-productive..............................   26      5.9    32      8.7    24      7.1
                                                 --     ----    --     ----    --     ----
          Total...............................   66     16.0    74     18.0    52     13.4
                                                 ==     ====    ==     ====    ==     ====
Development Wells:
  Natural gas.................................   --       --    --       --     9      1.3
  Oil.........................................    5       .2     4       .6     6      1.2
  Non-productive..............................    2       .6    --       --     1       .1
                                                 --     ----    --     ----    --     ----
          Total...............................    7       .8     4       .6    16      2.6
                                                 ==     ====    ==     ====    ==     ====
</TABLE>
 
     At December 31, 1996, the Company was in the process of drilling 2 gross
(.6 net) wells that are not reflected in the table.
 
     The Company does not own any drilling rigs, and the majority of its
drilling activities are conducted by industry participant operators or
independent contractors under standard drilling contracts.
 
PRODUCTIVE WELLS AND ACREAGE
 
  Productive Wells
 
     The following table sets forth the Company's ownership interest as of
December 31, 1996 in productive natural gas and oil wells in the areas
indicated.
 
<TABLE>
<CAPTION>
                                                 NATURAL GAS       OIL           TOTAL
                                                 -----------   ------------   ------------
                   PROVINCE                      GROSS   NET   GROSS   NET    GROSS   NET
                   --------                      -----   ---   -----   ----   -----   ----
<S>                                              <C>     <C>   <C>     <C>    <C>     <C>
Anadarko Basin.................................   15     3.0     2       .2    17      3.2
Gulf Coast.....................................   --     --     --       --    --       --
West Texas Region..............................    3     1.1    75     17.3    78     18.4
Other..........................................   --     --      1       .5     1       .5
                                                  --     ---    --     ----    --     ----
          Total................................   18     4.1    78     18.0    96     22.1
                                                  ==     ===    ==     ====    ==     ====
</TABLE>
 
     Productive wells consist of producing wells and wells capable of
production, including wells waiting on pipeline connection. Wells that are
completed in more than one producing horizon are counted as one well. Of the
gross wells reported above, none had multiple completions.
 
  Acreage
 
     Undeveloped acreage includes leased acres on which wells have not been
drilled or completed to a point that would permit the production of commercial
quantities of oil and gas, regardless of whether or not such acreage contains
proved reserves. A gross acre is an acre in which an interest is owned. A net
acre is deemed to exist when the sum of fractional ownership interests in gross
acres equals one. The number of net acres is the sum of the fractional interests
owned in gross acres expressed as whole numbers and fractions thereof. The
 
                                       35
<PAGE>   37
 
following table sets forth the approximate developed and undeveloped acreage in
which the Company held a leasehold mineral or other interest at December 31,
1996:
 
<TABLE>
<CAPTION>
                                      DEVELOPED        UNDEVELOPED           TOTAL
                                    --------------   ----------------   ----------------
             PROVINCE               GROSS     NET     GROSS     NET      GROSS     NET
             --------               ------   -----   -------   ------   -------   ------
<S>                                 <C>      <C>     <C>       <C>      <C>       <C>
Anadarko Basin....................   5,646   1,536    45,037   13,669    50,683   15,205
Gulf Coast........................      --      --     3,738    3,226     3,738    3,226
West Texas Region.................   5,087   1,307    38,106   11,380    43,193   12,687
Other.............................      --      --   161,420   58,513   161,420   58,513
                                    ------   -----   -------   ------   -------   ------
  Total...........................  10,733   2,843   248,301   86,788   259,034   89,631
                                    ======   =====   =======   ======   =======   ======
</TABLE>
 
     In addition, the Company has preseismic lease options to acquire an
additional 107,711 acres, substantially all of which expire within one year.
 
     All the leases for the undeveloped acreage summarized in the preceding
table will expire at the end of their respective primary terms unless the
existing leases are renewed or production has been obtained from the acreage
subject to the lease prior to that date, in which event the lease will remain in
effect until the cessation of production. The following table sets forth the
minimum remaining terms of leases for the gross and net undeveloped acreage:
 
<TABLE>
<CAPTION>
                                                               ACRES EXPIRING
                                                              -----------------
                                                               GROSS      NET
                                                              -------    ------
<S>                                                           <C>        <C>
Twelve Months Ending:
  December 31, 1997.........................................   59,133    19,695
  December 31, 1998.........................................  114,661    41,469
  December 31, 1999.........................................   48,928     5,609
  Thereafter................................................   25,579    20,015
                                                              -------    ------
          Total.............................................  248,301    86,788
                                                              =======    ======
</TABLE>
 
VOLUMES, PRICES AND PRODUCTION COSTS
 
     The following table sets forth the production volumes, average prices
received and average production costs associated with the Company's sale of
natural gas and oil for the periods indicated.
 
   
<TABLE>
<CAPTION>
                                                             YEAR ENDED DECEMBER 31,
                                                            --------------------------
                                                             1994      1995      1996
                                                            ------    ------    ------
<S>                                                         <C>       <C>       <C>
Production:
  Natural gas (MMcf)......................................     165       271       698
  Oil (MBbls).............................................     140       177       227
  Natural gas equivalent (MMcfe)..........................   1,002     1,332     2,060
Average sales price:
  Natural gas (per Mcf)...................................  $ 1.76    $ 1.62    $ 2.30
  Oil (per Bbl)...........................................   16.30     17.76     19.98
Average production expenses and taxes (per Mcfe)..........  $  .62    $  .69    $  .53
</TABLE>
    
 
                                       36
<PAGE>   38
 
COSTS INCURRED AND CAPITALIZED COSTS
 
   
     The costs incurred in natural gas and oil acquisition, exploration and
development activities follow (in thousands):
    
 
   
<TABLE>
<CAPTION>
                                                                 DECEMBER 31,
                                                              ------------------
                                                               1995       1996
                                                              -------    -------
<S>                                                           <C>        <C>
Costs incurred for the year:
  Exploration...............................................  $ 6,893    $10,527
  Property acquisition......................................    1,885      6,195
  Development...............................................      713      1,328
  Proceeds from participants................................   (1,296)    (4,111)
                                                              -------    -------
                                                              $ 8,195    $13,939
                                                              =======    =======
</TABLE>
    
 
   
     Costs incurred represent amounts incurred by the Company for exploration,
property acquisition and development activities. Periodically, the Company will
receive proceeds from participants subsequent to project initiation for an
assignment of an interest in the project. These payments are represented by
proceeds from participants.
    
 
EXPLORATION STAFF
 
     Over the last six years the Company has assembled an exploration staff that
includes nine geophysicists, six geologists, one petroleum engineer, three
computer applications specialists, three geophysical/geological/engineering
technicians, four landmen and three lease and division order analysts. Brigham's
nine geophysicists have different but complementary backgrounds, and their
diversity of experience in varied geological and geophysical settings, combined
with various technical specializations (from hardware and systems to software
and seismic data processing), provide the Company with valuable technical
intellectual resources. The Company's team of explorationists have over 200
years of exploration experience and approximately 65 years of 3-D CAEX
workstation experience, most of which was acquired at Brigham and various major
and large independent oil companies. The Company complements and leverages its
exploration staff by seeking out alliances or retainer relationships with
geologists having extensive experience in a particular area of interest.
 
3-D SEISMIC TECHNOLOGY
 
     The Company's strategy is to use 3-D seismic and other advanced
technologies, including CAEX, to systematically explore and develop domestic
onshore natural gas and oil provinces. In general, 3-D seismic is the process of
acquiring seismic data along multiple lines and grids. The primary advantage of
3-D seismic over 2-D seismic is that it provides information with respect to
multiple horizontal and vertical points within a geologic formation instead of
information on a single vertical line or multiple vertical lines within the
formation. Acquiring larger amounts of data relating to a geologic formation
allows a user to better correlate the data and, in some cases, obtain a greater
understanding and image of the formation. Although it is impossible to predict
with certainty the specific configuration or composition of any underground
geologic formation, the use of 3-D seismic data provides clearer and more
accurate projected images of complex geologic formations, which can assist a
user in evaluating whether to drill for natural gas and oil reserves. If a
decision to drill is made, 3-D seismic data can also help in determining the
optimal location to drill.
 
     CAEX is the process of accumulating and analyzing the various seismic,
production and other data obtained relating to a geographic area. In general,
CAEX involves accumulating various 2-D and 3-D seismic data with respect to a
potential drilling location, correlating that data with historical well control
and production data from similar properties and analyzing the available data
through computer programs and modeling techniques to project the likely geologic
composition of a potential drilling location and potential locations of
undiscovered natural gas and oil reserves. This process relies on a comparison
of actual data with respect to the potential drilling location and historical
data with respect to the density and sonic characteristics
 
                                       37
<PAGE>   39
 
of different types of rock formations, hydrocarbons and other subsurface
minerals, resulting in a projected three dimensional image of the subsurface.
This modeling is performed through the use of advanced interactive computer
workstations and various combinations of available computer programs that have
been developed solely for this application.
 
   
     Brigham has invested extensively in the advanced computer hardware and
software necessary for 3-D seismic exploration. The Company has both Landmark
and Geoquest CAEX workstations. This workstation flexibility provides the
Company the opportunity to interpret a project on the particular CAEX
workstation that it believes is best suited for defining those particular
geologic objectives. Brigham's explorationists can access a diverse software
tool kit including SeisWorks, StratWorks, SeisCube, SurfCube, ZAP, Zmap+, ARIES,
SynTool, Poststack, Continuity Cube, TDQ, AutoPix, MapView, GeoViz, Voxels,
SynView, CSA (Computed Seismic Attributes), Surface Slice, Hampson -- Russell
AVO Analysis and Modeling and ZEH Graphics CGMage Builder (graphics montage
tool).
    
 
     The Company believes that its use of 3-D seismic technology provides it
with a number of benefits in the exploration, delineation and development
process that are not generally available to those who only use 2-D seismic data
and conventional processing methods. In particular, the Company believes that it
obtains clearer and more accurate projected images of underground formations
through computer modeling, and is therefore better able to identify potential
locations of hydrocarbon accumulations based on the characteristics of the
formations and analogies made with nearby fields and formations where
hydrocarbons have been found. This enhanced data has been used to assist the
Company in eliminating potential drilling locations that might otherwise have
been drilled had the Company relied solely on 2-D seismic data. This data has
also been used to assist the Company in attempting to identify the most
desirable location for the wellbore to increase the prospects of a successful
exploratory or development well and production from the reservoir.
 
INDUSTRY ALLIANCES
 
   
     Pursuant to an alliance with Veritas Seismic Ltd., Brigham has acquired
approximately 400 square miles of 3-D seismic data in the Anadarko Basin and has
agreed to acquire from 700 to 1,375 additional square miles of data to be
divided among numerous projects in that province. In exchange for the Company's
commitment to Veritas, the Company and its assignees only pay a portion of the
3-D acquisition costs as the data is acquired. As the Company leases acreage or
drills wells, it pays Veritas the balance of the costs in the form of leasing
and drilling fees. Veritas has agreed to make a designated 3-D seismic crew
available to the Company on a continuous basis and, as long as the Company has a
project area ready for surveying and field seismic acquisition, to send the crew
from one project area to the next without interruption. If the Company does not
have a project area designated upon completion of one project, and Veritas has
not been able to secure an intervening project from a third party, the Company
is obligated to pay Veritas a stand-by fee. The Company has never incurred a
stand-by fee to Veritas. These arrangements afford the Company access to 3-D
seismic data acquisition in a compressed cycle time, providing the Company with
operational efficiencies.
    
 
   
     In addition, Veritas currently maintains and operates two seismic data
processing workstations in Brigham's offices. Supervised by Brigham's
geophysicists, the vendor's employees process in the Company's offices most of
the Company's 3-D data. The associated improvement in communication and
integration, from field data acquisition to processing, reduces project cycle
times, and therefore costs, while improving the quality of the data for
Brigham's subsequent interpretation.
    
 
   
     The Company has entered into alliances with Vintage Petroleum, Inc.
("Vintage") and Stephens Production Company ("Stephens") providing for their
participation with Brigham in all projects that the Company conducts within the
3-D seismic program that it is now completing with Veritas in the Anadarko
Basin. Under that program, the Company and its participants have acquired 400
square miles of data and may acquire up to 275 more. Vintage and Stephens bear a
disproportionate share of all pre-seismic and certain seismic costs on all
projects in the program. Net of the interests of Vintage and Stephens, the
Company holds a 37.5% interest in the program. The Company believes that this
leveraging of its costs is possible because of the expertise and knowledge that
the Company has developed, enabling the Company to build its revenue and cash
flow base at a time when it has been capital constrained. With respect to a
subsequent program with
    
 
                                       38
<PAGE>   40
 
   
Veritas anticipated to start in July 1997 -- in which the Company plans to
acquire from 500 to 1,100 square miles of 3-D seismic data -- the Company plans
to retain at least a 75% working interest.
    
 
   
     In order to participate in wells drilled by the Company between April 1,
1996 and March 31, 1997, each of Gasco Limited Partnership ("Gasco") and Middle
Bay Oil Company, Inc. ("Middle Bay") agreed to fund 25% of the Company's
drilling costs and 12.5% of its completion cost for each well. In return, the
Company assigned to each an undivided 12.5% of the Company's interest in the
leasehold allocated to each completed well. As a result, the Company pays for
50% of costs attributable to its working interest to casing point, and 75% of
its completion costs, for 75% of its original working interest. The Company is
currently in discussions with Gasco to renew its agreement, although the
percentages of costs borne and interest assigned may vary under any renewal or
extension of this agreement. The Company believes that these agreements have
been beneficial because they have allowed the Company to leverage its working
interests in its properties by requiring it to bear a smaller proportion of
costs than it has retained in working interests.
    
 
NATURAL GAS AND OIL MARKETING AND MAJOR CUSTOMERS
 
   
     Most of the Company's natural gas and oil production is sold by its
operators under price sensitive or spot market contracts. The revenues generated
by the Company's operations are highly dependent upon the prices of and demand
for natural gas and oil. The price received by the Company for its natural gas
and oil production depends on numerous factors beyond the Company's control,
including seasonality, the condition of the United States economy, foreign
imports, political conditions in other oil-producing and natural gas-producing
countries, the actions of the Organization of Petroleum Exporting Countries and
domestic government regulation, legislation and policies. Decreases in the
prices of natural gas and oil could have an adverse effect on the carrying value
of the Company's proved reserves and the Company's revenues, profitability and
cash flow. Although the Company is not currently experiencing any significant
involuntary curtailment of its oil or natural gas production, market, economic
and regulatory factors may in the future materially affect the Company's ability
to sell its oil or natural gas production. See "Risk Factors -- Volatility of
Natural Gas and Oil Prices" and "Risk Factors -- Marketability of Production"
and "Management's Discussion and Analysis of Financial Condition and Results of
Operations." For the year ended December 31, 1996, sales to Cobra Oil and Gas
Corporation, Maynard Oil Company and Scurlock Permian Corporation were
approximately 16%, 12% and 10%, respectively, of the Company's natural gas and
oil revenues. Due to the availability of other markets and pipeline connections,
the Company does not believe that the loss of any single natural gas or oil
customer would have a material adverse effect on the Company's results of
operations.
    
 
COMPETITION
 
     The oil and gas industry is highly competitive in all of its phases. The
Company encounters competition from other oil and gas companies in all areas of
its operations, including the acquisition of seismic options and lease options
on properties. The Company's competitors include major integrated oil and
natural gas companies and numerous independent oil and natural gas companies,
individuals and drilling and income programs. Many of its competitors are large,
well established companies with substantially larger operating staffs and
greater capital resources than the Company's and which, in many instances, have
been engaged in the exploration and production business for a much longer time
than the Company. Such companies may be able to pay more for seismic and lease
options on natural gas and oil properties and exploratory prospects and to
define, evaluate, bid for and purchase a greater number of properties and
prospects than the Company's financial or human resources permit. The Company's
ability to acquire additional properties and to discover reserves in the future
will be dependent upon its ability to evaluate and select suitable properties
and to consummate transactions in a highly competitive environment. See "Risk
Factors -- Competition" and "Risk Factors -- Substantial Capital Requirements."
 
OPERATING HAZARDS AND UNINSURED RISKS
 
     Drilling activities are subject to many risks, including the risk that no
commercially productive reservoirs will be encountered. There can be no
assurance that new wells drilled by the Company will be productive or that the
Company will recover all or any portion of its investment. Drilling for natural
gas and oil may involve
 
                                       39
<PAGE>   41
 
unprofitable efforts, not only from dry wells, but from wells that are
productive but do not produce sufficient net revenues to return a profit after
drilling, operating and other costs. The cost of drilling, completing and
operating wells is often uncertain. The Company's drilling operations may be
curtailed, delayed or canceled as a result of numerous factors, many of which
are beyond the Company's control, including title problems, weather conditions,
compliance with governmental requirements and shortages or delays in the
delivery of equipment and services. The Company's future drilling activities may
not be successful and, if unsuccessful, such failure may have a material adverse
effect on the Company's future results of operations and financial condition.
See "Risk Factors -- Dependence on Exploratory Drilling Activities."
 
     In addition, the Company's use of 3-D seismic technology requires greater
pre-drilling expenditures than traditional drilling strategies. Although the
Company believes that its use of 3-D seismic technology will increase the
probability of success, unsuccessful wells are likely to occur. There can be no
assurance that the Company's drilling program will be successful or that
unsuccessful drilling efforts will not have a material adverse effect on the
Company.
 
     The Company's operations are subject to hazards and risks inherent in
drilling for and producing and transporting natural gas and oil, such as fires,
natural disasters, explosions, encountering formations with abnormal pressures,
blowouts, cratering, pipeline ruptures and spills, any of which can result in
the loss of hydrocarbons, environmental pollution, personal injury claims and
other damage to properties of the Company and others. The Company maintains
insurance against some but not all of the risks described above. In particular,
the insurance maintained by the Company does not cover claims relating to
failure of title to natural gas and oil leases, trespass during 3-D survey
acquisition or surface change attributable to seismic operations, business
interruption or loss of revenues due to well failure. In certain circumstances
in which insurance is available the Company may not purchase it. The occurrence
of an event that is not covered, or not fully covered, by insurance could have a
material adverse effect on the Company's financial condition and results of
operations.
 
EMPLOYEES
 
   
     On February 15, 1997, the Company had 33 full-time employees. None is
represented by any labor union. The Company believes its relations with its
employees are good. The Company also relies on several regional broker service
companies to provide field landmen to the Company. One of these companies,
Brigham Land Management, is owned by Vincent M. Brigham, who is the brother of
Ben M. Brigham, the Company's President, Chief Executive Officer and Chairman of
the Board. See "Certain Transactions."
    
 
OTHER FACILITIES
 
   
     Through August 1997, the Company has leased approximately 17,000 square
feet of office space in Dallas, Texas, where its principal offices are located.
When the Company's lease expires, the Company plans to relocate its principal
executive offices to Austin, Texas, where it has leased approximately 28,000
square feet of office space at 6300 Bridgepoint Parkway, Building 2, Suite 500,
Austin, Texas 78730. The Company also leases a 4,100 square foot office at 450
Gears Road, Suite 240, Houston, Texas 77067.
    
 
TITLE TO PROPERTIES
 
     The Company believes it has satisfactory title to all of its producing
properties in accordance with standards generally accepted in the oil and gas
industry. The Company's properties are subject to customary royalty interests,
liens incident to operating agreements, liens for current taxes and other
burdens which the Company believes do not materially interfere with the use of
or affect the value of such properties. The Company's Revolving Credit Facility
is secured by substantially all of the Company's natural gas and oil properties.
 
GOVERNMENTAL REGULATION
 
     The Company's natural gas and oil exploration, production and related
operations are subject to extensive rules and regulations promulgated by federal
and state agencies. Failure to comply with such rules and
 
                                       40
<PAGE>   42
 
regulations can result in substantial penalties. The regulatory burden on the
oil and gas industry increases the Company's cost of doing business and affects
its profitability. Although the Company believes it is in substantial compliance
with all applicable laws and regulations, because those laws and regulations are
frequently amended or reinterpreted, the Company is unable to predict the future
cost or impact of complying with such laws.
 
     The State of Texas and many other states require permits for drilling
operations, drilling bonds and reports concerning operations and impose other
requirements relating to the exploration and production of natural gas and oil.
These states also have statutes or regulations addressing conservation matters,
including provisions for the unitization or pooling of natural gas and oil
properties, the establishment of maximum rates of production from wells and the
regulation of spacing, plugging and abandonment of such wells.
 
     The Federal Energy Regulatory Commission ("FERC") regulates interstate
natural gas transportation rates and service conditions, which affect the
marketing of gas produced by the Company, as well as the revenues received by
the Company for sales of such production. Since the mid-1980s, FERC has issued a
series of orders, culminating in Order Nos. 636, 636-A and 636-B ("Order 636"),
that have significantly altered the marketing and transportation of gas. Order
636 mandates a fundamental restructuring of interstate pipeline sales and
transportation service, including the unbundling by interstate pipelines of the
sale, transportation, storage and other components of the city-gate sales
services such pipelines previously performed. One of FERC's purposes in issuing
the order was to increase competition within all phases of the natural gas
industry. Numerous parties have filed petitions for review of Order 636, as well
as orders in individual pipeline restructuring proceedings. In July 1996, Order
636 was generally upheld on appeal, and the portions remanded for further action
do not appear to materially affect the Company. Because Order 636 may be
modified as a result of the appeals, it is difficult to predict the ultimate
impact of the orders on the Company and its gas marketing efforts. Generally,
Order 636 has eliminated or substantially reduced the interstate pipelines'
traditional role as wholesalers of natural gas and has substantially increased
competition and volatility in natural gas markets.
 
     The price the Company receives from the sale of natural gas liquids and oil
is affected by the cost of transporting products to markets. Effective January
1, 1995, FERC implemented regulations establishing an indexing system for
transportation rates for oil pipelines, which, generally, would index such rates
to inflation, subject to certain conditions and limitations. The Company is not
able to predict with certainty the effect, if any, of these regulations on its
operations. However, the regulations may increase transportation costs or reduce
well head prices for natural gas liquids and oil. See "Risk Factors -- 
Compliance with Government Regulations."
 
ENVIRONMENTAL MATTERS
 
     The Company's operations and properties are subject to extensive and
changing federal, state and local laws and regulations relating to environmental
protection, including the generation, storage, handling, emission,
transportation and discharge of materials into the environment, and relating to
safety and health. The recent trend in environmental legislation and regulation
generally is toward stricter standards, and this trend will likely continue.
These laws and regulations may require the acquisition of a permit or other
authorization before construction or drilling commences and for certain other
activities; limit or prohibit construction, drilling and other activities on
certain lands lying within wilderness and other protected areas; and impose
substantial liabilities for pollution resulting from the Company's operations.
The permits required for various of the Company's operations are subject to
revocation, modification and renewal by issuing authorities. Governmental
authorities have the power to enforce compliance with their regulations, and
violations are subject to fines or injunction, or both. In the opinion of
management, the Company is in substantial compliance with current applicable
environmental laws and regulations, and the Company has no material commitments
for capital expenditures to comply with existing environmental requirements.
Nevertheless, changes in existing environmental laws and regulations or in
interpretations thereof could have a significant impact on the Company, as well
as the oil and gas industry in general. The Comprehensive Environmental
Response, Compensation and Liability Act and comparable state statutes impose
strict, joint and several liability on owners and operators of sites and on
persons who disposed of or arranged for the
 
                                       41
<PAGE>   43
 
disposal of "hazardous substances" found at such sites. It is not uncommon for
the neighboring land owners and other third parties to file claims for personal
injury and property damage allegedly caused by the hazardous substances released
into the environment. The Resource Conservation and Recovery Act and comparable
state statutes govern the disposal of "solid waste" and "hazardous waste" and
authorize imposition of substantial fines and penalties for noncompliance.
Although CERCLA currently excludes petroleum from its definition of "hazardous
substance," state laws affecting the Company's operations impose clean-up
liability relating to petroleum and petroleum related products. In addition,
although RCRA classifies certain oil field wastes as "non-hazardous," such
exploration and production wastes could be reclassified as hazardous wastes
thereby making such wastes subject to more stringent handling and disposal
requirements.
 
   
     Federal regulations require certain owners or operators of facilities that
store or otherwise handle oil, such as the Company, to prepare and implement
spill prevention, control countermeasure and response plans relating to the
possible discharge of oil into surface waters. The Oil Pollution Act of 1990
contains numerous requirements relating to the prevention of and response to oil
spills into waters of the United States. For onshore facilities that may affect
waters of the United States, the OPA requires an operator to demonstrate $10
million in financial responsibility, and for offshore facilities the financial
responsibility requirement is at least $35 million. Regulations are currently
being developed under federal and state laws concerning oil pollution prevention
and other matters that may impose additional regulatory burdens on the Company.
In addition, the Clean Water Act and analogous state laws require permits to be
obtained to authorize discharge into surface waters or to construct facilities
in wetland areas. With respect to certain of its operations, the Company is
required to maintain such permits or meet general permit requirements. The EPA
recently adopted regulations concerning discharges of storm water runoff. This
program requires covered facilities to obtain individual permits, participate in
a group or seek coverage under an EPA general permit. The Company believes that
it will be able to obtain, or be included under, such permits, where necessary,
and to make minor modifications to existing facilities and operations that would
not have a material effect on the Company.
    
 
     The Company has acquired leasehold interests in numerous properties that
for many years have produced natural gas and oil. Although the previous owners
of these interests have used operating and disposal practices that were standard
in the industry at the time, hydrocarbons or other wastes may have been disposed
of or released on or under the properties. In addition, some of the Company's
properties are operated by third parties over whom the Company has no control.
Notwithstanding the Company's lack of control over properties operated by
others, the failure of the operator to comply with applicable environmental
regulations may, in certain circumstances, adversely impact the Company. See
"Risk Factors -- Compliance with Environmental Regulations" and "Management's
Discussion and Analysis of Financial Condition and Results of Operations -- 
Other Matters."
 
LEGAL PROCEEDINGS
 
     The Company is not a party to any material legal proceedings.
 
                                       42
<PAGE>   44
 
                                   MANAGEMENT
 
DIRECTORS AND EXECUTIVE OFFICERS
 
     The following table sets forth certain information regarding the executive
officers and directors of the Company:
 
<TABLE>
<CAPTION>
                   NAME                     AGE                    POSITION
                   ----                     ---                    --------
<S>                                         <C>   <C>
Ben M. Brigham............................  37    President, Chief Executive Officer and
                                                  Chairman of the Board
Anne L. Brigham...........................  35    Executive Vice President, Secretary and
                                                  Director
Jon L. Glass..............................  41    Vice President -- Exploration and Director
Craig M. Fleming..........................  39    Chief Financial Officer
David T. Brigham..........................  36    Vice President -- Legal
A. Lance Langford.........................  34    Vice President -- Operations
Harold D. Carter..........................  58    Consultant and Director
Alexis M. Cranberg........................  41    Director
Gary J. Milavec...........................  35    Director
Stephen P. Reynolds.......................  45    Director
</TABLE>
 
     Set forth below is a description of the backgrounds of the executive
officers and directors of the Company.
 
     Ben M. "Bud" Brigham has served as President, Chief Executive Officer and
Chairman of the Board of the Company since founding the Company in 1990. From
1984 to 1990, Mr. Brigham served as an exploration geophysicist with Rosewood
Resources, an independent oil and gas exploration and production company. Mr.
Brigham began his career in Houston as a seismic data processing geophysicist
for Western Geophysical, a provider of 3-D seismic services, after earning his
B.S. in Geophysics from the University of Texas.
 
     Anne L. Brigham has served as Executive Vice President, Secretary and a
Director of the Company since its inception in 1990. Before joining the Company
full-time in 1991, Ms. Brigham practiced law in the oil and gas and real estate
sections of Thompson & Knight, P.C. Ms. Brigham worked as a geologist for Hunt
Petroleum Corporation, an independent oil and gas exploration and production
company, for over two years before attending law school. Ms. Brigham holds a
B.S. in Geology from the University of Texas and a J.D. from Southern Methodist
University.
 
   
     Jon L. Glass joined the Company in 1992 and has served as Vice
President -- Exploration and a Director of the Company since 1995. From 1984 to
1992, Mr. Glass served in various capacities with Santa Fe Minerals, an oil and
gas exploration company, in a variety of staff and managerial positions mainly
focused on Santa Fe Minerals' exploration activities in the midcontinent and
Gulf of Mexico (onshore and offshore). During this time Mr. Glass also assisted
in the development of exploration and acquisition opportunities for Santa Fe
Minerals in Canada and South America. Mr. Glass' early geological experience
includes three years with Mid-America Pipeline Company and two years with Texaco
USA, serving mainly as a midcontinent exploration geologist. Mr. Glass holds a
B.S. and an M.S. in Geology from Oklahoma State University and an M.B.A. from
the University of Tulsa.
    
 
     Craig M. Fleming has served as the Chief Financial Officer of the Company
since 1993. From 1990 to 1993, Mr. Fleming served as Controller of Odyssey
Petroleum Co., Ltd., an independent energy company. From 1988 to 1990, Mr.
Fleming served as Controller and Treasurer for Harken Exploration Company, an
independent energy company. Mr. Fleming began his career with Arthur Anderson &
Co. in the Oil and Gas Audit Division and is a Certified Public Accountant. Mr.
Fleming holds a B.B.A. in Accounting from Texas A&M University.
 
                                       43
<PAGE>   45
 
     David T. Brigham joined the Company in 1992 and has served as Vice
President -- Legal of the Company since 1994. From 1987 to 1992, Mr. Brigham was
an oil and gas attorney with Worsham, Forsythe, Sampels & Wooldridge. Before
attending law school, Mr. Brigham was a landman for Wagner & Brown Oil and Gas
Producers, an independent oil and gas exploration and production company. Mr.
Brigham holds a B.B.A. in Petroleum Land Management and a J.D. from Texas Tech
University.
 
     A. Lance Langford joined the Company as Manager of Operations in 1995 and
has served as Vice President Operations since January 1997. From 1987 to 1995,
Mr. Langford served in various engineering capacities with Meridian Oil Inc.,
handling a variety of reservoir, production and drilling responsibilities. Mr.
Langford holds a B.S. in Petroleum Engineering from Texas Tech University.
 
   
     Harold D. Carter has served as a Director of and consultant to the Company
since 1992. Mr. Carter has more than 30 years experience in the oil and gas
industry and has been an independent consultant since 1990. Prior to consulting,
Mr. Carter served as Executive Vice President of Pacific Enterprises Oil Company
(USA). Before that, Mr. Carter was associated for 20 years with Sabine
Corporation, ultimately serving as President and Chief Operating Officer from
1986 to 1989. Mr. Carter consults for Endowment Advisors, Inc. with respect to
its EEP Partnerships and Associated Energy Managers, Inc. with respect to its
Energy Income Fund, L.P. and is a director of Abraxas Petroleum Corporation. Mr.
Carter has a B.B.A. in Petroleum Land Management from the University of Texas
and has completed the Program for Management Development at the Harvard
University Business School.
    
 
     Alexis M. Cranberg has served as a Director of the Company since 1992. Mr.
Cranberg is President of Aspect Management Corporation, an oil and gas
exploration and investment company. In addition, Mr. Cranberg is a Director for
Westport Oil and Gas Company, Inc. and a past Director of General Atlantic
Resources, Inc. and United Meridian Corporation. He holds a B.S. in Petroleum
Engineering from the University of Texas and an M.B.A. from Stanford University.
 
     Gary J. Milavec has served as a Director of the Company since 1995. Mr.
Milavec is a Senior Vice President of RIMCO, a full service investment
management firm specializing in the energy industry. Prior to joining RIMCO in
1990, Mr. Milavec spent two years in the corporate finance department of
Rauscher Pierce Refsnes, Inc. and three years as a geological engineer with
Shell Western E&P, Inc. He also serves as a director of Universal Seismic
Associates, Inc. and Texoil, Inc. Mr. Milavec holds B.S. in Geology from the
University of Rochester, an M.S. in Geology from the University of Oklahoma and
an M.B.A. from the University of Houston.
 
     Stephen P. Reynolds has served as a Director of the Company since 1996. Mr.
Reynolds is a managing member of General Atlantic Partners, LLC ("GAP LLC") and
has been with GAP LLC or its predecessor entities since April 1980. Mr. Reynolds
is also President of GAP III Investors, Inc., the general partner of General
Atlantic Partners III, L.P., and is a general partner and limited partner of
GAP-Brigham Partners, L.P. Mr. Reynolds is on the board of directors of Solo
Serve Corporation, a publicly traded off-price soft goods retail company, and
Computer Learning Centers, Inc., a publicly traded company providing technology
related training. Mr. Reynolds holds a B.A. in Economics from Amherst College
and a Masters degree in Accounting from New York University.
 
     All directors are elected to serve until the next annual meeting of
stockholders and until their successors are elected and qualified. Executive
officers are generally elected annually by the Board of Directors to serve,
subject to the discretion of the Board of Directors, until their successors are
elected or appointed.
 
     There is no family relationship between any of the directors or between any
director and any executive officer of the Company except that Ben M. Brigham and
Anne L. Brigham are married and David T. Brigham is the brother of Ben M.
Brigham. For information regarding certain business relationships between the
Company and certain of its directors, see "Certain Transactions."
 
COMMITTEES OF THE BOARD
 
     Upon completion of the Offering, the Company will establish two standing
committees of the Board of Directors: an Audit Committee and a Compensation
Committee. Messrs. Carter, Cranberg and Milavec are
 
                                       44
<PAGE>   46
 
expected to be members of the Audit Committee and Compensation Committee
following completion of the Offering. The Audit Committee will review the
functions of the Company's management and independent accountants pertaining to
the Company's financial statements and perform such other related duties and
functions as are deemed appropriate by the Audit Committee or the Board of
Directors. The Compensation Committee will recommend to the Board of Directors
the base salaries, bonuses and other incentive compensation for the Company's
officers. The Board of Directors has designated the Compensation Committee as
the administrator of the Company's 1997 Incentive Plan. See
"Management -- Employee Benefit Plans -- 1997 Incentive Plan."
 
DIRECTOR COMPENSATION
 
     Fees and Expenses; Other Arrangements. Directors who are also employees of
the Company are not separately compensated for serving on the Board of
Directors. Directors who are not employees of the Company receive $5,000 per
year and $500 per meeting for their services as directors. In addition, the
Company reimburses Directors for the expenses incurred in connection with
attending meetings of the Board of Directors and its committees.
 
     Pursuant to a consulting agreement with Harold D. Carter that expires May
1, 1997, the Company pays Mr. Carter $7,200 per month to spend approximately 50%
of his working time performing such consulting and advisory services regarding
the operations of the Company as the Company requests, including service on the
Management Committee of the Company's predecessor partnership.
 
     Alexis M. Cranberg and Stephen P. Reynolds served on the management
committee of the Company's predecessor partnership pursuant to the terms of an
agreement with General Atlantic, and Gary J. Milavec served on the committee
pursuant to the terms of an agreement with RIMCO. The Company is not obligated
to nominate any of the three to serve as a Director of the Company in the
future.
 
   
     Director Stock Options. The Company's stockholders have approved the 1997
Director Stock Option Plan, pursuant to which each newly elected nonemployee
director shall be granted an option to purchase 1,000 shares of Common Stock and
each nonemployee director will receive an option to purchase 500 shares of
Common Stock on December 31 of each year. The options under the plan are granted
at fair market value on the grant date and become exercisable, subject to
certain conditions, in five equal annual installments on the first five
anniversaries of the grant date. The options terminate ten years from the grant
date, unless terminated sooner. 25,000 shares of Common Stock have been
authorized and reserved for issuance pursuant to the plan.
    
 
LIMITATION OF LIABILITY AND INDEMNIFICATION MATTERS
 
     In accordance with Section 102(b)(7) of the Delaware General Corporation
Law ("DGCL"), the Company's Certificate of Incorporation includes a provision
that, to the fullest extent permitted by law, eliminates the personal liability
of members of its Board of Directors to the Company or its stockholders for
monetary damages for breach of fiduciary duty as a director. Such provision does
not eliminate or limit the liability of a director (1) for any breach of a
director's duty of loyalty to the Company or its stockholders, (2) for acts or
omissions not in good faith or which involve intentional misconduct or a knowing
violation of a law, (3) for paying an unlawful dividend or approving an illegal
stock repurchase (as provided in Section 174 of the DGCL) or (4) for any
transaction from which the director derived an improper personal benefit.
 
     The Company has entered into indemnity agreements with each of its
executive officers and directors that provide for indemnification in certain
instances against liability and expenses incurred in connection with proceedings
brought by or in the right of the Company or by third parties by reason of a
person serving as an officer or director of the Company.
 
     The Company believes that these provisions and agreements will assist the
Company in attracting and retaining qualified individuals to serve as directors
and officers.
 
                                       45
<PAGE>   47
 
COMPENSATION COMMITTEE INTERLOCKS AND INSIDER PARTICIPATION
 
     None of the members of the Compensation Committee is or has been an
employee of the Company. Mr. Carter is and has been since 1992 a consultant to
the Company. No executive officer of the Company serves as a member of the Board
of Directors or compensation committee of any entity that has one or more
executive officers serving as a member of the Company's Board of Directors or
Compensation Committee. All of the Company's directors, or their affiliates,
have acquired capital stock of the Company. See "Certain Transactions."
 
EXECUTIVE COMPENSATION
 
     The following table sets forth all compensation paid for the last fiscal
year to the Company's Chief Executive Officer and each of the Company's other
executive officers whose annual salary exceeded $100,000 for the fiscal year
ended December 31, 1996. The table does not include perquisites and other
personal benefits because the aggregate amount of such compensation does not
exceed the lesser of (i) $50,000 or (ii) 10% of individual combined salary and
bonus for the named executive officers in each year.
 
                           SUMMARY COMPENSATION TABLE
 
   
<TABLE>
<CAPTION>
                                                                   LONG-TERM
                                                                  COMPENSATION
                                                            ------------------------
                                  ANNUAL COMPENSATION       RESTRICTED     SHARES
          NAME AND             --------------------------     STOCK      UNDERLYING       ALL OTHER
     PRINCIPAL POSITION        YEAR    SALARY    BONUS(1)     AWARDS     OPTIONS(2)    COMPENSATION(3)
     ------------------        ----   --------   --------   ----------   -----------   ---------------
<S>                            <C>    <C>        <C>        <C>          <C>           <C>
Ben M. Brigham...............  1996   $144,000    $15,000       --            --           $4,817
  President, Chief Executive
     Officer and Chairman of
     the Board
Jon L. Glass.................  1996    109,782      3,223       --            --               --
  Vice
     President -- Exploration
Craig M. Fleming.............  1996    102,919      8,063       --            --               --
  Chief Financial Officer
David T. Brigham.............  1996     94,874     10,505       --            --               --
  Vice President -- Legal
</TABLE>
    
 
- ---------------
 
(1) Includes, for Jon L. Glass, Craig M. Fleming and David T. Brigham, bonuses
    earned under the Company's Incentive Bonus Plan of $3,223, $4,202 and
    $5,496, respectively. See "Employment Benefit Plans -- Incentive Bonus
    Plan."
 
   
(2) Does not include options to purchase Common Stock granted in February 1997
    at an exercise price of $5.00 in the amount of 208,333 shares for Jon L.
    Glass, 69,444 shares for Craig M. Fleming and 69,444 shares for David T.
    Brigham.
    
 
(3) Consists of premiums paid by the Company under life and disability insurance
    plans of $1,404 and $3,413, respectively.
 
  Employment Agreements
 
     The Company employs Ben M. Brigham under an Employment Agreement (the
"Employment Agreement") as President and Chief Executive Officer of the Company
for a five year term that began in February 1997. The Employment Agreement
contains rollover provisions so that at all times the term of the Employment
Agreement shall be not less than three years. The agreement provides for an
annual salary of $275,000, which the Board of Directors may further increase
from time to time. Mr. Brigham is also entitled to an annual cash bonus, not to
exceed 75% of his then current salary, determined based on criteria established
by the Board of Directors. Under the Employment Agreement, Mr. Brigham is
entitled to participate in any employee benefit programs that the Company
provides to its executive officers. The only employee benefit programs that the
Company offers to its officers and employees are group insurance coverage and
participation
 
                                       46
<PAGE>   48
 
in the Company's 401(k) Retirement Plan, the 1997 Incentive Plan and the
Incentive Bonus Plan. If Mr. Brigham terminates his employment for good reason,
which includes a material reduction of Mr. Brigham's position without cause or
his written consent, breach of a material provision of the Employment Agreement
or improper notice of termination, or if the Company terminates Mr. Brigham
without cause, the Company must pay Mr. Brigham a sum equal to the amount of his
annual base salary that he would have received during the remainder of his
employment term plus the average of his annual bonuses received in the preceding
two years times the number of years in the remainder of his employment term. Mr.
Brigham's agreement also contains a three-year non-compete and confidentiality
clause with standard terms.
 
     Each of the other executive officers of the Company is a party to a
confidentiality and noncompete agreement contained in agreements relating to the
officers' restricted stock. See "Management -- Employee Benefit
Plans -- Employees' Restricted Stock."
 
EMPLOYEE BENEFIT PLANS
 
     Employees' Restricted Stock. In February 1997, the Company, in connection
with the Exchange, issued 66,964 shares, 44,643 shares and 44,643 shares of
restricted stock to Jon L. Glass, Craig M. Fleming and David T. Brigham,
respectively, in exchange for restricted limited partnership interests issued to
them in 1994. Each agreement relating to the restricted stock contains
confidentiality, noncompete and vesting provisions. The shares awarded Messrs.
Brigham and Fleming vest over a three-year period -- 30% in each of July 1997
and 1998 and 40% in July 1999. 16.67% of Mr. Glass's shares have already vested,
28.33% vest in each of July 1997 and 1998, and 26.67% vest in July 1999.
 
   
     1997 Incentive Plan. The Board of Directors and the stockholders of the
Company approved the adoption of the Company's 1997 Incentive Plan (the "1997
Incentive Plan") as of February 27, 1997. The Compensation Committee selects
participants in the 1997 Incentive Plan are selected by the Compensation
Committee from among those key employees and others who hold positions of
responsibility with the Company and whose performance may have a significant
effect on the success of the Company. An aggregate of 1,588,169 shares of Common
Stock have been authorized and reserved for issuance pursuant to the 1997
Incentive Plan. In March 1997, options were granted to purchase a total of
644,097 shares of Common Stock at an exercise price per share of $5.00. These
options vest over six years. Jon L. Glass, Craig M. Fleming and David T. Brigham
were granted options to purchase 208,334 shares, 69,445 shares and 69,445 shares
of Common Stock, respectively. Their options vest as follows: 30% on July 1,
1998; 20% on July 1, 1999; 16.66% on July 1, 2000; 16.67% on July 1, 2001; and
the balance on July 1, 2002.
    
 
     Subject to the provisions of the 1997 Incentive Plan, the Compensation
Committee is authorized to determine the type or types of awards made to each
participant and the terms, conditions and limitations applicable to each award.
In addition, the Compensation Committee has the exclusive power to interpret the
1997 Incentive Plan and to adopt rules and regulations that it may deem
necessary or appropriate, in keeping with the objectives of the 1997 Incentive
Plan.
 
     Pursuant to the 1997 Incentive Plan, participants will be eligible to
receive awards consisting of stock options, stock appreciation rights, stock,
restricted stock, cash or any combination of the foregoing. Stock options may be
either incentive stock options within the meaning of Section 422 of the Internal
Revenue Code of 1986, as amended, or nonqualified stock options.
 
   
     Incentive Bonus Plan. In connection with the Exchange, the Company has
adopted the Incentive Bonus Plan (the "Incentive Bonus Plan") previously
established by the Company's predecessor partnership. The Incentive Bonus Plan
is designed to pay cash compensation and bonuses to eligible employees of the
Company. Under the Incentive Bonus Plan, the Company maintains an incentive
account for each calendar year (each an "Incentive Account") and a discretionary
bonus account (the "Discretionary Bonus Account"). Prior to the beginning of
each calendar year the President of the Company designates the employees of the
Company who are eligible to participate in the Incentive Account being
established for such year, and each such employee's percentage of interest (an
"Account Percentage") in such Incentive Account. Subject to certain adjustments
provided under the Incentive Bonus Plan, each Incentive Account is credited with
an
    
 
                                       47
<PAGE>   49
 
amount equal to one-half of the net revenue received by the Company which is
equivalent to a one percent interest in the Company's net revenue interest in
the oil and gas produced from each Company well drilled or reentered after April
30, 1992, and the Discretionary Bonus Account is credited with an amount equal
to the amount credited to each Incentive Account. The President has discretion
to allocate a greater interest to the accounts. Within thirty days after each
March 31 and September 30, an employee who has been designated to have an
Account Percentage in the Incentive Account established for a particular year
receives cash compensation equal to his or her Account Percentage in such
Incentive Account multiplied by the amount credited to that Incentive Account
for the six-month period then ended. In addition, the President of the Company
has the discretion to award cash bonuses to any Company employee from the
amounts credited to the Discretionary Bonus Account. The participation of an
employee under the Incentive Bonus Plan terminates when he or she ceases to be
an employee of the Company for any reason. The President of the Company may
amend or terminate the Incentive Bonus Plan at any time.
 
                              CERTAIN TRANSACTIONS
 
     In connection with the land work necessary prior to and during 3-D seismic
acquisitions, the Company engages Brigham Land Management ("BLM"), an
independent company owned and managed by Vincent M. Brigham, a brother of Ben M.
Brigham, who is the Company's President, Chief Executive Officer and Chairman of
the Board. BLM specializes in conducting the field land work necessary prior to
and during 3-D seismic acquisitions. BLM's regional expertise is in the Anadarko
Basin and the Texas Panhandle, and to a lesser extent, West Texas. BLM performs
these services for the Company using BLM's employees and independent
contractors. BLM performs approximately one-third of the Company's work in the
Anadarko Basin. In 1994, 1995 and 1996, the Company paid BLM $310,000, $382,000
and $596,000, respectively. Other participants in the Company's 3-D seismic
projects reimbursed the Company for most of these amounts. Based on its
experience with other firms in the area, the Company believes that BLM's charges
are at or below those of other firms.
 
   
     In 1994, the Company, through its subsidiary Quest Resources, L.L.C.,
formed Venture Acquisitions, L.P. ("Venture") with affiliates of RIMCO, a holder
of in excess of 5% of the Common Stock, to provide the Company with the capital
to acquire interests in potential drilling locations, producing properties and
3-D seismic projects. The RIMCO affiliates have contributed $5.2 million to
Venture, and the Company has contributed $286,138. Until the first payout under
the Venture limited partnership agreement, the Company's share of all capital
costs is 5%, and the Company's share of revenues and related production expenses
and costs is 10%. Between the first and second payout levels, the Company's
share of capital costs and revenues and related production expenses and costs is
25% and thereafter increases to 50%. Venture acquired an interest in (i) a 3-D
project, including a 3-D delineated producing well, for approximately $525,000
in 1994, (ii) a 3-D project for approximately $75,000 in 1995 and (iii) two 3-D
delineated potential drilling locations and 3-D seismic data for approximately
$83,000 in 1996. The Company billed Venture approximately $3,200 in 1994,
$14,924 in 1995 and $16,500 in 1996 for its proportionate share of exploration
and overhead costs. Because RIMCO was not an affiliate of the Company when the
Venture partnership was formed, the Company believes that the terms of the
Venture partnership are no less favorable than could be obtained from an
unaffiliated third party. Gary J. Milavec, a director of the Company, is
employed by RIMCO.
    
 
   
     In November 1994, the Company, certain RIMCO affiliates and other unrelated
industry participants entered into a geophysical exploration agreement creating
an area of mutual interest in its Esperson Dome Project in Liberty and Harris
Counties, Texas. The Company financed its participation in this project by
assigning its interest, and obligation to bear costs, to Vaquero Gas Company,
Inc. ("Vaquero"), a RIMCO affiliate, subject to a 5% net profits overriding
royalty interest and the right to receive up to 50% of Vaquero's interest on the
occurrence of certain payouts. The Company also retained responsibility for
managing the 3-D seismic data acquisition and interpretation of the data after
it had been acquired. During 1995 and 1996, the Company received approximately
$25,000 and $123,000, respectively, from the RIMCO affiliates, including
Vaquero, for workstation time and geoscientists' time in interpreting the 3-D
seismic data that were acquired. Because RIMCO was not an affiliate of the
Company when the project was initiated and the interest to
    
 
                                       48
<PAGE>   50
 
Vaquero was transferred, it believes that the terms of the arrangement are no
less favorable than could be obtained from an unaffiliated third party.
 
     In January 1997, the Company, RIMCO and Tigre Energy Corporation ("Tigre")
entered into an agreement under which the Company has been initially assigned an
undivided 25% interest (subject to a proportionately reduced 3% overriding
royalty interest) in a project located in Vermillion Parish, Louisiana in return
for paying certain costs of acquiring 3-D seismic and land within the project
area. The Company also has the option to acquire an additional 12.5% working
interest from RIMCO and an additional 37.5% working interest from Tigre in parts
of the project. The Company believes that the arrangements with RIMCO affiliates
relating to Tigre Point are on terms no less favorable than could be obtained
from an unaffiliated third party, because RIMCO and Tigre, an unaffiliated third
party, are participants in the project on substantially similar terms.
 
   
     The Company and an affiliate of Universal Seismic Associates, Inc. ("USA"),
a public company in which RIMCO affiliates beneficially own approximately 18% of
the outstanding common stock, have entered into a geophysical exploration
agreement covering an area of mutual interest on the Gulf Coast. Under the terms
of the agreement, USA will conduct a 3-D seismic program established by the
Company and USA and process the data acquired under the program at cost, and the
Company will interpret the resulting seismic data for the benefit of the Company
and USA at no charge to USA. Subject to a party electing not to participate in
an acquired interest, the Company and USA will each own an undivided 50%
interest in all land interests acquired within the area of mutual interest.
Through December 31, 1996, the Company had not incurred any costs under those
arrangements. Based on its experience in acquiring 3-D seismic data, the Company
believes that it will acquire 3-D seismic data under this agreement on terms,
and that the arrangement is on terms, no less favorable than could be obtained
from an unaffiliated third party. The Company is currently negotiating with an
affiliate of USA for participation in another South Texas project in which USA
would conduct any 3-D seismic programs within the project area at USA's cost and
the Company would interpret the resulting seismic data for the benefit of the
Company and USA.
    
 
   
     In 1993 and 1994 the Company issued to RIMCO 10% Notes in a principal
amount of $3.0 million and $4.9 million, respectively. In 1995 the Company
issued RIMCO additional 10% Notes in a principal amount of $2.6 million, and in
the same year, issued RIMCO 5% Notes in a principal amount of $16.0 million,
$10.5 million of which was used to repay all the outstanding 10% Notes. The 5%
Notes have been exchanged for 1,754,464 shares of Common Stock in the Exchange.
In 1994, 1995 and 1996, the Company paid RIMCO $591,826, $631,989 and $809,332,
respectively, in interest payments on the 5% Notes and the 10% Notes. In 1994,
1995 and 1996, the Company distributed to RIMCO $52,900, $102,107 and $82,097,
respectively for RIMCO's overriding royalty interest in certain natural gas and
oil properties. As part of the Exchange, the Company has agreed to pay to RIMCO
an amount equal to the interest the Company would have been currently paid on
the 5% Notes through the earlier to occur the date of the closing of the
Offering or September 30, 1997.
    
 
     Pursuant to a consulting agreement with Harold D. Carter that expires May
1, 1997, the Company pays Mr. Carter $7,200 per month to spend approximately 50%
of his working time performing such consulting and advisory services regarding
the operations of the Company as the Company requests, including service on the
Management Committee of the Company's predecessor partnership. Pursuant to this
agreement, Mr. Carter received $72,000 in 1994, $72,000 in 1995 and $79,200 in
1996.
 
     In 1995 and 1996, the Company paid $35,000 and $110,000 to Aspect and
affiliates of Alexis Cranberg, a director of the Company, to acquire interests
in a project in Grady County, Oklahoma and a project in Hardeman and Wilbarger
Counties, Texas and Jackson County, Oklahoma. Based on its experience in the
industry, the Company believes that these transactions are on terms no less
favorable than could be obtained from an unaffiliated third party. The Company
billed Aspect and other affiliates of Alexis Cranberg $201,000 in 1994, $13,000
in 1995 and $68,000 in 1996 for its proportionate share of exploration costs
related to the projects.
 
     The Company has entered into a Registration Rights Agreement with General
Atlantic Partners III, L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P.
II, RIMCO Partners, L.P. III and RIMCO
 
                                       49
<PAGE>   51
 
   
Partners, L.P. IV, Ben M. Brigham, Anne L. Brigham, Harold D. Carter, Craig M.
Fleming, David T. Brigham and Jon L. Glass. Pursuant to the Registration Rights
Agreement, Anne and Ben Brigham, acting together, the RIMCO entities, acting
together, and the General Atlantic entities, acting together, each may
separately require the Company to register securities, on one occasion, if the
shares to be registered have an estimated aggregate offering price to the public
of at least $3.0 million. One additional registration is allowed if any
registrable securities requested to be included in a previous registration
statement were not disposed of in accordance with that previous registration.
The Registration Rights Agreement also provides "piggyback" registration rights
after the Offering for all registrations of registrable securities for the
Company or another security holder. In an underwritten offering, however, the
Company may exclude all or a portion of the securities being registered pursuant
to "piggyback" registration rights if the managing underwriter determines that
including those securities would raise a substantial doubt about whether the
proposed offering could be consummated. The Registration Rights Agreement
contains customary indemnity by the Company in favor of persons selling
securities in a registration governed by the Registration Rights Agreement, and
by those persons in favor of the Company, relating to the information included
in or omitted from the Registration Statement.
    
 
   
                             PRINCIPAL STOCKHOLDERS
    
 
     The following table sets forth certain information regarding the beneficial
ownership of the Company's Common Stock as of February 27, 1997, by (i) each
person the Company knows to be the beneficial owner of 5% or more of the
outstanding shares of Common Stock, (ii) each named executive officer, (iii)
each director of the Company and (iv) all executive officers and directors of
the Company as a group. Except as indicated in the footnotes to this table and
pursuant to applicable community property laws, the Company believes that each
stockholder named in this table has sole investment and voting power with
respect to the shares set forth opposite such stockholder's name.
 
   
<TABLE>
<CAPTION>
                                                   SHARES BENEFICIALLY   SHARES BENEFICIALLY
                                                   OWNED PRIOR TO THE      OWNED AFTER THE
                                                       OFFERING(1)           OFFERING(1)
                                                   -------------------   -------------------
                BENEFICIAL OWNER                    NUMBER     PERCENT    NUMBER     PERCENT
                ----------------                   ---------   -------   ---------   -------
<S>                                                <C>         <C>       <C>         <C>
Ben M. Brigham(2)................................  3,848,821    43.11%   3,848,821    32.27%
  5949 Sherry Lane, Suite 1616
  Dallas, Texas 75225
Anne L. Brigham(2)...............................  3,848,821    43.11%   3,848,821    32.27%
  5949 Sherry Lane, Suite 1616
  Dallas, Texas 75225
General Atlantic Partners, L.L.C.(3).............  2,807,143    31.44%   2,807,143    23.53%
  Three Pickwick Plaza, Suite 200
  Greenwich, Connecticut 06830
Resource Investors Management Company(4).........  1,754,464    19.65%   1,754,464    14.71%
  600 Travis Street, Suite 6875
  Houston, Texas 77002
Craig M. Fleming(5)..............................     44,643     *          44,643     *
Jon L. Glass(6)..................................     66,964     *          66,964     *
David T. Brigham(7)..............................     44,643     *          44,643     *
Harold D. Carter.................................    341,893     3.83%     341,893     2.87%
Gary J. Milavec(8)...............................         --       --           --       --
Alexis M. Cranberg...............................         --       --           --       --
Stephen P. Reynolds(9)...........................         --       --           --       --
All directors and executive officers as a group
  (10 persons)(5)(6)(7)(8)(9)(10)................  4,346,964    48.69%   4,346,964    36.44%
</TABLE>
    
 
                                       50
<PAGE>   52
 
- ---------------
 
  *  Represents less than 1%.
 
   
 (1) Shares beneficially owned and percentage of ownership are based on
     8,928,571 shares of Common Stock outstanding before the Offering and
     11,928,571 shares of Common Stock outstanding after the closing. Beneficial
     ownership is determined in accordance with the rules of the SEC and
     generally includes voting or disposition power with respect to securities.
    
 
   
 (2) Includes 1,929,911 shares owned by Ben M. Brigham and 1,929,910 shares
     owned by Anne L. Brigham, who are husband and wife. If the Underwriters'
     over-allotment option is exercised in full, (i) Anne L. Brigham and Ben M.
     Brigham will each sell 47,619 shares pursuant to options granted to the
     Underwriters and (ii) the number and percentage of outstanding shares
     beneficially owned by Anne L. Brigham and Ben M. Brigham will be 3,753,583
     and 30.56%, respectively.
    
 
   
 (3) Includes 2,679,418 shares held by General Atlantic Partners III, L.P. ("GAP
     III"); and 127,725 shares held by GAP-Brigham Partners, L.P.
     ("GAP-Brigham") (collectively, "the General Atlantic Entities"). The
     general partner of GAP III is GAP III Investors, Inc., a Delaware
     corporation. The general partner of GAP-Brigham is Stephen P. Reynolds.
    
 
   
 (4) Includes 612,308 shares held by RIMCO Partners, L.P. II, 307,031 shares
     held by RIMCO Partners, L.P. III and 835,125 shares held by RIMCO Partners,
     L.P. IV (collectively, the "RIMCO Partnerships"). RIMCO is the general
     partner of each of the RIMCO Partnerships.
    
 
 (5) Includes 44,643 shares of restricted stock, which vest as follows: 30% in
     July 1997, 30% in July 1998 and 40% in July 1999.
 
 (6) Includes 66,964 shares of restricted stock, which vest as follows: 28.33%
     in July 1997, 28.33% in July 1998 and 26.67% in July 1999.
 
 (7) Includes 44,643 shares of restricted stock, which vest as follows: 30% in
     July 1997, 30% in July 1998 and 40% in July 1999.
 
   
 (8) Gary J. Milavec is a Senior Vice President of RIMCO, the general partner of
     each of the RIMCO Partnerships. As such, Mr. Milavec may be deemed to share
     voting and investment power with respect to the 612,308 shares held by
     RIMCO Partners, L.P. II, the 307,031 shares held by RIMCO Partners, L.P.
     III and the 835,125 shares held by RIMCO Partners, L.P. IV. Mr. Milavec
     disclaims beneficial ownership of shares beneficially owned by RIMCO and
     the RIMCO Partnerships.
    
 
   
 (9) Stephen P. Reynolds is the general partner and a limited partner in
     GAP-Brigham and is President of GAP III Investors, Inc., the general
     partner of GAP III. As such, Mr. Reynolds may be deemed to share voting and
     investment power with respect to the 2,679,418 shares held by GAP III and
     the 127,725 shares held by GAP-Brigham. Mr. Reynolds disclaims beneficial
     ownership of shares owned by GAP III and GAP-Brigham.
    
 
   
(10) If the Underwriters' over-allotment is exercised in full, (i) all directors
     and officers as a group will sell 95,238 shares pursuant to options granted
     to the Underwriters and (ii) the number and percentage of outstanding
     shares beneficially owned by all directors and officers as a group will be
     4,251,726 and 34.61%, respectively.
    
 
                                       51
<PAGE>   53
 
                          DESCRIPTION OF CAPITAL STOCK
 
   
     The authorized capital stock of the Company consists of 30 million shares
of Common Stock, par value $.01 per share, and 10 million shares of preferred
stock, par value $.01 per share ("Preferred Stock"). 11,928,571 shares of Common
Stock will be issued and outstanding upon completion of the Offering (12,283,333
shares if the Underwriters exercise their over-allotment option in full). As of
March 31, 1997, the Company had outstanding 8,928,571 shares of Common Stock
held of record by 11 stockholders and stock options for an aggregate of 644,097
shares.
    
 
COMMON STOCK
 
     The holders of Common Stock are entitled to one vote for each share held of
record on all matters submitted to the stockholders. The Certificate of
Incorporation of the Company does not allow the stockholders to take action by
less than unanimous consent. Each share of Common Stock is entitled to
participate equally in dividends, if, as and when declared by the Company's
Board of Directors, and in the distribution of assets in the event of
liquidation, subject in all cases to any prior rights of outstanding shares of
Preferred Stock. The Company has never paid cash dividends on its Common Stock.
The shares of Common Stock have no preemptive or conversion rights, redemption
rights, or sinking fund provisions. The outstanding shares of Common Stock are,
and the shares of Common Stock offered hereby upon issuance and sale will be,
duly authorized, validly issued, fully paid, and nonassessable.
 
PREFERRED STOCK
 
     The Company has no outstanding Preferred Stock. The Company is authorized
to issue 10 million shares of Preferred Stock. The Company's Board of Directors
may establish, without stockholder approval, one or more classes or series of
Preferred Stock having the number of shares, designations, relative voting
rights, dividend rates, liquidation and other rights, preferences, and
limitations that the Board of Directors may designate. The Company believes that
this power to issue Preferred Stock will provide flexibility in connection with
possible corporate transactions. The issuance of Preferred Stock, however, could
adversely affect the voting power of holders of Common Stock and restrict their
rights to receive payments upon liquidation of the Company. It could also have
the effect of delaying, deferring or preventing a change in control of the
Company. The Company does not currently plan to issue Preferred Stock.
 
DELAWARE LAW PROVISIONS
 
     The Company is a Delaware corporation and is subject to Section 203 of the
Delaware General Corporation Law. Generally, Section 203 prohibits the Company
from engaging in a "business combination" (as defined in Section 203) with an
"interested stockholder" (defined generally as a person owning 15% or more of
the Company's outstanding voting stock) for three years following the date that
person becomes an interested stockholder, unless (a) before that person became
an interested stockholder, the Company's Board of Directors approved the
transaction in which the interested stockholder became an interested stockholder
or approved the business combination; (b) upon completion of the transaction
that resulted in the interested stockholder's becoming an interested
stockholder, the interested stockholder owns at least 85% of the voting stock
outstanding at the time the transaction commenced (excluding stock held by
directors who are also officers of the Company and by employee stock plans that
do not provide employees with the right to determine confidentially whether
shares held subject to the plan will be tendered in a tender or exchange offer);
or (c) following the transaction in which that person became an interested
stockholder, the business combination is approved by the Company's Board of
Directors and authorized at a meeting of stockholders by the affirmative vote of
the holders of at least two-thirds of the outstanding voting stock not owned by
the interested stockholder.
 
     Under Section 203, these restrictions also do not apply to certain business
combinations proposed by an interested stockholder following the announcement or
notification of one of certain extraordinary transactions involving the Company
and a person who was not an interested stockholder during the previous three
years or who became an interested stockholder with the approval of a majority of
the Company's directors, if that
 
                                       52
<PAGE>   54
 
extraordinary transaction is approved or not opposed by a majority of the
directors who were directors before any person became an interested stockholder
in the previous three years or who were recommended for election or elected to
succeed such directors by a majority of such directors then in office.
 
REGISTRATION RIGHTS
 
   
     The Company has entered into a Registration Rights Agreement with General
Atlantic Partners III, L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P.
II, RIMCO Partners, L.P. III and RIMCO Partners, L.P. IV, Ben M. Brigham, Anne
L. Brigham, Harold D. Carter, Craig M. Fleming, David T. Brigham and Jon L.
Glass. Pursuant to the Registration Rights Agreement, Anne and Ben Brigham,
acting together, the General Atlantic entities, acting together, and the RIMCO
entities, acting together, each may separately require the Company to register
securities, on one occasion, if the shares to be registered have an estimated
aggregate offering price to the public of at least $3 million. One additional
registration is allowed if any registrable securities requested to be included
in a previous registration statement were not disposed of in accordance with
that previous registration. The Registration Rights Agreement also provides
"piggyback" registration rights after the Offering for all registrations of
registrable securities for the Company or another security holder. In an
underwritten offering, however, the Company may exclude all or a portion of the
securities being registered pursuant to "piggyback" registration rights if the
managing underwriter determines that including those securities would raise a
substantial doubt about whether the proposed offering could be consummated. The
Registration Rights Agreement contains customary indemnity by the Company in
favor of persons selling securities in a registration governed by the
Registration Rights Agreement, and by those persons in favor of the Company,
relating to the information included in or omitted from the Registration
Statement.
    
 
TRANSFER AGENT AND REGISTRAR
 
   
     The Transfer Agent and Registrar for the Common Stock is American Stock
Transfer & Trust Company.
    
 
                        SHARES ELIGIBLE FOR FUTURE SALE
 
   
     Upon completion of the Offering, the Company will have 11,928,571 shares of
Common Stock outstanding (12,283,333 shares if the Underwriters exercise their
over-allotment option in full). Of these 11,928,571 shares, the shares of Common
Stock offered hereby will be freely transferable without restriction under the
Securities Act unless they are held by the Company's affiliates, as that term is
used in Rule 144 under the Securities Act. The Company issued the remaining
8,928,571 shares of Common Stock in reliance on exemptions from the registration
requirements of the Securities Act, and those shares are "restricted" securities
under Rule 144. Those shares may not be sold publicly unless they are registered
under the Securities Act, sold in compliance with Rule 144, or sold in a
transaction that is exempt from registration. The Company believes that the
earliest date on which the 8,928,571 shares of its Common Stock currently
outstanding will be eligible for sale under Rule 144 is February 27, 1998.
Therefore, no shares will be eligible for immediate sale in the public market
without restriction under Rule 144(k), and no shares will be eligible for
immediate sale under the volume and other limitations of Rule 144. Beginning
February 27, 1998, all of the shares of Common Stock currently outstanding will
become eligible for sale under Rule 144, based on current SEC rules and subject
to compliance with the volume and other requirements of Rule 144. Beginning
February 27, 1999, all of those shares of Common Stock will become eligible for
sale under Rule 144(k) if they are not held by affiliates of the Company.
    
 
   
     In general, under Rule 144 a person (or persons whose sales are
aggregated), including an affiliate, who has beneficially owned shares for at
least one year is entitled to sell in broker transactions, within any three-
month period commencing 90 days after the Offering, a number of shares that does
not exceed the greater of (i) 1% of the then outstanding Common Stock
(approximately 119,000 shares immediately after the Offering) or (ii) the
average weekly trading volume in the Common Stock during the four calendar weeks
preceding the sale, subject to the filing of a Form 144 with respect to the sale
and other limitations. In addition, a person who was not an affiliate of the
Company during the three months preceding a sale and who
    
 
                                       53
<PAGE>   55
 
has beneficially owned the shares proposed to be sold for at least two years is
entitled to sell the shares under Rule 144(k) without regard to the
manner-of-sale, volume and other limitations of Rule 144. The SEC has proposed
modifications to Rule 144 that could change some of these requirements. All
shares of Common Stock, other than those offered hereby, are subject to lock-up
agreements with the Underwriters for 180 days after the date of this Prospectus.
See "Underwriting."
 
   
     The holders of approximately 8,421,428 shares of Common Stock and their
permitted transferees are entitled to demand registration of those shares under
the Securities Act beginning 180 days after the date of this Prospectus, and the
holders of approximately 8,928,571 shares of Common Stock are entitled to
"piggyback" registration rights. See "Description of Capital
Stock -- Registration Rights."
    
 
   
     Approximately 8,908,571 shares of Common Stock are subject to "lock-up"
agreements; these shares will be released from such agreements 180 days after
the date of this Prospectus. See "Underwriting."
    
 
   
     Options covering 644,097 shares of Common Stock have been issued, with an
exercise price of $5.00 per share, subject to vesting.
    
 
     Prior to the Offering, there has been no public market for the securities
of the Company. No prediction can be made of the effect, if any, that the sale
or availability for sale of shares of additional Common Stock will have on the
market price of the Common Stock. Nevertheless, sales of substantial numbers of
shares by existing stockholders or by stockholders purchasing in the Offering
could have a negative effect on the market price of the Common Stock.
 
                                  UNDERWRITING
 
   
     The Underwriters named below (the "Underwriters"), for whom Bear, Stearns &
Co. Inc., Howard, Weil, Labouisse, Friedrichs Incorporated and Rauscher Pierce
Refsnes, Inc. are acting as Representatives (the "Representatives"), have
severally agreed, subject to the terms and conditions of the Underwriting
Agreement, to purchase from the Company the aggregate number of shares of Common
Stock set forth opposite their names below:
    
 
   
<TABLE>
<CAPTION>
                                             NUMBER
              UNDERWRITER                   OF SHARES
              -----------                   ---------
<S>                                         <C>
Bear, Stearns & Co. Inc. ...............
Howard, Weil, Labouisse, Friedrichs
  Incorporated..........................
Rauscher Pierce Refsnes, Inc. ..........
 
                                            ---------
          Total.........................    3,000,000
                                            =========
</TABLE>
    
 
     The Underwriting Agreement provides that the obligations of the
Underwriters thereunder are subject to the approval of certain legal matters by
their counsel and to various other conditions. The nature of the obligations of
the Underwriters is such that they are committed to purchase all of the shares
of Common Stock offered hereby if any are purchased.
 
     The Representatives have advised the Company that the Underwriters propose
initially to offer the shares of Common Stock offered hereby directly to the
public at the initial public offering price set forth on the cover page of this
Prospectus. The Underwriters may allow a selected dealer concession of not more
than $     per share, and the Underwriters may allow, and such dealers may
reallow, concessions not in excess of $     per share to certain other dealers.
After the initial public offering, the public offering price and concessions and
reallowances to dealers may be changed by the Representatives.
 
                                       54
<PAGE>   56
 
   
     The Company and the Selling Stockholders have granted an option to the
Underwriters, exercisable at any time during the 30-day period after the date of
this Prospectus, to purchase from the Company and the Selling Stockholders up to
an additional 450,000 shares of Common Stock at the initial public offering
price set forth on the cover page of this Prospectus, less the underwriting
discount. Of this amount, an option to purchase 354,762 shares has been granted
by the Company, 47,619 shares by Anne L. Brigham and 47,619 shares by Ben M.
Brigham. The Underwriters may exercise such option solely for the purpose of
covering over-allotments, if any, made in connection with the sale of the shares
of Common Stock offered hereby. To the extent that the Underwriters exercise
this option, each Underwriter will be committed, subject to certain conditions,
to purchase a number of the additional shares of Common Stock proportionate to
such Underwriter's purchase obligations set forth in the table set forth above.
In the event of a partial exercise of the option, the option shall be satisfied
first from the shares of Anne L. Brigham and Ben M. Brigham.
    
 
   
     During and after the Offering, the Underwriters may purchase and sell the
Common Stock in the open market. These transactions may include over-allotment
and stabilizing transactions and purchases to cover syndicate short positions
created in connection with the Offering. The Underwriters may also impose a
penalty bid, whereby selling concessions allowed to syndicate members or other
broker-dealers in respect of the Common Stock sold in the Offering for their
account may be reclaimed by the syndicate if such Common Stock is repurchased by
the syndicate in stabilizing or covering transactions. These activities may
stabilize, maintain or otherwise affect the market price of the Common Stock,
which may be higher than the price that might otherwise prevail in the open
market, and, if commenced, may be discontinued at any time.
    
 
     The Underwriting Agreement provides that the Company and the Selling
Stockholders will indemnify the several Underwriters against certain
liabilities, including liabilities under the Securities Act, or will contribute
to payments the Underwriters may be required to make in respect thereof.
 
   
     Each of the Company, its officers, directors, and optionholders, and the
holders of all but 20,000 shares of its outstanding Common Stock, have entered
into "lock-up" agreements with the Underwriters with respect to the sale of
shares of Common Stock. Under these agreements, the Company, its officers,
directors, certain stockholders and optionholders have agreed not to offer,
sell, agree to sell, grant any option for the sale of or otherwise dispose of,
directly or indirectly, any shares of Common Stock (or any security convertible
into, exercisable for or exchangeable for Common Stock) without the consent of
Bear, Stearns & Co. Inc. for a period of 180 days after the date of this
Prospectus, except that the Company may issue shares of Common Stock upon the
exercise of options granted under its stock option plans. After the expiration
of the "lock-up" agreements, such persons will be entitled to sell, distribute
or otherwise dispose of the Common Stock that they hold subject to the
provisions of applicable securities laws.
    
 
   
     The Underwriters are reserving up to 150,000 shares of Common Stock in the
Offering for sales to officers, directors and employees of the Company and their
friends and relatives at the initial public offering price. Any shares of Common
Stock not purchased by those persons will be sold to the general public in the
Offering.
    
 
     The Representatives have informed the Company that they do not expect sales
to discretionary accounts by the Underwriters to exceed five percent of the
total number of shares of Common Stock offered by them.
 
     Prior to the Offering, there has been no public market for the Common
Stock. The initial public offering price will be determined by negotiation
between the Company and the Representatives. Among the factors which will be
considered in these negotiations are the Company's history, capital structure
and financial condition, its past and present earnings and the trend of such
earnings, prospects for the Company and its industry, the present state of the
Company's development, the recent market prices of publicly-held companies that
the Company and the Representatives believe to be comparable to the Company and
general conditions prevailing in the securities markets at the time of the
Offering.
 
                                       55
<PAGE>   57
 
                                 LEGAL MATTERS
 
     Certain legal matters in connection with the Common Stock being offered
hereby will be passed upon for the Company by Thompson & Knight, P.C., Dallas,
Texas. Certain legal matters will be passed upon for the Underwriters by Vinson
& Elkins L.L.P., Dallas, Texas.
 
                                    EXPERTS
 
     The financial statements of Brigham Oil and Gas, L.P. as of December 31,
1996 and 1995 and for each of the three years in the period ended December 31,
1996 and the Balance Sheet of Brigham Exploration Company as of February 26,
1997 included in this Prospectus have been so included in reliance on the
reports of Price Waterhouse LLP, independent accountants, given on authority of
said firm as experts in auditing and accounting.
 
     The letter of Cawley, Gillespie & Associates, Inc., independent oil and gas
consultants, set forth in this Prospectus as Appendix A has been included herein
in reliance upon the firm as expert with respect to the matters contained in
that letter. In addition, the information with respect to the reserve reports
prepared by Cawley Gillespie has been included herein in reliance upon by the
firm as experts with respect to such information.
 
                             AVAILABLE INFORMATION
 
     The Company has filed with the Commission a Registration Statement on Form
S-1 (as amended and together with all exhibits thereto, the "Registration
Statement") under the Securities Act, with respect to the shares of Common Stock
offered by this Prospectus. This Prospectus constitutes a part of the
Registration Statement and does not contain all of the information set forth in
the Registration Statement, certain parts of which are omitted from this
Prospectus as permitted by the rules and regulations of the SEC. Statements in
this Prospectus about the contents of any contract or other document are not
necessarily complete; reference is made in each instance to the copy of the
contract or other document filed as an exhibit to the Registration Statement.
Each such statement is qualified in all respects by such reference. The
Registration Statement and accompanying exhibits and schedules may by inspected
and copies may be obtained (at prescribed rates) at the public reference
facilities of the SEC at Judiciary Plaza, 450 Fifth Street, N.W., Room 1024,
Washington, D.C. 20549. Copies of the Registration Statement may also be
inspected at the SEC's regional offices at 7 World Trade Center, Suite 1300, New
York, New York 10048 and Citicorp Center, 500 West Madison Street, Suite 1400,
Chicago, Illinois 60661-2511. In addition, the Common Stock will be listed on
the Nasdaq National Market, 1735 K Street, N.W., Washington, D.C. 20006-1500,
where such material may also be inspected and copied.
 
     As a result of the Offering, the Company will become subject to the
information and periodic reporting requirements of the Securities Exchange Act
of 1934, and, in accordance therewith, will file periodic reports, proxy
statements and other information with the SEC. Such periodic reports, proxy
statements and other information will be available for inspection and copying at
the public reference facilities and regional offices referred to above. In
addition, these reports, proxy statements and other information may also be
obtained from the web site that the SEC maintains at http://www.sec.gov.
 
     The Company intends to furnish its shareholders annual reports containing
consolidated financial statements certified by its independent auditors and
quarterly reports for each of the first three quarters of each fiscal year
containing unaudited financial information.
 
                                       56
<PAGE>   58
 
                     GLOSSARY OF CERTAIN OIL AND GAS TERMS
 
     The following are abbreviations and definitions of certain terms commonly
used in the oil and gas industry and this Prospectus.
 
     Bbl. One stock tank barrel, or 42 U.S. gallons liquid volume, used herein
in reference to oil or other liquid hydrocarbons.
 
     Bcf. One billion cubic feet.
 
     Bcfe. One billion cubic feet of natural gas equivalent. In reference to
natural gas, natural gas equivalents are determined using the ratio of 6 Mcf of
natural gas to 1 Bbl of oil, condensate of natural gas liquids.
 
     Completion. The installation of permanent equipment for the production of
oil or natural gas.
 
     Developed Acreage. The number of acres which are allocated or assignable to
producing wells or wells capable of production.
 
     Development Well. A well drilled within the proved area of an oil or
natural gas reservoir to the depth of a stratigraphic horizon known to be
productive.
 
     Drilling Costs. The costs associated with drilling and completing a well
(exclusive of seismic and land acquisition costs for that well and future
development costs associated with proved undeveloped reserves added by the well)
divided by total proved reserve additions.
 
     Dry Well. A well found to be incapable of producing either oil or natural
gas in sufficient quantities to justify completion of an oil or gas well.
 
     Exploratory Well. A well drilled to find and produce oil or natural gas in
an unproved area, to find a new reservoir in a field previously found to be
productive of oil or gas in another reservoir, or to extend a known reservoir.
 
     Finding and Development Costs. Capital costs incurred in the acquisition,
exploration and development of proved oil and natural gas reserves divided by
proved reserve additions.
 
     Gross Acres or Gross Wells. The total acres or wells, as the case may be,
in which the Company has a working interest.
 
     MBbl. One thousand barrels of oil or other liquid hydrocarbons.
 
     Mcf. One thousand cubic feet of natural gas.
 
     Mcfe. One thousand cubic feet of natural gas equivalent.
 
     MMBbl. One million barrels of oil or other liquid hydrocarbons.
 
     MMBtu. One million Btu, or British Thermal Units. One British Thermal Unit
is the quantity of heat required to raise the temperature of one pound of water
by one degree Fahrenheit.
 
     MMcf. One million cubic feet of natural gas.
 
     MMcfe. One million cubic feet of natural gas equivalent.
 
     Net Acres or Net Wells. Gross acres or wells multiplied, in each case, by
the percentage working interest owned by the Company.
 
     Net Production. Production that is owned by the Company less royalties and
production due others.
 
     Oil. Crude oil or condensate.
 
     Operator. The individual or company responsible for the exploration,
development, and production of an oil or gas well or lease.
 
     Present Value of Future Net Revenues or PV-10. The pretax present value of
estimated future revenues to be generated from the production of proved reserves
calculated in accordance with SEC guidelines, net of
 
                                       57
<PAGE>   59
 
estimated production and future development costs, using prices and costs as of
the date of estimation without future escalation, without giving effect to
non-property related expenses such as general and administrative expenses, debt
service and depreciation, depletion and amortization, and discounted using an
annual discount rate of 10%.
 
     Proved Developed Reserves. Reserves that can be expected to be recovered
through existing wells with existing equipment and operating methods.
 
     Proved Reserves. The estimated quantities of crude oil, natural gas and
natural gas liquids which geological and engineering data demonstrate with
reasonable certainty to be recoverable in future years from known reservoirs
under existing economic and operating conditions.
 
     Proved Undeveloped Reserves. Reserves that are expected to be recovered
from new wells on undrilled acreage or from existing wells where a relatively
major expenditure is required for recompletion.
 
     Royalty. An interest in an oil and gas lease that gives the owner of the
interest the right to receive a portion of the production from the leased
acreage (or of the proceeds of the sale thereof), but generally does not require
the owner to pay any portion of the costs of drilling or operating the wells on
the leased acreage. Royalties may be either landowner's royalties, which are
reserved by the owner of the leased acreage at the time the lease is granted, or
overriding royalties, which are usually reserved by an owner of the leasehold in
connection with a transfer to a subsequent owner.
 
     Spud. Start drilling a new well (or restart).
 
   
     Success Rate. The number of wells on which production casing has been run
for a completion attempt as a percentage of the number of wells drilled.
    
 
     2-D Seismic. The method by which a cross-section of the earth's subsurface
is created through the interpretation of reflecting seismic data collected along
a single source profile.
 
     3-D Seismic. The method by which a three dimensional image of the earth's
subsurface is created through the interpretation of reflection seismic data
collected over surface grid. 3-D seismic surveys allow for a more detailed
understanding of the subsurface than do conventional surveys and contribute
significantly to field appraisal, development and production.
 
     Working Interest. An interest in an oil and gas lease that gives the owner
of the interest the right to drill for and produce natural gas and oil on the
leased acreage and requires the owner to pay a share of the costs of drilling
and production operations.
 
                                       58
<PAGE>   60
 
                         INDEX TO FINANCIAL STATEMENTS
 
<TABLE>
<CAPTION>
                                                              PAGE
                                                              ----
<S>                                                           <C>
Unaudited Pro Forma Financial Statements of Brigham
  Exploration Company.......................................  F1-2
  Unaudited Pro Forma Balance Sheet.........................  F1-3
  Unaudited Pro Forma Statement of Operations...............  F1-4
  Notes to the Unaudited Pro Forma Financial Statements.....  F1-5
Balance Sheet of Brigham Exploration Company
  Report of Independent Accountants.........................  F2-1
  Balance Sheet as of February 26, 1997.....................  F2-2
  Notes to the Balance Sheet................................  F2-3
Financial Statements of Brigham Oil & Gas, L.P.
  Report of Independent Accountants.........................  F3-1
  Balance Sheets as of December 31, 1995 and 1996...........  F3-2
  Statements of Operations for the Years Ended December 31,
     1994, 1995, and 1996...................................  F3-3
  Statements of Partners' Capital as of December 31, 1994,
     1995, and 1996.........................................  F3-4
  Statements of Cash Flows for the Years Ended December 31,
     1994, 1995, and 1996...................................  F3-5
  Notes to the Financial Statements.........................  F3-6
</TABLE>
 
                                      F1-1
<PAGE>   61
 
                          BRIGHAM EXPLORATION COMPANY
                     (A NEWLY FORMED DELAWARE CORPORATION)
 
                    UNAUDITED PRO FORMA FINANCIAL STATEMENTS
 
   
     The following Unaudited Pro Forma Financial Statements of the Company have
been prepared to give effect to the Exchange described below, the issuance of
employee stock options under the 1997 Incentive Plan and the issuance of Common
Stock pursuant to the Offering (and the application of the estimated net
proceeds therefrom) as if these events had taken place on December 31, 1996 for
purposes of the Unaudited Pro Forma Balance Sheet and as if these events had
taken place on January 1, 1996 for purposes of the Unaudited Pro Forma Statement
of Operations.
    
 
   
     Under the Exchange Agreement, effective February 27, 1997, the following
transactions occurred: (i) GAP III and the limited partners of the Partnership
transferred all their partnership interests to the Company in exchange for an
aggregate of 3,314,286 shares of Common Stock, (ii) the stockholders of Brigham,
Inc. transferred all of the issued and outstanding stock of Brigham, Inc. to the
Company in exchange for an aggregate of 3,859,821 shares of Common Stock and
(iii) Resource Investors Management Company ("RIMCO") exchanged all of the 5%
Convertible Unsecured Subordinated Notes of the Partnership for 1,754,464 shares
of Common Stock. These transactions are referred to herein as the "Exchange." As
a result of the Exchange, Brigham Exploration Company owns, directly or
indirectly, all the partnership interests in the Partnership and conducts its
active business operations through the Partnership. No instruments, agreements
or rights exist which may be converted, exchanged into, or otherwise become
interests in the Partnership. Brigham, Inc.'s only asset is its investment in
the Partnership.
    
 
     The Unaudited Pro Forma Financial Statements of the Company are not
necessarily indicative of the results for the periods presented had the
Exchange, the issuance of employee stock options under the 1997 Incentive Plan
and the issuance of Common Stock pursuant to the Offering (and the application
of the estimated net proceeds therefrom) taken place on January 1, 1996. In
addition, future results may vary significantly from the results reflected in
the accompanying Unaudited Pro Forma Financial Statements because of normal
production declines, changes in product prices, and the success of future
exploration and development activities, among other factors. This information
should be read in conjunction with the Balance Sheet of Brigham Exploration
Company and the Financial Statements of Brigham Oil & Gas, L.P., and the notes
thereto, all included elsewhere herein.
 
                                      F1-2
<PAGE>   62
 
                          BRIGHAM EXPLORATION COMPANY
 
                       UNAUDITED PRO FORMA BALANCE SHEET
                               DECEMBER 31, 1996
                                 (IN THOUSANDS)
 
   
<TABLE>
<CAPTION>
                                                                                              PRO FORMA
                                                    BRIGHAM OIL     PRO FORMA                 OFFERING      PRO FORMA
                                                   AND GAS, L.P.   ADJUSTMENTS   PRO FORMA   ADJUSTMENTS   AS ADJUSTED
                                                   -------------   -----------   ---------   -----------   -----------
<S>                                                <C>             <C>           <C>         <C>           <C>
                                                        ASSETS
 
Current assets:
  Cash and cash equivalents......................     $ 1,447       $     --      $ 1,447      $28,545(d)    $21,992
                                                                                                (8,000)(e)
  Accounts receivable............................       2,696             --        2,696           --         2,696
  Prepaid expenses...............................         152             --          152           --           152
                                                      -------       --------      -------      -------       -------
        Total current assets.....................       4,295             --        4,295       20,545        24,840
                                                      -------       --------      -------      -------       -------
Natural gas and oil properties, at cost, net.....      28,005             --       28,005           --        28,005
Other property and equipment, at cost, net.......         532             --          532           --           532
Drilling advances paid...........................         419             --          419           --           419
Other noncurrent assets..........................         363             --          363           --           363
                                                      -------       --------      -------      -------       -------
                                                      $33,614       $     --      $33,614      $20,545       $54,159
                                                      =======       ========      =======      =======       =======
 
                                LIABILITIES AND PARTNERS' CAPITAL/STOCKHOLDERS' EQUITY
 
Current liabilities:
  Accounts payable...............................     $ 2,937       $     --      $ 2,937      $    --       $ 2,937
  Accrued drilling costs.........................         915             --          915           --           915
  Participant advances received..................       1,137             --        1,137           --         1,137
  Other current liabilities......................         628             --          628           --           628
                                                      -------       --------      -------      -------       -------
        Total current liabilities................       5,617             --        5,617           --         5,617
                                                      -------       --------      -------      -------       -------
Notes payable....................................       8,000             --        8,000       (8,000)(e)        --
Subordinated notes payable -- related party......      16,000        (16,000)(b)       --           --            --
Deferred interest payable -- related party.......         433           (433)(b)       --           --            --
Other noncurrent liabilities.....................         320             --          320           --           320
Deferred income tax liability....................          --          5,112(a)     5,112           --         5,112
Partners' capital/stockholders' equity:
  Partners' capital:
    General partners.............................       3,190         (3,190)(b)       --           --            --
    Limited partners.............................          54            (54)(b)       --           --            --
  Stockholders' equity:
    Preferred stock, $.01 par value, 10 million
      shares authorized..........................          --             --           --           --            --
    Common stock, $.01 par value, 30 million
      shares authorized..........................          --             89(b)        89           30(d)        119
    Additional paid-in-capital...................          --         19,588(b)    22,486       28,515(d)     51,001
                                                                       2,898(c)
    Unearned stock compensation..................          --         (2,898)(c)   (2,898)          --        (2,898)
    Accumulated deficit..........................          --         (5,112)(a)   (5,112)          --        (5,112)
                                                      -------       --------      -------      -------       -------
        Total partners' capital/stockholders'
          equity.................................       3,244         11,321       14,565       28,545        43,110
                                                      -------       --------      -------      -------       -------
                                                      $33,614       $     --      $33,614      $20,545       $54,159
                                                      =======       ========      =======      =======       =======
</TABLE>
    
 
  The Company uses the full cost method to account for its natural gas and oil
                                  properties.
 
    See accompanying notes to the Unaudited Pro Forma Financial Statements.
 
                                      F1-3
<PAGE>   63
 
                          BRIGHAM EXPLORATION COMPANY
 
                  UNAUDITED PRO FORMA STATEMENT OF OPERATIONS
                          YEAR ENDED DECEMBER 31, 1996
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)
 
   
<TABLE>
<CAPTION>
                                                                                       PRO FORMA
                                           BRIGHAM OIL     PRO FORMA                   OFFERING        PRO FORMA
                                          AND GAS, L.P.   ADJUSTMENTS     PRO FORMA   ADJUSTMENTS     AS ADJUSTED
                                          -------------   -----------     ---------   -----------     -----------
<S>                                       <C>             <C>             <C>         <C>             <C>
Revenues:
  Natural gas and oil sales.............     $6,141         $    --        $6,141       $   --          $6,141
  Workstation revenue...................        627              --           627           --             627
                                             ------         -------        ------       ------          ------
                                              6,768              --         6,768           --           6,768
                                             ------         -------        ------       ------          ------
Costs and expenses:
  Lease operating.......................        726              --           726           --             726
  Production taxes......................        362              --           362           --             362
  General and administrative............      2,199              --         2,199           --           2,199
  Amortization of stock compensation....         --             516(c)        516           --             516
  Depletion of natural gas and oil
     properties.........................      2,323              51(c)      2,374           --           2,374
  Depreciation and amortization.........        487              --           487           --             487
                                             ------         -------        ------       ------          ------
                                              6,097             567         6,664           --           6,664
                                             ------         -------        ------       ------          ------
          Operating income (loss).......        671            (567)          104           --             104
                                             ------         -------        ------       ------          ------
Other income (expense):
  Interest income.......................         52              --            52           --              52
  Interest expense......................       (373)             --          (373)         373(e)           --
  Interest expense -- related party.....       (800)            800(b)         --           --              --
                                             ------         -------        ------       ------          ------
Net income (loss) before income taxes...       (450)            233          (217)         373             156
Income tax benefit......................         --             161(a)        161         (127)(a)          34
                                             ------         -------        ------       ------          ------
  Net income (loss).....................     $ (450)        $   394        $  (56)      $  246          $  190
                                             ======         =======        ======       ======          ======
  Net income (loss) per common share....                                   $ 0.00                       $ 0.02
                                                                           ======                       ======
  Weighted average number of common
     shares outstanding.................                                    9,266                       12,266
                                                                           ======                       ======
</TABLE>
    
 
    See accompanying notes to the Unaudited Pro Forma Financial Statements.
 
                                      F1-4
<PAGE>   64
 
                          BRIGHAM EXPLORATION COMPANY
 
             NOTES TO THE UNAUDITED PRO FORMA FINANCIAL STATEMENTS
 
1. BASIS OF PRESENTATION
 
   
     The accompanying Unaudited Pro Forma Financial Statements of the Company
have been prepared to give effect to the Exchange, the issuance of employee
stock options under the 1997 Incentive Plan and the issuance of Common Stock
pursuant to the Offering (and the application of the estimated net proceeds
therefrom) as if such transactions had taken place on December 31, 1996 for
purposes of the Unaudited Pro Forma Balance Sheet and as if the transactions had
taken place on January 1, 1996 for purposes of the Unaudited Pro Forma Statement
of Operations. The Company was formed in February 1997 with a capitalization of
$30. As the Exchange is the conversion of a partnership to a corporation, the
Exchange has been accounted for as a reorganization.
    
 
   
2. PRO FORMA ADJUSTMENTS AND PRO FORMA OFFERING ADJUSTMENTS
    
 
     The Unaudited Pro Forma Financial Statements reflect the following pro
forma adjustments related to the consummation of the Exchange, the issuance of
employee stock options under the 1997 Incentive Plan and the issuance of Common
Stock pursuant to the Offering (and the application of the estimated net
proceeds therefrom).
 
     a. To record current and deferred federal income tax expense as if the
        Partnership had been a taxable entity.
 
   
     b. To record (i) the issuance of 3,859,821 shares of Common Stock of the
        Company in exchange for all of the issued and outstanding stock of
        Brigham, Inc., (ii) the issuance of 3,314,286 shares of Common Stock of
        the Company in exchange for all of the partnership interests of the
        Partnership's other general partner and its limited partners and (iii)
        the issuance of 1,754,464 shares of Common Stock of the Company in
        exchange for all of the subordinated notes payable.
    
 
   
     c. To record unearned compensation and the amortization thereon related to
        employee stock options granted under the 1997 Incentive Plan in March
        1997. A portion of the amortization of the unearned compensation was
        capitalized as part of the Company's amortizable base of the full cost
        pool to the extent that this cost was directly attributable to
        acquisition, exploration and development activities. Depletion of
        natural gas and oil properties was adjusted accordingly.
    
 
   
     d. To reflect the issuance of 3,000,000 shares of Common Stock at the
        assumed initial public offering price of $10.50 per share for estimated
        proceeds of $28,545,000, net of estimated underwriting discounts and
        expenses of this Offering.
    
 
     e. To record the partial use of the estimated net proceeds of the Offering
        to fully repay borrowings under the Revolving Credit Facility.
 
3. INCOME TAXES
 
     Upon consummation of the Exchange, the Company will record a deferred tax
liability or asset for temporary differences between the financial statement and
tax bases of assets and liabilities at the Exchange date given the provisions of
enacted tax laws. Assuming the Exchange had occurred on December 31, 1996, the
Company would have incurred an estimated charge of $5.1 million to record a
deferred tax liability primarily reflecting the difference between the tax bases
and the financial statement bases of the Partnership's natural gas and oil
properties. As this will be a nonrecurring charge, it has not been included in
the Unaudited Pro Forma Statement of Operations. The ultimate tax bases and
related difference from financial statement bases cannot be ultimately
determined until consummation of the Exchange, and such basis differences will
change depending upon the level and nature of operations and the amount of
taxable income and deductions allocated to the partners through the date of the
Exchange. Such basis differences could vary materially from this estimate.
 
                                      F1-5
<PAGE>   65
 
                          BRIGHAM EXPLORATION COMPANY
 
      NOTES TO THE UNAUDITED PRO FORMA FINANCIAL STATEMENTS -- (CONTINUED)
 
4. NET LOSS PER COMMON SHARE
 
   
     Pro forma net loss per common share is presented giving effect to the
number of shares outstanding subsequent to the Exchange (8,928,571 shares) and
giving effect to 644,097 stock options issued under the 1997 Incentive Plan on
February 28, 1997. These options, which have an exercise price of $5.00 per
share, are treated as Common Stock equivalents. The number of equivalent shares
was determined by the treasury stock method based on the offering price of
$10.50 per share. In addition to the effect of these events, pro forma, as
adjusted, net loss per common share gives effect to the 3,000,000 shares of
Common Stock issued pursuant to the Offering.
    
 
                                      F1-6
<PAGE>   66
 
                       REPORT OF INDEPENDENT ACCOUNTANTS
 
To the Board of Directors
and Stockholders of Brigham Exploration Company
 
     In our opinion, the accompanying balance sheet presents fairly, in all
material respects, the financial position of Brigham Exploration Company at
February 26, 1997, in conformity with generally accepted accounting principles.
This balance sheet is the responsibility of the Company's management; our
responsibility is to express an opinion on the balance sheet based on our audit.
We conducted our audit in accordance with generally accepted auditing standards
which require that we plan and perform the audit to obtain reasonable assurance
about whether the balance sheet is free of material misstatement. An audit
includes examining, on a test basis, evidence supporting the amounts and
disclosures in the balance sheet, assessing the accounting principles used and
significant estimates made by management, and evaluating the overall financial
statement presentation. We believe that our audit provides a reasonable basis
for the opinion expressed above.
 
PRICE WATERHOUSE LLP
 
Houston, Texas
   
February 26, 1997, except as to Notes 1 and 3,
    
   
which are as of February 27, 1997
    
 
                                      F2-1
<PAGE>   67
 
                          BRIGHAM EXPLORATION COMPANY
                     (A NEWLY FORMED DELAWARE CORPORATION)
 
                                 BALANCE SHEET
                               FEBRUARY 26, 1997
 
   
<TABLE>
<S>                                       <C>
Assets:
  Cash..................................  $30
                                          ===
Stockholders' equity:
  Preferred stock, $.01 par value, 10
     million shares authorized, none
     issued and outstanding.............  $--
  Common stock, $.01 par value, 30
     million shares authorized, 3 shares
     issued and outstanding.............   --
  Additional paid-in capital............   30
                                          ---
          Total stockholders' equity....  $30
                                          ===
</TABLE>
    
 
                  See accompanying notes to the balance sheet.
 
                                      F2-2
<PAGE>   68
 
                          BRIGHAM EXPLORATION COMPANY
                     (A NEWLY FORMED DELAWARE CORPORATION)
 
                           NOTES TO THE BALANCE SHEET
                               FEBRUARY 26, 1997
 
1. ORGANIZATION AND BUSINESS PURPOSE
 
   
     Brigham Exploration Company (the "Company") is a Delaware corporation
formed on February 25, 1997 for the purpose of exchanging its common stock for
the common stock of Brigham, Inc. and the partners' interests in Brigham Oil &
Gas, L.P. (the "Partnership"). Subsequent to the Exchange, which occurred on
February 27, 1997, the Company and its subsidiary hold all Partnership
interests. Additionally, the Company exchanged shares with the holder of the
Partnership's subordinated convertible notes which would otherwise be
convertible into a 19.65% interest in the Partnership. These transactions are
referred to as the "Exchange". In completing the Exchange, the Company issued
8,928,571 shares of common stock to the stockholders of Brigham, Inc., the
partners of the Partnership and the holder of the Partnership's subordinated
notes payable. As the Exchange is the conversion of a partnership into a
corporation, the Exchange has been accounted for as a reorganization.
    
 
   
     The Company expects to initiate a public issuance of common stock in early
1997.
    
 
2. STOCKHOLDERS' EQUITY
 
     The Board of Directors of the Company is empowered, without approval of
stockholders, to cause shares of preferred stock to be issued in one or more
series. The Board of Directors is authorized to fix and determine variations in
designations, preferences and relative, participating, optional or other special
rights and the limitations or restrictions of such rights and voting powers.
 
     Holders of common stock are entitled to one vote per share in the election
of directors and on all other matters submitted to a vote of common
stockholders. The common stock does not have cumulative voting rights. Holders
of common stock are entitled to receive dividends, if any, as may be declared by
the Board of Directors out of funds legally available therefore, subject to any
preferential dividend rights of holders of outstanding preferred stock.
 
3. STOCK COMPENSATION
 
   
     The Board of Directors and stockholders of the Company anticipate the
adoption of an incentive plan, to be effective upon completion of the Exchange,
which will provide for the issuance of stock options, stock appreciation rights,
stock, restricted stock, cash or any combination of the foregoing. The objective
of this plan will be to reward key employees whose performance may have a
significant effect on the success of the Company. The Compensation Committee of
the Board of Directors will determine the type of awards made to each
participant and the terms, conditions and limitations applicable to each award.
An aggregate of 1,588,169 shares of common stock will be reserved for issuance
pursuant to this plan with 644,097 shares subject to initial grants of stock
options at an exercise price less than the public offering price. The Company
estimates that the fair value of these options on their grant date, using the
Black-Scholes option-pricing model, will be $4.6 million. In accordance with
SFAS No. 123, the Company has elected to follow the accounting provisions of
Accounting Principles Board Opinion No. 25 for stock-based compensation and
record unearned compensation, a deduction from stockholders' equity, for the
difference between the market value of the Company's stock on the grant date and
the exercise price of the options. This amount, which the Company estimates will
be $2.9 million, will be amortized over the appropriate vesting period.
    
 
   
     The Board of Directors and stockholders of the Company also anticipate the
adoption of the 1997 Director Stock Option Plan, pursuant to which each newly
elected nonemployee director shall be granted an option to purchase 1,000 shares
of common stock and each nonemployee director will receive an option to purchase
500 shares of common stock on December 31 of each year. An aggregate of 25,000
shares of common stock will be reserved for issuance pursuant to this plan. The
exercise price of options granted under
    
 
                                      F2-3
<PAGE>   69
 
   
this plan will be equal to the fair market value of the underlying common stock
on the date of grant. No compensation expense will result from options granted
under this plan.
    
 
   
     On February 27, 1997, in connection with the Exchange (see Note 1), three
employees who had been granted restricted interests in the Partnership in 1994
transferred, upon the initial filing of a registration statement with the SEC
for a public offering of common stock, these partnership interests to the
Company in exchange for 156,250 shares of restricted common stock. The terms of
the restricted stock and the restricted partnership interests are substantially
the same. The shares vest over a three year period ending in 1999. No
compensation expense will result from this exchange.
    
 
                                      F2-4
<PAGE>   70
 
                       REPORT OF INDEPENDENT ACCOUNTANTS
 
To the Partners of
Brigham Oil & Gas, L.P.
 
     In our opinion, the accompanying balance sheets and the related statements
of operations, of partners' capital and of cash flows present fairly, in all
material respects, the financial position of Brigham Oil & Gas, L.P. at December
31, 1996 and 1995, and the results of its operations and its cash flows for each
of the three years in the period ended December 31, 1996, in conformity with
generally accepted accounting principles. These financial statements are the
responsibility of the Partnership's management; our responsibility is to express
an opinion on these financial statements based on our audits. We conducted our
audits of these statements in accordance with generally accepted auditing
standards which require that we plan and perform the audit to obtain reasonable
assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements, assessing the
accounting principles used and significant estimates made by management, and
evaluating the overall financial statement presentation. We believe that our
audits provide a reasonable basis for the opinion expressed above.
 
PRICE WATERHOUSE LLP
 
Houston, Texas
   
February 26, 1997, except as to Notes 1 and 4,
    
   
which are as of February 27, 1997
    
 
                                      F3-1
<PAGE>   71
 
                            BRIGHAM OIL & GAS, L.P.
 
                                 BALANCE SHEETS
                                 (IN THOUSANDS)
 
   
<TABLE>
<CAPTION>
                                             DECEMBER 31,
                                          ------------------
                                           1995       1996
                                          -------    -------
<S>                                       <C>        <C>
                           ASSETS
 
Current assets:
  Cash and cash equivalents.............  $ 1,802    $ 1,447
  Accounts receivable...................    1,256      2,696
  Prepaid expenses......................      177        152
                                          -------    -------
          Total current assets..........    3,235      4,295
                                          -------    -------
Natural gas and oil properties, at cost,
  net (including $3,460 and $7,068,
  respectively, not subject to
  depletion)............................   18,538     28,005
Other property and equipment, at cost,
  net...................................      684        532
Drilling advances paid..................      127        419
Other noncurrent assets.................      332        363
                                          -------    -------
                                          $22,916    $33,614
                                          =======    =======
 
             LIABILITIES AND PARTNERS' CAPITAL
 
Current liabilities:
  Accounts payable......................  $ 1,318    $ 2,937
  Accrued drilling costs................      588        915
  Participant advances received.........      333      1,137
  Other current liabilities.............      689        628
                                          -------    -------
          Total current liabilities.....    2,928      5,617
                                          -------    -------
Notes payable...........................       --      8,000
Subordinated notes payable -- related
  party.................................   16,000     16,000
Deferred interest payable -- related
  party.................................      113        433
Other noncurrent liabilities............      181        320
Commitments and contingencies
Partners' capital:
  General partners......................    3,620      3,190
  Limited partners......................       74         54
                                          -------    -------
          Total partners' capital.......    3,694      3,244
                                          -------    -------
                                          $22,916    $33,614
                                          =======    =======
</TABLE>
    
 
The Partnership uses the full cost method to account for its natural gas and oil
                                  properties.
 
              See accompanying notes to the financial statements.
 
                                      F3-2
<PAGE>   72
 
                            BRIGHAM OIL & GAS, L.P.
 
                            STATEMENTS OF OPERATIONS
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)
 
   
<TABLE>
<CAPTION>
                                                               YEAR ENDED DECEMBER 31,
                                                              --------------------------
                                                               1994      1995      1996
                                                              -------   -------   ------
<S>                                                           <C>       <C>       <C>
Revenues:
  Natural gas and oil sales.................................  $ 2,565   $ 3,578   $6,141
  Workstation revenue.......................................      815       635      627
                                                              -------   -------   ------
                                                                3,380   4,213..    6,768
                                                              -------   -------   ------
Costs and expenses:
  Lease operating...........................................      491       761      726
  Production taxes..........................................      126       165      362
  General and administrative................................    1,785     1,897    2,199
  Depletion of natural gas and oil properties...............    1,104     1,626    2,323
  Depreciation and amortization.............................      561       533      487
                                                              -------   -------   ------
                                                                4,067     4,982    6,097
                                                              -------   -------   ------
          Operating income (loss)...........................     (687)     (769)     671
                                                              -------   -------   ------
Other income (expense):
  Interest income...........................................       56       128       52
  Interest expense..........................................      (76)     (187)    (373)
  Interest expense -- related party.........................     (592)     (749)    (800)
                                                              -------   -------   ------
          Net loss..........................................  $(1,299)  $(1,577)  $ (450)
                                                              =======   =======   ======
Unaudited pro forma information (Notes 1 and 2)
  Net loss..................................................                      $ (450)
  Pro forma Exchange adjustments............................                         233
                                                                                  ------
  Pro forma net loss before taxes...........................                        (217)
  Pro forma income tax benefit..............................                         161
                                                                                  ------
  Pro forma net loss........................................                      $  (56)
                                                                                  ======
  Pro forma net loss per common share.......................                      $ 0.00
                                                                                  ======
  Pro forma weighted average number of common shares
     outstanding............................................                       9,266
                                                                                  ======
</TABLE>
    
 
              See accompanying notes to the financial statements.
 
                                      F3-3
<PAGE>   73
 
                            BRIGHAM OIL & GAS, L.P.
 
                        STATEMENTS OF PARTNERS' CAPITAL
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                              GENERAL     LIMITED
                                                              PARTNERS    PARTNERS     TOTAL
                                                              --------    --------    -------
<S>                                                           <C>         <C>         <C>
Balance at December 31, 1993................................  $ 6,364       $206      $ 6,570
          Net loss..........................................   (1,239)       (60)      (1,299)
                                                              -------       ----      -------
Balance at December 31, 1994................................    5,125        146        5,271
          Net loss..........................................   (1,505)       (72)      (1,577)
                                                              -------       ----      -------
Balance at December 31, 1995................................    3,620         74        3,694
          Net loss..........................................     (430)       (20)        (450)
                                                              -------       ----      -------
Balance at December 31, 1996................................  $ 3,190       $ 54      $ 3,244
                                                              =======       ====      =======
</TABLE>
 
              See accompanying notes to the financial statements.
 
                                      F3-4
<PAGE>   74
 
                            BRIGHAM OIL & GAS, L.P.
 
                            STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                                 YEAR ENDED DECEMBER 31,
                                                              -----------------------------
                                                               1994       1995       1996
                                                              -------   --------   --------
<S>                                                           <C>       <C>        <C>
Cash flows from operating activities:
  Net loss..................................................  $(1,299)  $ (1,577)  $   (450)
  Adjustments to reconcile net loss to cash provided by
     operating activities:
     Depletion of natural gas and oil properties............    1,104      1,626      2,323
     Depreciation and amortization..........................      561        533        487
     Changes in working capital and other items:
       (Increase) decrease in accounts receivable...........    2,074        413     (1,440)
       (Increase) decrease in prepaid expenses..............      (29)      (107)        25
       Increase (decrease) in accounts payable..............   (1,451)       128      1,619
       Increase (decrease) in participant advances
          received..........................................     (170)        92        804
       Increase (decrease) in other current liabilities.....     (121)       151         60
       Increase in deferred interest payable -- related
          party.............................................       --        113        320
       Other noncurrent assets..............................      (43)       (26)      (224)
       Other noncurrent liabilities.........................       --         37        186
                                                              -------   --------   --------
          Net cash provided by operating activities.........      626      1,383      3,710
                                                              -------   --------   --------
Cash flows from investing activities:
  Additions to natural gas and oil properties...............   (5,445)    (7,935)   (13,612)
  Proceeds from the sale of natural gas and oil
     properties.............................................       --         --      2,149
  Additions to other property and equipment.................      (62)       (51)       (41)
  (Increase) decrease in drilling advances paid.............       44        (19)      (292)
                                                              -------   --------   --------
          Net cash used by investing activities.............   (5,463)    (8,005)   (11,796)
                                                              -------   --------   --------
Cash flows from financing activities:
  Proceeds from issuance of subordinated notes payable......       --     16,000         --
  Increase in notes payable.................................    4,950      2,560      8,000
  Repayment of notes payable................................       --    (10,510)        --
  Principal payments on capital lease obligations...........     (316)      (326)      (269)
                                                              -------   --------   --------
          Net cash provided by financing activities.........    4,634      7,724      7,731
                                                              -------   --------   --------
Net increase (decrease) in cash and cash equivalents........     (203)     1,102       (355)
Cash and cash equivalents, beginning of year................      903        700      1,802
                                                              -------   --------   --------
Cash and cash equivalents, end of year......................  $   700   $  1,802   $  1,447
                                                              =======   ========   ========
Supplemental disclosure of cash flow information:
  Cash paid during the period for interest..................  $   667   $    654   $    762
                                                              =======   ========   ========
Supplemental disclosure of noncash investing and financing
  activities:
  Capital lease asset additions.............................  $   361   $    208   $    101
                                                              =======   ========   ========
</TABLE>
 
              See accompanying notes to the financial statements.
 
                                      F3-5
<PAGE>   75
 
                            BRIGHAM OIL & GAS, L.P.
 
                       NOTES TO THE FINANCIAL STATEMENTS
 
1. ORGANIZATION AND NATURE OF OPERATIONS
 
     Brigham Oil & Gas, L.P. (the "Partnership") was formed in May 1992 to
explore and develop onshore domestic natural gas and oil properties using 3-D
seismic imaging and other advanced technologies. Since its inception, the
Partnership has focused its exploration and development of natural gas and oil
properties in the Permian and Hardeman Basins of West Texas, the Anadarko Basin
and the Gulf Coast.
 
   
     Brigham, Inc. is the managing general partner of the Partnership and owned
a 54% interest in the Partnership. Brigham, Inc. generally directs all
activities of the Partnership. Until February 27, 1997, the other general
partner held a 38% interest in the Partnership, had participating rights in
certain Major Decisions, as defined, and had a preference in the allocation of
profits and other items.
    
 
   
     Pursuant to an Exchange Agreement dated February 26, 1997 (the "Exchange
Agreement") and upon the initial filing on February 27, 1997 of a registration
statement with the Securities and Exchange Commission for a public offering of
common stock, the shareholders of Brigham, Inc. transferred all of the
outstanding stock of Brigham, Inc. to a newly formed entity, Brigham Exploration
Company (the "Company"), in exchange for shares of common stock of the Company.
Brigham, Inc. is a Texas corporation whose only asset is its ownership interest
in the Partnership. Pursuant to the Exchange Agreement, the Partnership's other
general partner and the limited partners also transferred all of their
partnership interests to the Company in exchange for shares of common stock of
the new entity. Furthermore, the holders of the subordinated convertible notes
(see Note 4) transferred these notes to the Company in exchange for shares of
common stock. As a result of these transactions, hereafter referred to as the
"Exchange," the Company now owns all the partnership interests in the
Partnership.
    
 
2. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES
 
  Basis of Accounting
 
     The preparation of financial statements in conformity with generally
accepted accounting principles requires management to make estimates and
assumptions that affect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the date of the financial
statements and the reported amounts of revenues and expenses during the
reporting period. Actual results may differ from those estimates.
 
  Cash and Cash Equivalents
 
     The Partnership considers all highly liquid financial instruments with an
original maturity of three months or less to be cash equivalents.
 
  Property and Equipment
 
   
     The Partnership uses the full cost method of accounting for its investment
in natural gas and oil properties. Under this method, all acquisition,
exploration and development costs, including leasehold acquisition costs,
geological and geophysical expenditures, dry hole costs and tangible and
intangible development costs, incurred for the purpose of finding natural gas
and oil reserves are capitalized. Included in the Partnership's investment in
natural gas and oil properties as of December 31, 1994, 1995 and 1996 are
general and administrative costs of $1,320,114, $1,640,196 and $1,826,013,
respectively. These capitalized general and administrative costs consist
primarily of the compensation and benefit costs of exploration department
personnel which are directly attributable to the Partnership's acquisition,
exploration and development activities. Other internal costs (primarily
including office rent and technical computer maintenance and support) are
capitalized to the extent they are attributable to the Partnership's natural gas
and oil property acquisition and exploration activities and would not otherwise
be incurred if such activities were not being undertaken.
    
 
                                      F3-6
<PAGE>   76
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
   
     The capitalized costs of the Partnership's natural gas and oil properties
plus future development, dismantlement, restoration and abandonment costs (the
"Amortizable Base"), net of estimated salvage values, are amortized using the
unit-of-production method based upon estimates of total proved reserve
quantities. The Partnership's capitalized costs of its natural gas and oil
properties, net of accumulated depletion, are limited to the total of estimated
future net cash flows from proved natural gas and oil reserves, discounted at
ten percent, plus the cost of unevaluated properties. The Partnership's only
active cost center since inception has been the United States of America. There
are many factors, including global events, that may influence the production,
processing, marketing and valuation of natural gas and oil. A reduction in the
valuation of natural gas and oil properties resulting from declining prices or
production could adversely impact depletion rates and ceiling test limitations.
    
 
     All costs directly associated with the acquisition and evaluation of
unproved properties are initially excluded from the Amortizable Base. Upon the
interpretation by the Partnership of the 3-D seismic data associated with
unproved properties, the geological and geophysical costs of acreage that is not
specifically identified as prospective are added to the Amortizable Base.
Geological and geophysical costs associated with prospective acreage, as well as
leasehold costs, are added to the Amortizable Base when the prospects are
drilled. Costs of prospective acreage are reviewed annually for impairment on a
property-by-property basis.
 
   
     Effective January 1, 1996, the Partnership conformed its accounting policy
for the full cost method of accounting to that permitted by Rule 4-10 of the
Security and Exchange Commission's Regulation S-X. The financial statements of
prior years have been restated to apply the new accounting policy retroactively.
The accounting change reduced the Partnership's net loss as previously reported
in 1994 and 1995 by $1,186,005 and $1,389,840, respectively.
    
 
     Other property and equipment, which primarily consists of 3-D seismic
interpretation workstations, are depreciated on a straight-line basis over the
estimated useful lives of the assets after considering salvage value. Estimated
useful lives are as follows:
 
<TABLE>
<S>                                       <C>
Furniture and fixtures..................  10 years
Machinery and equipment.................   5 years
3-D seismic interpretation workstations
  and software..........................   3 years
</TABLE>
 
     Betterments and major improvements that extend the useful lives are
capitalized, while expenditures for repairs and maintenance of a minor nature
are expensed as incurred.
 
  Revenue Recognition
 
   
     Joint interest owners may take more or less than their ownership interest
of natural gas volumes from jointly owned reservoirs. The Partnership follows
the sales method of accounting for imbalances. Under this method, the
Partnership records a liability if its sales of natural gas volumes in excess of
its entitlements from a jointly owned reservoir exceed its interest in the
remaining estimated natural gas reserves of such reservoir. Volumetric
production is monitored to minimize imbalances, and such imbalances as of
December 31, 1994, 1995 and 1996 were not significant.
    
 
     Net realized gains or losses arising from the Partnership's crude oil price
swaps (see Note 7) are recognized in the period incurred as a component of
natural gas and oil sales.
 
     Industry participants in the Partnership's seismic programs are charged on
an hourly basis for the work performed by the Partnership on its 3-D seismic
interpretation workstations. The Partnership recognizes workstation revenue as
service is provided.
 
                                      F3-7
<PAGE>   77
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
  Federal and State Income Taxes
 
     The financial statements include only those assets, liabilities and
operations that relate to the business of the Partnership. The financial
statements do not include any assets, liabilities or operations attributable to
the partners' individual activities. No provision has been made for income taxes
since these taxes are the responsibility of the partners.
 
   
     Upon consummation of the Exchange, the Company will record a deferred tax
liability or asset for temporary differences between the financial statement and
tax bases of assets and liabilities at the Exchange date given the provisions of
enacted tax laws. Assuming the Exchange had occurred on December 31, 1996, the
Company would have incurred an estimated charge of $5.1 million to record a
deferred tax liability primarily reflecting the difference between the tax bases
and the financial statement bases of the Partnership's natural gas and oil
properties. The ultimate tax bases and related difference from financial
statement bases have not been determined and such basis differences will change
depending upon the level and nature of operations and the amount of taxable
income and deductions allocated to the partners through the date of the
Exchange. Such basis differences could vary materially from this estimate.
    
 
  Unaudited Pro Forma Information
 
     The Partnership's legal form has no relation to the capital structure of
the Company after the Exchange. As a result, historical loss per unit amounts
are not relevant and have not been presented.
 
     Pro forma net loss for the year ended December 31, 1996 reflects the
Exchange, including income taxes that would have been recorded had the
Partnership been a taxable entity. Pro forma exchange adjustments primarily
represent the amortization of the compensation expense related to employee stock
options granted upon the formation of the Company (see Note 8), and the
reduction of interest expense related to the transfer of the subordinated notes
payable to the Company as part of the Exchange. Pro forma income taxes have been
included in the Statement of Operations pursuant to the rules and regulations of
the SEC for instances when a partnership becomes subject to federal income
taxes.
 
     Pro forma net loss per common share is presented giving effect to the
number of shares outstanding subsequent to the Exchange (8,928,571 shares) and
giving effect to the shares to be issued under the anticipated February 1997
employee stock option grants (see Note 8). Pro forma net loss per common share
was calculated using the treasury stock method.
 
  Reclassification of Prior Years
 
     Prior year financial statements have been reclassified to conform to 1996
presentations.
 
                                      F3-8
<PAGE>   78
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
3. PROPERTY AND EQUIPMENT
 
     Property and equipment, at cost, are summarized as follows (in thousands):
 
<TABLE>
<CAPTION>
                                             DECEMBER 31,
                                          ------------------
                                           1995       1996
                                          -------    -------
<S>                                       <C>        <C>
Natural gas and oil properties..........  $25,765    $37,555
Accumulated depletion...................   (7,227)    (9,550)
                                          -------    -------
                                           18,538     28,005
                                          -------    -------
Other property and equipment:
  3-D seismic interpretation
     workstations and software..........    1,351      1,456
  Office furniture and equipment........      347        384
  Accumulated depreciation..............   (1,014)    (1,308)
                                          -------    -------
                                              684        532
                                          -------    -------
                                          $19,222    $28,537
                                          =======    =======
</TABLE>
 
     On January 30, 1996, the Partnership sold its interest in certain producing
properties for $2.1 million. A gain or loss was not recognized on this
transaction because the Partnership applies the full cost method of accounting
for its investment in natural gas and oil properties.
 
4. NOTES PAYABLE AND SUBORDINATED NOTES PAYABLE
 
     The notes payable pertain to a revolving credit facility, due 1999, entered
into by the Partnership in April 1996. This facility provides for borrowings up
to $25 million and is secured by the Partnership's natural gas and oil
properties. The Partnership's borrowings under the revolving credit facility are
limited to a borrowing base determined semiannually by the lender. This
determination is based upon the Partnership's proved natural gas and oil
properties.
 
     The amounts outstanding under the revolving credit facility bear interest,
at the borrower's option, at the Base Rate or (i) LIBOR plus 1.75% if the
principal outstanding is less than or equal to 50% of the borrowing base, (ii)
LIBOR plus 2.0% if the principal outstanding is less than or equal to 75% but
more than 50% of the borrowing base, and (iii) LIBOR plus 2.25% if the principal
outstanding is greater than 75% of the borrowing base. The Base Rate is the
fluctuating of interest per annum established from time to time by the lender.
The Company also pays a quarterly commitment fee of 0.5% per annum for the
unused portion of the borrowing base.
 
   
     The Company is subject to certain covenants under the terms of the
revolving credit facility. The financial ratios that the Partnership was
required to meet at December 31, 1996 were as follows: (i) the ratio of current
assets, as defined in the borrowing agreement, to current liabilities must be at
least 1.0 to 1.0, and (ii) the debt service coverage ratio of net cash flow to
debt service for the three months ended December 31, 1996 must be at least 2.25
to 1.0. The revolving credit facility contains certain other affirmative and
negative covenants, including limitations on additional indebtedness and
restrictions on the payment of dividends. The Partnership is currently in
compliance with all covenants.
    
 
   
     The subordinated notes payable bear interest at 5% per annum and are due in
2002. The notes are convertible into a 19.65% interest in the Partnership at any
time prior to maturity and are unsecured. A representative of the holders of
these notes is a member of the Partnership's management committee. Interest
payments of 3% are due semi-annually and the remaining 2% is deferred until
maturity. As part of the Exchange (see Note 1), the holders of these notes
exchanged the notes for shares of the Company's common stock.
    
 
                                      F3-9
<PAGE>   79
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
5. CAPITAL LEASE OBLIGATIONS
 
     Property under capital leases consists of the following (in thousands):
 
<TABLE>
<CAPTION>
                                           DECEMBER 31,
                                          --------------
                                          1995     1996
                                          -----    -----
<S>                                       <C>      <C>
3-D seismic interpretation workstations
  and software..........................  $ 668    $ 525
Office furniture and equipment..........     58       17
                                          -----    -----
                                            726      542
Accumulated depreciation and
  amortization..........................   (324)    (305)
                                          -----    -----
                                          $ 402    $ 237
                                          =====    =====
</TABLE>
 
     The obligations under capital leases are at fixed interest rates ranging
from 11% to 17% and are collateralized by property, plant and equipment. The
future minimum lease payments under the capital leases and the present value of
the net minimum lease payments at December 31, 1996 are as follows (in
thousands):
 
<TABLE>
<S>                                                           <C>
1997........................................................  $ 204
1998........................................................    105
1999........................................................     28
                                                              -----
Total minimum lease payments................................    337
Estimated executory costs included in capital leases........    (74)
                                                              -----
Net minimum lease payments..................................    263
Amounts representing interest...............................    (32)
                                                              -----
Present value of net minimum lease payments.................    231
Less: current portion.......................................   (133)
                                                              -----
Noncurrent portion..........................................  $  98
                                                              =====
</TABLE>
 
6. COMMITMENTS AND CONTINGENCIES
 
     The Partnership is, from time to time, party to certain lawsuits and claims
arising in the ordinary course of business. While the outcome of lawsuits and
claims cannot be predicted with certainty, management does not expect these
matters to have a materially adverse effect on the financial condition, results
of operations or cash flows of the Partnership.
 
     The Partnership leases office equipment and space under operating leases
expiring at various dates through 2007. The future minimum annual rental
payments under the noncancelable terms of these leases at December 31, 1996, are
as follows (in thousands):
 
<TABLE>
<S>                                                           <C>
1997........................................................  $  526
1998........................................................     610
1999........................................................     610
2000........................................................     543
2001........................................................     543
Thereafter..................................................     272
                                                              ------
                                                              $3,104
                                                              ======
</TABLE>
 
     The Partnership has an option to cancel an office space lease at July 1,
2002. Additional rental payments of $2.6 million will be required for years 2002
through 2007 if the Partnership does not elect to cancel the lease.
 
                                      F3-10
<PAGE>   80
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
     Rental expense for the years ended December 31, 1994, 1995 and 1996 was
$202,923, $239,715 and $253,112, respectively.
 
     Since the Partnership's major products are commodities, significant changes
in the prices of natural gas and oil could have a significant impact on the
Partnership's results of operations for any particular year.
 
     As of December 31, 1996, there were no known environmental or other
regulatory matters related to the Partnership's operations which are reasonably
expected to result in a material liability to the Partnership. Compliance with
environmental laws and regulations has not had, and is not expected to have, a
material adverse effect on the Partnership's capital expenditures, earnings or
competitive position.
 
     During 1996, approximately 16%, 12% and 10% of the Partnership's natural
gas and oil production was sold to three separate customers. During 1995,
approximately 14%, 11%, 10%, and 10% of the Partnership's natural gas and oil
production was sold to four separate customers. During 1994, approximately 15%,
15%, 13%, 13%, and 11% of the Partnership's natural gas and oil production was
sold to five separate customers. However, due to the availability of other
markets, the Partnership does not believe that the loss of any one of these
individual customers would adversely affect the Partnership's result of
operations.
 
7. FINANCIAL INSTRUMENTS
 
     The Partnership periodically enters into crude oil price swap agreements
which require payments to (or receipts from) counterparties based on the
differential between a fixed price and a variable price for a fixed quantity of
crude oil without the exchange of the underlying crude oil volumes. The notional
amounts of these derivative financial instruments are based on planned
production from existing wells. The Partnership uses these derivative financial
instruments to manage market risks resulting from fluctuations in crude oil
prices. Crude oil price swaps are effective in minimizing these risks by
creating essentially equal and offsetting market exposures. The derivative
financial instruments held by the Partnership are not leveraged and are held for
purposes other than trading.
 
     At December 31, 1996, the Partnership was a party to crude oil price swap
based on an average notional volume of 7,550 barrels of crude oil per month and
a fixed price of $22.70 per barrel. The contract expires in May 1997. The fair
market value of the crude oil price swap at December 31, 1996, based on the
market price of crude oil in December 1996, was $41,902.
 
     The Partnership's non-derivative financial instruments include cash and
cash equivalents, accounts receivable, accounts payable and long-term debt. The
carrying amount of cash and cash equivalents, accounts receivable and accounts
payable approximate fair value because of their immediate or short maturities.
The carrying value of the Partnership's revolving credit facility (see Note 4)
approximates its fair market value since it bears interest at floating market
interest rates. At December 31, 1996, the carrying amount of the Partnership's
subordinated notes payable exceeded the fair market value by $1.9 million, based
on current rates offered to the Partnership for debt of the same remaining
maturity.
 
     The Partnership's accounts receivable relate to natural gas and oil sales
to various industry companies, amounts due from industry participants for
expenditures made by the Partnership on their behalf and workstation revenues.
Credit terms, typical of industry standards, are of a short-term nature and the
Partnership does not require collateral. The Partnership's accounts receivable
at December 31, 1996 do not represent significant credit risks as they are
dispersed across many counterparties. Counterparties to the crude oil price
swaps are investment grade financial institutions. Accordingly, the Partnership
does not anticipate any material effect on its financial position or results of
operations as a result of nonperformance by the third parties on the crude oil
price swaps.
 
                                      F3-11
<PAGE>   81
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
8. EMPLOYEE BENEFIT PLANS
 
  Retirement Savings Plan
 
     During 1996 the Partnership adopted a defined contribution 401(k) plan for
substantially all of its employees. Eligible employees may contribute up to 15%
of their compensation to this plan. The 401(k) plan provides that the
Partnership may, at its discretion, match employee contributions. The
Partnership did not match employee contributions in 1996.
 
  Stock Compensation
 
     The Board of Directors and stockholders of the Company (see Note 1)
anticipate the adoption of an incentive plan, to be effective upon completion of
the Exchange (see Note 1), which will provide for the issuance of stock options,
stock appreciation rights, stock, restricted stock, cash or any combination of
the foregoing. The objective of this plan will be to reward key employees whose
performance may have a significant effect on the success of the Company. An
aggregate of 1,588,169 shares of the Company's common stock will be reserved for
issuance pursuant to this plan. The Compensation Committee of the Board of
Directors will determine the type of awards made to each participant and the
terms, conditions and limitations applicable to each award.
 
     The Company's Board of Directors also anticipates that it will grant
644,097 stock options prior to the completion of the proposed initial public
offering (see Note 1). These options will be granted under the incentive plan
established as part of the Exchange and will have an exercise price less than
the public offering price. This grant will result in noncash compensation
expense which will be recognized over the appropriate vesting period.
 
     In 1994 three employees were granted restricted interests in the
Partnership which vest in increments through July 1999. At the date of grant,
the value of these interests was immaterial. On February 26, 1997, in connection
with the Exchange Agreement (see Note 1), the three employees agreed to
transfer, upon the initial filing in early 1997 of a Registration Statement with
the SEC for a public offering of common stock, these partnership interests to
the Company in exchange for 156,250 shares of restricted common stock of the
Company. The terms of the restricted stock and the restricted partnership
interests are substantially the same. The shares vest over a three-year period
ending in 1999. No compensation expense will result from this exchange.
 
9. RELATED PARTY TRANSACTIONS
 
   
     During the years ended December 31, 1994, 1995 and 1996, the Partnership
paid approximately $310,000, $382,000 and $596,000, respectively, in fees for
land acquisition services performed by a company owned by a brother of the
Partnership's President and Chief Executive Officer. Other participants in the
Partnership's 3-D seismic projects reimbursed the partnership for most of these
amounts.
    
 
     The Partnership also participates in various industry projects with
affiliates of the holder of the subordinated notes payable (see Note 4). During
1995 and 1996, the Partnership received approximately $25,000 and $123,000,
respectively, for workstation time and geoscientists' time spent interpreting
3-D seismic data and workstation use. In addition, the Partnership sold to an
affiliate of the holders of the subordinated notes payable an interest in (i) a
3-D project for approximately $525,000 in 1994, (ii) a 3-D project for
approximately $75,000 in 1995 and (iii) two 3-D delineated potential drilling
locations and 3-D seismic data for approximately $83,000 in 1996.
 
     In 1995 and 1996, the Partnership paid $35,000 and $110,000 for working
interests in natural gas and oil properties owned by affiliates of a member of
the Partnership's management committee. The Partnership
 
                                      F3-12
<PAGE>   82
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
billed the affiliates $201,000, $13,000 and $68,000 in 1994, 1995 and 1996,
respectively, for their proportionate share of the costs related to this
project.
 
     A limited partner and member of the Partnership's management committee
served as a consultant to the Partnership on various aspects of the
Partnership's business and strategic issues. Fees paid for these services by the
Partnership were $72,000 for each of the twelve month periods ended December 31,
1994 and 1995 and $79,200 for the twelve month period ended December 31, 1996.
 
10. NATURAL GAS AND OIL EXPLORATION AND PRODUCTION ACTIVITIES
 
     The tables presented below provide supplemental information about natural
gas and oil exploration and production activities as defined by SFAS No. 69,
"Disclosures about Oil and Gas Producing Activities."
 
  Results of Operations for Natural Gas and Oil Producing Activities (in
thousands)
 
<TABLE>
<CAPTION>
                                                             YEAR ENDED DECEMBER 31,
                                                             ------------------------
                                                              1994     1995     1996
                                                             ------   ------   ------
<S>                                                          <C>      <C>      <C>
Natural gas and oil sales..................................  $2,565   $3,578   $6,141
Costs and expenses:
  Lease operating..........................................     491      761      726
  Production taxes.........................................     126      165      362
  Depletion of natural gas and oil properties..............   1,104    1,626    2,323
                                                             ------   ------   ------
Total costs and expenses...................................   1,721    2,552    3,411
                                                             ------   ------   ------
                                                             $  844   $1,026   $2,730
                                                             ======   ======   ======
Depletion per physical unit of production (equivalent Mcf
  of gas)..................................................  $ 1.10   $ 1.22   $ 1.13
                                                             ======   ======   ======
</TABLE>
 
     Natural gas and oil sales reflect the market prices of net production sold
or transferred, with appropriate adjustments for royalties, net profits interest
and other contractual provisions. Lease operating expenses include lifting costs
incurred to operate and maintain productive wells and related equipment,
including such costs as operating labor, repairs and maintenance, materials,
supplies and fuel consumed. Production taxes include production and severance
taxes. No provision has been made for income taxes since these taxes are the
responsibility of the partners (see Note 2). Depletion of natural gas and oil
properties relates to capitalized costs incurred in acquisition, exploration and
development activities. Results of operations do not include interest expense
and general corporate amounts.
 
  Costs Incurred and Capitalized Costs
 
     The costs incurred in natural gas and oil acquisition, exploration and
development activities follow (in thousands):
 
<TABLE>
<CAPTION>
                                                                 DECEMBER 31,
                                                              ------------------
                                                               1995       1996
                                                              -------    -------
<S>                                                           <C>        <C>
Costs incurred for the year:
  Exploration...............................................  $ 6,893    $10,527
  Property acquisition......................................    1,885      6,195
  Development...............................................      713      1,328
  Proceeds from participants................................   (1,296)    (4,111)
                                                              -------    -------
                                                              $ 8,195    $13,939
                                                              =======    =======
</TABLE>
 
                                      F3-13
<PAGE>   83
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
     Costs incurred represent amounts incurred by the Partnership for
exploration, property acquisition and development activities. Periodically, the
Partnership will receive proceeds from participants subsequent to project
initiation for an assignment of an interest in the project. These payments are
represented by proceeds from participants.
 
     Capitalized costs related to natural gas and oil acquisition, exploration
and development activities follow (in thousands):
 
<TABLE>
<CAPTION>
                                                                 DECEMBER 31,
                                                              ------------------
                                                               1995       1996
                                                              -------    -------
<S>                                                           <C>        <C>
Cost of natural gas and oil properties at year-end:
  Proved....................................................  $22,305    $30,487
  Unproved..................................................    3,460      7,068
                                                              -------    -------
  Total capitalized costs...................................   25,765     37,555
  Accumulated depletion.....................................   (7,227)    (9,550)
                                                              -------    -------
                                                              $18,538    $28,005
                                                              =======    =======
</TABLE>
 
     Following is a summary of costs (in thousands) excluded from depletion at
December 31, 1996, by year incurred. At this time, the Partnership is unable to
predict either the timing of the inclusion of these costs and the related
natural gas and oil reserves in its depletion computation or their potential
future impact on depletion rates.
 
<TABLE>
<CAPTION>
                                                         YEAR ENDED DECEMBER 31,
                                                        -------------------------
                                         PRIOR YEARS    1994     1995      1996      TOTAL
                                         -----------    -----    -----    -------    ------
<S>                                      <C>            <C>      <C>      <C>        <C>
Property acquisition...................    $1,418        $434     $694     $2,515    $5,061
Exploration............................       480          51      234      1,242     2,007
                                           ------        ----     ----     ------    ------
Total..................................    $1,898        $485     $928     $3,757    $7,068
                                           ======        ====     ====     ======    ======
</TABLE>
 
11. NATURAL GAS AND OIL RESERVES AND RELATED FINANCIAL DATA (UNAUDITED)
 
     Information with respect to the Partnership's natural gas and oil producing
activities is presented in the following tables. Reserve quantities as well as
certain information regarding future production and discounted cash flows were
determined by the Partnership's independent petroleum consultants and internal
petroleum reservoir engineer.
 
                                      F3-14
<PAGE>   84
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
  Natural Gas and Oil Reserve Data
 
     The following tables present the Partnership's estimates of its proved
natural gas and oil reserves. The Partnership emphasizes that reserve estimates
are approximates and are expected to change as additional information becomes
available. Reservoir engineering is a subjective process of estimating
underground accumulations of natural gas and oil that cannot be measured in an
exact way, and the accuracy of any reserve estimate is a function of the quality
of available data and of engineering and geological interpretation and judgment.
Accordingly, there can be no assurance that the reserves set forth herein will
ultimately be produced nor can there be assurance that the proved undeveloped
reserves will be developed within the periods anticipated. A substantial portion
of the reserve balances were estimated utilizing the volumetric method, as
opposed to the production performance method.
 
<TABLE>
<CAPTION>
                                          NATURAL GAS      OIL
                                            (MMCF)       (MBBLS)
                                          -----------    -------
<S>                                       <C>            <C>
Proved reserves at December 31, 1993....       227          336
  Revisions to previous estimates.......       102          (26)
  Extensions, discoveries and other
     additions..........................     3,415          852
  Production............................      (165)        (140)
                                            ------        -----
Proved reserves at December 31, 1994....     3,579        1,022
  Revisions to previous estimates.......    (1,600)        (214)
  Extensions and discoveries............     2,555        1,055
  Sales of minerals-in-place............        (6)         (14)
  Production............................      (271)        (177)
                                            ------        -----
Proved reserves at December 31, 1995....     4,257        1,672
  Revisions of previous estimates.......    (1,005)        (232)
  Extensions, discoveries and other
     additions..........................     7,742          996
  Purchase of minerals-in-place.........       260            3
  Sales of minerals-in-place............      (299)        (272)
  Production............................      (698)        (227)
                                            ------        -----
Proved reserves at December 31, 1996....    10,257        1,940
                                            ======        =====
Proved developed reserves at December
  31:
  1994..................................     1,849          915
  1995..................................     3,819        1,274
  1996..................................     6,034        1,453
</TABLE>
 
     Proved reserves are estimated quantities of crude natural gas and oil which
geological and engineering data indicate with reasonable certainty to be
recoverable in future years from known reservoirs under existing economic and
operating conditions. Proved developed reserves are proved reserves which can be
expected to be recovered through existing wells with existing equipment and
operating methods.
 
                                      F3-15
<PAGE>   85
 
                            BRIGHAM OIL & GAS, L.P.
 
                NOTES TO THE FINANCIAL STATEMENTS -- (CONTINUED)
 
  Standardized Measure of Discounted Future Net Cash Inflows and Changes Therein
 
     The following table presents a standardized measure of discounted future
net cash inflows (in thousands) relating to proved natural gas and oil reserves.
Future cash flows were computed by applying year end prices of natural gas and
oil relating to the Partnership's proved reserves to the estimated year-end
quantities of those reserves. Future price changes were considered only to the
extent provided by contractual agreements in existence at year-end. Future
production and development costs were computed by estimating those expenditures
expected to occur in developing and producing the proved natural gas and oil
reserves at the end of the year, based on year-end costs. Actual future cash
inflows may vary considerably and the standardized measure does not necessarily
represent the fair value of the Partnership's natural gas and oil reserves.
 
<TABLE>
<CAPTION>
                                                   DECEMBER 31,
                                          -------------------------------
                                           1994        1995        1996
                                          -------    --------    --------
<S>                                       <C>        <C>         <C>
Future cash inflows.....................  $22,544    $ 38,333    $ 84,987
Future development and production
  costs.................................   (8,148)    (12,543)    (20,998)
                                          -------    --------    --------
Future net cash inflows.................  $14,396    $ 25,790    $ 63,989
                                          =======    ========    ========
Standardized measure of future net cash
  inflows discounted at 10% per annum...  $10,240    $ 18,222    $ 44,506(1)
                                          =======    ========    ========
</TABLE>
 
- ---------------
 
(1) The earnings of the Partnership are not subject to income taxes as the
    Partnership is a non-taxpaying entity (see Note 2). Once the Partnership
    consummates the proposed Exchange (see Note 1), the successor entity will be
    a taxable corporation. The estimated pro forma income taxes, discounted at
    10%, are approximately $12,146,000 as of December 31, 1996, resulting in pro
    forma discounted net cash flows of approximately $32,360,000 as of December
    31, 1996.
 
   
     The average natural gas and oil prices used to calculate the future net
cash inflows at December 31, 1996 were $3.62 per Mcf and $24.66 per barrel,
respectively. At December 31, 1996 and February 14, 1997, respectively, the
NYMEX price for oil was $25.92 per barrel and $22.41 per barrel and the NYMEX
price for natural gas was $2.76 per MMBtu and $1.97 per MMBtu.
    
 
     Changes in the future net cash inflows (in thousands) discounted at 10% per
annum follow:
 
<TABLE>
<CAPTION>
                                                  DECEMBER 31,
                                          -----------------------------
                                           1994       1995       1996
                                          -------    -------    -------
<S>                                       <C>        <C>        <C>
Beginning of period.....................  $ 3,158    $10,240    $18,222
  Sales of natural gas and oil produced,
     net of production costs............   (1,948)    (2,652)    (5,053)
  Development costs incurred............       69        169        246
  Extensions and discoveries............    9,124     11,669     29,457
  Purchases of minerals-in-place........       --         --        384
  Sales of minerals-in-place............       --       (198)    (2,380)
  Net change in prices and production
     costs..............................      139      1,394      7,023
  Change in future development costs....     (619)       419        303
  Changes in production rates and
     other..............................       36       (364)      (342)
  Revisions of quantity estimates.......     (130)    (3,479)    (5,176)
  Accretion of discount.................      411      1,024      1,822
                                          -------    -------    -------
End of period...........................  $10,240    $18,222    $44,506
                                          =======    =======    =======
</TABLE>
 
                                      F3-16
<PAGE>   86
 
                                                                      APPENDIX A
 
                               February 14, 1997
 
Mr. Jon L. Glass
Brigham Oil & Gas, L.P.
5949 Sherry Lane, Suite 1616
Dallas, Texas 75225
 
  Re: Evaluation
      BRIGHAM OIL & GAS, L.P. INTERESTS
      Proved Reserves
      As of December 31, 1996
 
      Pursuant to the Guidelines of the Securities and
      Exchange Commission for Reporting Partnership
      Reserves and Future Net Revenue
 
Dear Mr. Glass:
 
     As requested, we are submitting our estimated proven reserves and future
net cash flows, as of December 31, 1996, attributable to the interests of
Brigham Oil & Gas, L.P. in certain oil and natural gas properties. The evaluated
properties are located in various counties in Kansas, New Mexico, Oklahoma and
Texas. This report was prepared using constant prices and costs and conforms to
the guidelines of the Securities and Exchange Commission (SEC).
 
     Composite forecasts for the total proved, proved developed producing,
proved developed non-producing and proved undeveloped estimates are presented by
category in the accompanying Tables I-P, I-PDP, I-PDNP and I-PUD, respectively.
The estimated net proved reserves and future net cash flow for all three
categories are summarized as follows:
 
   
<TABLE>
<CAPTION>
                                                NET RESERVES                         FUTURE NET CASH FLOW
                                   --------------------------------------    -------------------------------------
                                         OIL                  GAS                                    PRESENT WORTH
            CATEGORY                  (BARRELS)              (MCF)                  TOTAL               AT 10%
            --------               ----------------    ------------------    --------------------    -------------
<S>                                <C>                 <C>                   <C>                     <C>
Proved Developed:
  Producing......................     1,293,456             4,880,441            $38,532,070          $28,543,340
  Non-Producing..................       159,238             1,153,825              5,649,492            2,395,028
  Proved Undeveloped.............       487,216             4,222,257             19,806,950           13,567,850
                                      ---------            ----------            -----------          -----------
          Total Proved...........     1,939,910            10,256,523            $63,988,512          $44,506,218
                                      =========            ==========            ===========          ===========
</TABLE>
    
 
     Future revenue is prior to deducting state production taxes and ad valorem
taxes. Future net cash flow is after deducting these taxes, future capital costs
and operating expenses, but before consideration of federal income taxes. In
accordance with SEC guidelines, the future net cash flow has been discounted at
an annual rate of ten percent to determine its "present worth". The present
worth is shown to indicate the effort of time on the value of money and should
not be construed as being the fair market value of the properties.
 
     The oil reserves include oil and condensate. Oil volumes are expressed in
barrels (42 U.S. gallons). Gas volumes are expressed in thousands of standard
cubic feet (Mcf) at contract temperature and pressure base.
 
     Our estimates are for proved reserves only and do not include any probable
or possible reserves nor have any values been attributed to interests in acreage
beyond the location for which undeveloped reserves have been estimated.
 
     Oil and gas prices being received at December 31, 1996 were utilized as
furnished. Direct lease operating expenses are based on historical data for 1995
and 1996 and do not include general and administrative
 
                                       A-1
<PAGE>   87
 
overhead. Investments are capital costs for pumping unit installations,
work-overs and drilling costs and were utilized as furnished. All economic
factors were held constant in accordance with SEC guidelines.
 
     An on-site field inspection of the properties has not been performed nor
have the mechanical operation or condition of the wells and their related
facilities been examined nor have the wells been tested by Cawley, Gillespie &
Associates, Inc. Possible environmental liability related to the properties has
not been investigated nor considered. The cost of plugging and the salvage value
of equipment at abandonment have not been included.
 
     The reserve classifications and the economic considerations used herein
conform to the criteria of the Securities and Exchange Commission. The reserves
and economics are predicated on regulatory agency classifications, rules,
policies, laws, taxes and royalties currently in effect except as noted herein.
The possible effects of changes in legislation or other Federal or State
restrictive actions which could affect the reserves and economics have not been
considered.
 
     The proved reserve estimates and economic forecasts were based upon
interpretations of data furnished by your office and available from our files.
All estimates represent our best judgment based on the data available at the
time of preparation. It should be realized that the reserve estimates, the
reserves actually recovered, the revenue derived therefrom and the actual costs
incurred could be more or less than the estimated amounts. Additionally, the
prices and costs may vary from those utilized which may increase or decrease
both the estimated proved reserve volumes and future net revenues therefrom.
 
     Ownership interests in the oil and natural gas properties were accepted as
furnished by Brigham Oil & Gas, L.P., and has not been independently confirmed.
We are independent registered professional engineers and geologists. We do not
own an interest in the properties of Brigham Oil & Gas, L.P. and are not
employed on a contingent basis. Our workpapers and related data utilized in the
preparation of these estimates are available in our office.
 
                                     Yours very truly,
 
                                     Cawley, Gillespie & Associates, Inc.
 
                                                 /s/ AARON CAWLEY
                                     -------------------------------------------
                                                 Aaron Cawley, P.E.
                                              Executive Vice President
 
                                       A-2
<PAGE>   88
 
======================================================
 
    NO DEALER, SALESPERSON OR OTHER PERSON HAS BEEN AUTHORIZED TO GIVE ANY
INFORMATION OR TO MAKE ANY REPRESENTATIONS OTHER THAN THOSE CONTAINED IN THIS
PROSPECTUS IN CONNECTION WITH THE OFFER MADE BY THIS PROSPECTUS AND, IF GIVEN OR
MADE, SUCH INFORMATION OR REPRESENTATIONS MUST NOT BE RELIED UPON AS HAVING BEEN
AUTHORIZED BY THE COMPANY OR ANY OF THE UNDERWRITERS. THIS PROSPECTUS DOES NOT
CONSTITUTE AN OFFER TO SELL OR THE SOLICITATION OF ANY OFFER TO BUY ANY
SECURITIES OTHER THAN THE SHARES OF COMMON STOCK OFFERED BY THIS PROSPECTUS, NOR
DOES IT CONSTITUTE AN OFFER TO SELL OR A SOLICITATION OF ANY OFFER TO BUY THE
SHARES OF COMMON STOCK BY ANYONE IN ANY JURISDICTION IN WHICH SUCH OFFER OR
SOLICITATION IS NOT AUTHORIZED, OR IN WHICH THE PERSON MAKING SUCH OFFER OR
SOLICITATION IS NOT QUALIFIED TO DO SO, OR TO ANY PERSON TO WHOM IT IS UNLAWFUL
TO MAKE SUCH OFFER OR SOLICITATION. NEITHER THE DELIVERY OF THIS PROSPECTUS NOR
ANY SALE MADE HEREUNDER SHALL, UNDER ANY CIRCUMSTANCES, CREATE ANY IMPLICATION
THAT THE INFORMATION CONTAINED HEREIN IS CORRECT AS OF ANY TIME SUBSEQUENT TO
THE DATE HEREOF.
 
                               ------------------
 
                               TABLE OF CONTENTS
 
   
<TABLE>
<CAPTION>
                                           PAGE
                                           -----
<S>                                        <C>
Prospectus Summary.......................      3
Risk Factors.............................     10
The Company..............................     16
Use of Proceeds..........................     16
Dividend Policy..........................     17
Dilution.................................     17
Capitalization...........................     19
Selected Financial Data..................     20
Management's Discussion and Analysis of
  Financial Condition and Results of
  Operations.............................     22
Business and Properties..................     28
Management...............................     43
Certain Transactions.....................     48
Principal Stockholders...................     50
Description of Capital Stock.............     52
Shares Eligible for Future Sale..........     53
Underwriting.............................     54
Legal Matters............................     56
Experts..................................     56
Available Information....................     56
Glossary of Certain Oil and Gas Terms....     57
Index to Financial Statements............   F1-1
Letter of Cawley, Gillespie & Associates,
  Inc....................................    A-1
</TABLE>
    
 
      UNTIL      , 1997 (25 DAYS AFTER THE DATE OF THIS PROSPECTUS), ALL DEALERS
EFFECTING TRANSACTIONS IN THE SHARES OF THE COMMON STOCK, WHETHER OR NOT
PARTICIPATING IN THIS DISTRIBUTION, MAY BE REQUIRED TO DELIVER A PROSPECTUS.
THIS IS IN ADDITION TO THE OBLIGATION OF DEALERS TO DELIVER A PROSPECTUS WHEN
ACTING AS UNDERWRITERS AND WITH RESPECT TO THEIR UNSOLD ALLOTMENTS OR
SUBSCRIPTIONS.
 
======================================================
 
======================================================
 
   
                                3,000,000 SHARES
    
 
                       [BRIGHAM EXPLORATION COMPANY LOGO]
 
   
                                  COMMON STOCK
    
 
                           -------------------------
                                   PROSPECTUS
                           -------------------------
 
                            BEAR, STEARNS & CO. INC.
                                 HOWARD, WEIL,
                             LABOUISSE, FRIEDRICHS
                                  INCORPORATED
   
                         RAUSCHER PIERCE REFSNES, INC.
    
 
                                                 , 1997
 
======================================================
<PAGE>   89
 
                                    PART II
 
                     INFORMATION NOT REQUIRED IN PROSPECTUS
 
ITEM 13. OTHER EXPENSES OF ISSUANCE AND DISTRIBUTION
 
     The estimated expenses payable by Brigham Exploration Company (the
"Registrant" or the "Company") in connection with the registration of the
securities offered hereby, other than underwriting discounts and commissions,
are as follows:
 
   
<TABLE>
<S>                                                           <C>
SEC Registration Fee........................................  $ 16,553
NASD Filing Fee.............................................     5,963
Nasdaq National Market Listing Fee..........................    48,208
Blue Sky Qualification Fees and Expenses....................     5,000
Accounting Fees and Expenses................................   200,000
Legal Fees and Expenses.....................................   250,000
Engineering Fees and Expenses...............................    10,000
Transfer Agent and Registrar Fees...........................     3,500
Printing and Engraving Expenses.............................    89,000
Miscellaneous...............................................   121,776
                                                              --------
          Total.............................................  $750,000
                                                              ========
</TABLE>
    
 
   
ITEM 14. INDEMNIFICATION OF DIRECTORS AND OFFICERS
    
 
     In accordance with Section 102(b)(7) of the Delaware General Corporation
Law ("DGCL"), the Company's Certificate of Incorporation includes a provision
that, to the fullest extent permitted by law, eliminates the personal liability
of members of its Board of Directors to the Company or its stockholders for
monetary damages for breach of fiduciary duty as a director. Such provision does
not eliminate or limit the liability of a director (1) for any breach of a
director's duty of loyalty to the Company or its stockholders, (2) for acts or
omissions not in good faith or which involve intentional misconduct or a knowing
violation of a law, (3) for paying an unlawful dividend or approving an illegal
stock repurchase (as provided in Section 174 of the DGCL) or (4) for any
transaction from which the director derived an improper personal benefit.
 
     Under Section 145 of the DGCL, the Registrant has the power to indemnify
any person who was or is a party or is threatened to be made a party to any
threatened, pending or completed action, suit or proceeding (other than an
action by or in the right of the corporation) by reason of the fact that the
person is or was a director, officer, employee or agent of any corporation,
partnership, joint venture, trust or other enterprise, against any and all
expenses (including attorneys' fees), judgments, fines and amounts paid in
settlement and reasonably incurred in connection with such action, suit or
proceeding. The power to indemnify applies only if the person acted in good
faith and in a manner the person reasonably believed to be in or not opposed to
the best interests of the corporation, and with respect to any criminal action
or proceeding, had no reasonable cause to believe the person's conduct was
unlawful.
 
     In the case of an action by or in the right of the Registrant, no
indemnification may be made with respect to any claim, issue or matter as to
which such person shall have been adjudged to be liable to the Registrant unless
and only to the extent that the court of chancery or the court in which such
action or suit was brought shall determine that despite the adjudication of
liability such person is fairly and reasonably entitled to indemnity for such
expenses which the court shall deem proper. Section 145 of the DGCL further
provides that to the extent a director or officer of the Registrant has been
successful in the defense of any action, suit or proceeding referred to above or
in the defense of any claim, issue or matter therein, that person shall be
indemnified against expenses (including attorney's fees) actually and reasonably
incurred in connection therewith.
 
                                      II-1
<PAGE>   90
 
     The Registrant also has the power to purchase and maintain insurance on
behalf of any person covering any liability incurred in that person's capacity
as a director, officer, employee or agent of the corporation, or arising out of
that person's status as such, whether or not the corporation would have the
power to indemnify against the liability.
 
     The Certificate of Incorporation and Bylaws provide that the Registrant
will indemnify its officers and directors and former officers and directors
against any expenses, judgments or settlement payments sustained or paid by such
persons as a result of having acted as an officer or director of the Registrant,
or, at the request of the Registrant, as an officer, director, agent or employee
of another business entity. The Certificate of Incorporation and Bylaws further
provide that the Registrant may, by action of its Board of Directors, provide
indemnification to employees and agents of the Registrant, individually or as a
group, with the same scope and effect as the indemnification of directors and
officers.
 
     The form of Indemnity Agreement contained in Exhibit 10.28 provides for the
indemnification in certain instances against liability and expenses incurred in
connection with proceedings brought by or in the right of the Company or by
third parties by reason of a person serving as an officer or director of the
Company.
 
     The form of Underwriting Agreement contained in Exhibit 1 provides for
indemnification of the directors and officers signing the Registration Statement
and certain controlling persons of the Company against certain liabilities
(including certain liabilities under the Securities Act of 1933, (the
"Securities Act")) in certain instances by the Underwriters.
 
ITEM 15. RECENT SALES OF UNREGISTERED SECURITIES
 
     The following information relates to all securities issued or sold by the
Registrant since inception and not registered under the Securities Act.
 
     Unless otherwise specifically provided, each of the transactions described
below was conducted in reliance upon the exemption from registration provided in
Section 4(2) of the Securities Act and the rules and regulations promulgated
thereunder. Furthermore, each of the certificates representing the Registrant's
securities issued in connection with such transactions contains a restrictive
legend, as appropriate, requiring each person acquiring such securities from the
Registrant to furnish investment representations to the Registrant and stating
that no underwriters participated in such transactions.
 
   
     The Registrant was formed on February 25, 1997. Pursuant to the terms of an
Agreement and Plan of Reorganization dated February 26, 1997 (the "Exchange
Agreement") the Company became the holding company for Brigham Oil & Gas, L.P.,
which will conduct the Registrant's operations and was formed in May 1992 (the
"Partnership"). Pursuant to the terms of the Exchange Agreement, the limited
partners of the Partnership received 634,868 shares of the Registrant's common
stock. In addition, the general partners or their stockholders received
6,539,239 shares of the Registrant's common stock for each share of common stock
of the general partner owned by such stockholder. Each certificate issued in
connection with such exchange contained an appropriate restrictive legend.
    
 
   
     In August 1995, the Registrant issued $16 million principal amount of its
5% convertible subordinated notes (the "Notes") to Resource Investment
Management Company. Immediately after the consummation of the exchange described
above, RIMCO converted the Notes into 1,754,464 shares of the Registrant's
common stock. Each certificate issued in connection with that conversion
contained an appropriate restrictive legend.
    
 
   
     The Registrant and its predecessor have granted options to purchase an
aggregate of 644,097 shares of Common Stock and issued 156,250 shares of
restricted stock to officers and key employees.
    
 
                                      II-2
<PAGE>   91
 
ITEM 16. EXHIBITS AND FINANCIAL STATEMENT SCHEDULES
 
     (a) Exhibits:
 
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         1++             -- Form of Underwriting Agreement.
         2.1+            -- Exchange Agreement.
         3.1+            -- Certificate of Incorporation.
         3.2             -- Composite Bylaws, as currently in effect.
         4.1             -- Form of Common Stock Certificate.
         5               -- Opinion of Thompson & Knight, A Professional Corporation.
        10.1+            -- Agreement of Limited Partnership, dated May 1, 1992,
                            between Brigham Exploration Company and General Atlantic
                            Partners III, L.P. as general partners, and Harold D.
                            Carter and GAP-Brigham Partners, L.P. as limited
                            partners.
        10.1.1+          -- Amendment No. 1 to Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated May 1, 1992, by and among
                            Brigham Exploration Company, General Atlantic Partners
                            III, L.P., GAP-Brigham Partners, L.P. and Harold D.
                            Carter.
        10.1.2+          -- Amendment No. 2 to Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated September 30, 1994, by and
                            among Brigham Exploration Company, General Atlantic
                            Partners III, L.P., GAP-Brigham Partners, L.P., Harold D.
                            Carter and the additional signatories thereto.
        10.1.3+          -- Amendment No. 3 to Agreement of Limited Partnership of
                            Brigham Oil & Gas, L.P., dated August 24, 1995, by and
                            among Brigham Exploration Company, General Atlantic
                            Partners III, L.P., GAP-Brigham Partners, L.P., Harold D.
                            Carter, Craig M. Fleming, David T. Brigham and Jon L.
                            Glass.
        10.2+            -- Agreement of Limited Partnership of Venture Acquisitions,
                            L.P., dated September 23, 1994, by and between Quest
                            Resources, L.L.C. and RIMCO Energy, Inc. as general
                            partners, and RIMCO Production Company, Inc., RIMCO
                            Exploration Partners, L.P. I and RIMCO Exploration
                            Partners, L.P. II, as limited partners.
        10.3+            -- Regulations of Quest Resources, L.L.C.
        10.4+            -- Management and Ownership Agreement, dated September 23,
                            1994, by and among Brigham Oil & Gas, L.P., Brigham
                            Exploration Company, General Atlantic Partners III, L.P.,
                            Harold D. Carter, Ben M. Brigham and GAP-Brigham
                            Partners, L.P.
        10.5*+           -- Employment Agreement, dated May 1, 1992, by and between
                            Brigham Oil & Gas, L.P. and Ben M. Brigham.
        10.6*+           -- Consulting Agreement, dated May 2, 1995, by and between
                            Brigham Oil & Gas, L.P. and Harold D. Carter.
        10.7*            -- Employment Agreement, by and between Brigham Exploration
                            Company and Ben M. Brigham.
        10.8*            -- Form of Brigham Oil & Gas, L.P. Phantom Royalty Account
                            Participating Agreement.
        10.9*            -- 1997 Incentive Plan of Brigham Exploration Company
        10.9.1*          -- Form of Option Agreement for certain executive officers.
        10.9.2*          -- Option Agreement dated as of March 4, 1997, by and
                            between Brigham Exploration Company and Jon L. Glass.
</TABLE>
    
 
                                      II-3
<PAGE>   92
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.10*+          -- Incentive Bonus Plan dated as of February 28, 1997 of
                            Brigham, Inc. and Brigham Oil & Gas, L.P.
        10.11+           -- Note Purchase Agreement, dated August 24, 1995, by and
                            among Brigham Oil & Gas, L.P., RIMCO Partners, L.P. II,
                            RIMCO Partners, L.P. III and RIMCO Partners, L.P.
        10.11.1+         -- 5% Convertible Note Due September 1, 2002, dated August
                            24, 1995, executed by Brigham Oil & Gas, L.P. in favor of
                            RIMCO Partners, L.P. II in the principal sum of
                            $5,584,000.
        10.11.2+         -- 5% Convertible Subordinated Note Due September 1, 2002,
                            dated August 24, 1995, executed by Brigham Oil & Gas,
                            L.P. in favor of RIMCO Partners, L.P. III in the
                            principal sum of $2,800,000.
        10.11.3+         -- 5% Convertible Subordinated Note Due September 1, 2002,
                            dated August 24, 1995, executed by Brigham Oil & Gas,
                            L.P. in favor of RIMCO Partners, L.P. IV in the principal
                            sum of $7,616,000.
        10.12+           -- Loan Agreement, dated April 1, 1996, by and between
                            Brigham Oil & Gas, L.P. and Bank One, Texas, N.A.
        10.12.1+         -- Revolving Note, dated April 1, 1996, executed by Brigham
                            Oil & Gas, L.P., in favor of Bank One, Texas, N.A. in the
                            principle amount of $25,000,000.
        10.12.2+         -- Form of Mortgage, Security Agreement, Assignment of
                            Production and Financing Statement for New Mexico, dated
                            as of April 1, 1996, by Brigham Oil & Gas, L.P. and Bank
                            One, Texas, N.A.
        10.12.3+         -- Form of Mortgage, Security Agreement, Assignment of
                            Production and Financing Statement for Oklahoma, dated as
                            of April 1, 1996, by Brigham Oil & Gas, L.P. and Bank
                            One, Texas, N.A.
        10.12.4+         -- Form of Deed of Trust, Security Agreement, Assignment of
                            Production and Financing Statement for Texas, dated as of
                            April 1, 1996, by Brigham Oil & Gas, L.P. and Bank One,
                            Texas, N.A.
        10.13+           -- Office Lease, dated May 17, 1993, by and between Sterling
                            Plaza Ltd. and Brigham Oil & Gas, L.P.
        10.13.1+         -- First Amendment to Office Lease, dated April 8, 1994, by
                            and between ZML-Sterling Plaza Limited Partnership by its
                            agent, Equity Office Properties, Inc., and Brigham Oil &
                            Gas, L.P.
        10.13.2+         -- Second Amendment to Office Lease, dated June 29, 1994, by
                            and between ZML-Sterling Plaza Limited Partnership by its
                            agent, Equity Office Properties, Inc., and Brigham Oil &
                            Gas, L.P.
        10.13.3+         -- Third Amendment to Office Lease, dated December 30, 1996,
                            by and between ZML-Sterling Plaza Limited Partnership by
                            its agent, Equity Office Holdings, L.L.C., and Brigham
                            Oil & Gas, L.P.
        10.13.4+         -- Modification and Ratification of Lease, dated April 1,
                            1993.
        10.13.5+         -- Modification and Ratification of Lease, dated May 12,
                            1993.
        10.14+           -- Two Bridgepoint Lease Agreement, dated September 30,
                            1996, by and between Investors Life Insurance Company of
                            North America and Brigham Oil & Gas, L.P.
        10.15+           -- Anadarko Basin Seismic Operations Agreement, dated
                            February 15, 1996, by and between Brigham Oil & Gas, L.P.
                            and Veritas Geophysical, Ltd.
        10.15.1+         -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement, dated June 10, 1996, between Brigham Oil &
                            Gas, L.P. and Veritas Geophysical, Ltd.
</TABLE>
    
 
                                      II-4
<PAGE>   93
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.16+           -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Gasco
                            Limited Partnership.
        10.16.1+         -- Amendment to Expense Allocation and Participation
                            Agreement, dated October 21, 1996, between Brigham Oil &
                            Gas, L.P. and Gasco Limited Partnership.
        10.17+           -- Expense Allocation and Participation Agreement, dated
                            April 1, 1996, between Brigham Oil & Gas, L.P. and Middle
                            Bay Oil Company, Inc.
        10.17.1+         -- Amendment to Expense Allocation and Participation
                            Agreement, dated September 26, 1996, between Brigham Oil
                            & Gas, L.P. and Middle Bay Oil Company, Inc.
        10.17.2+         -- Letter Amendment to Expense Allocation and Participation
                            Agreement, dated May 20, 1996, between Brigham Oil & Gas,
                            L.P. and Middle Bay Oil Company, Inc.
        10.18+           -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and among Stephens Production Company and
                            Brigham Oil & Gas, L.P.
        10.19+           -- Anadarko Basin Joint Participation Agreement, dated May
                            1, 1996, by and between Vintage Petroleum, Inc. and
                            Brigham Oil & Gas, L.P.
        10.20+           -- Processing Alliance Agreement, dated July 20, 1993,
                            between Veritas Seismic Ltd. and Brigham Oil & Gas, L.P.
        10.20.1+         -- Letter Amendment to Processing Alliance Agreement, dated
                            November 3, 1994, between Veritas Seismic Ltd. and
                            Brigham Oil & Gas, L.P.
        10.21+           -- Agreement and Assignment of Interest, West Bradley
                            Project, dated September 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P.
        10.22            -- Agreement and Assignment of Interests in lands located in
                            Grady County, Oklahoma, West Bradley Project, dated
                            December 1, 1995, by and between Aspect Resources Limited
                            Liability Company, Brigham Oil & Gas, L.P. and Venture
                            Acquisitions, L.P.
        10.23+           -- Agreement and Assignment of Interests, West Bradley
                            Project, dated December 1, 1995, by and between Aspect
                            Resources Limited Liability Company and Brigham Oil &
                            Gas, L.P.
        10.24+           -- Geophysical Exploration Agreement, Hardeman Project,
                            Hardeman and Wilbarger Counties, Texas and Jackson
                            County, Oklahoma, dated March 15, 1993 by and among
                            General Atlantic Resources, Inc., Maynard Oil Company,
                            Ruja Muta Corporation, Tucker Scully Interests Ltd., JHJ
                            Exploration, Ltd., Cheyenne Petroleum Company, Antrim
                            Resources, Inc., and Brigham Oil & Gas, L.P.
        10.25+           -- Agreement and Partial Assignment of Interests in OK13-P
                            Prospect Area, Jackson County, Oklahoma (Hardeman
                            Project), dated August 1, 1995, by and between Brigham
                            Oil & Gas, L.P. and Aspect Resources Limited Liability
                            Company.
        10.26+           -- Agreement and Partial Assignment of Interests in Q140-E
                            Prospect Area, Hardeman County, Texas (Hardeman Project),
                            dated August 1, 1995, by and between Brigham Oil & Gas,
                            L.P. and Aspect Resources Limited Liability Company.
        10.27+           -- Agreement and Partial Assignment of Interests in Hankins
                            #1 Chappel Prospect Agreement, Jackson County, Oklahoma
                            (Hardeman Project), dated March 21, 1996, by and between
                            Brigham Oil & Gas, L.P., NGR, Ltd. and Aspect Resources
                            Limited Liability Company.
</TABLE>
    
 
                                      II-5
<PAGE>   94
   
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
        10.28*           -- Form of Indemnity Agreement between the Registrant and
                            each of its executive officers.
        10.29            -- Registration Rights Agreement dated February 26, 1997 by
                            and among Brigham Exploration Company, General Atlantic
                            Partners III L.P., GAP-Brigham Partners, L.P., RIMCO
                            Partners, L.P. II, RIMCO Partners L.P. III, and RIMCO
                            Partners, L.P. IV, Ben M. Brigham, Anne L. Brigham,
                            Harold D. Carter, Craig M. Fleming, David T. Brigham and
                            Jon L. Glass.
        10.30            -- 1997 Director Stock Option Plan.
        10.31            -- Form of Employee Stock Ownership Agreement.
        10.32            -- Unconditional Guaranty dated as of March 26, 1997, by
                            Brigham Exploration Company for the benefit of Bank One,
                            Texas, National Association.
        10.33            -- Agreement and Assignment of Interest in Geophysical
                            Exploration Agreement, Esperson Dome Project, dated
                            November 1, 1994, by and between Brigham Oil & Gas, L.P.
                            and Vaquero Gas Company.
        10.34            -- Geophysical Exploration Agreement, Southwest Danbury
                            Project, Brazoria County, Texas, dated as of July 1,
                            1996, by and among UNEXCO, Inc. and Brigham Oil & Gas,
                            L.P.
        10.35            -- Geophysical Exploration Agreement, Welder Project, Duval
                            County, Texas, dated as of October 1, 1996, by and among
                            UNEXCO, Inc. and Brigham Oil & Gas, L.P.
        10.36            -- Proposed Trade Structure, RIMCO/Tigre Project, Vermillion
                            Parish, Louisiana, among Brigham Oil & Gas, L.P., Tigre
                            Energy Corporation and Resource Investors Management
                            Company
        10.36.1          -- Letter relating to Proposed Trade Structure, RIMCO/Tigre
                            Project, dated January 31, 1997, from Resource Investors
                            Management Company to Brigham Oil & Gas, L.P.
        10.37            -- Anadarko Basin Seismic Operations Agreement II, dated as
                            of April 1, 1997, by and between Brigham Oil & Gas, L.P.
        10.37.1          -- Letter Amendment to Anadarko Basin Seismic Operations
                            Agreement II, dated March 20, 1997, between Brigham Oil &
                            Gas, L.P. and Veritas DGC Land, Inc.
        11.1             -- Computation of Pro Forma Net Loss Per Common Share.
        21               -- Subsidiaries of the Registrant.
        23.1             -- Consent of Thompson & Knight, A Professional Corporation
                            (included in Exhibit 5 above).
        23.2             -- Consent of Price Waterhouse LLP, independent accountants.
        23.3             -- Consent of Cawley, Gillespie & Associates, Inc.,
                            independent petroleum engineers.
        24.1             -- Powers of Attorney (included on the first signature page
                            to this Registration Statement).
        27+              -- Financial Data Schedule.
</TABLE>
    
 
- ---------------
 
   
 + Previously filed.
    
 
   
++ To be filed by amendment.
    
 
 * Management contract or compensatory plan.
 
     (b) Financial Statement Schedules: None.
 
                                      II-6
<PAGE>   95
 
ITEM 17. UNDERTAKINGS
 
     The undersigned Registrant hereby undertakes to provide to the Underwriters
at the closing specified in the Underwriting Agreements, certificates in such
denominations and registered in such names as required by the particular
Underwriter, to permit prompt delivery to each purchaser.
 
     The undersigned Registrant also hereby undertakes that:
 
          (1) For purposes of determining any liability under the Securities
     Act, the information omitted from the form of prospectus filed as part of
     this Registration Statement in reliance upon Rule 430A and contained in a
     form of prospectus filed by the registrant pursuant to Rule 424(b)(1) or
     (4) or 497(h) under the Securities Act shall be deemed to be part of this
     Registration Statement as of the time it was declared effective.
 
          (2) For the purpose of determining any liability under the Securities
     Act, each post-effective amendment that contains a form of prospectus shall
     be deemed to be a new registration statement relating to the securities
     offered therein, and the offering of such securities at that time shall be
     deemed to be the initial bona fide offering thereof.
 
     Insofar as indemnification for liabilities arising under the Securities Act
may be permitted to directors, officers and controlling persons of the
Registrant pursuant to the foregoing provisions, or otherwise, the registrant
has been advised that in the opinion of the Securities and Exchange Commission
such indemnification is against public policy as expressed in the Securities Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the registrant of expenses
incurred or paid by a director, officer or controlling person of the registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.
 
                                      II-7
<PAGE>   96
 
                                   SIGNATURES
 
   
     Pursuant to the requirements of the Securities Act of 1933, Brigham
Exploration Company has duly caused this Amendment No. 1 to Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in Dallas, Texas, on April 21, 1997.
    
 
                                            BRIGHAM EXPLORATION COMPANY
 
                                            By:      /s/ BEN M. BRIGHAM
                                              ----------------------------------
                                                        Ben M. Brigham
                                              President, Chief Executive Officer
                                                              and
                                                    Chairman of the Board
 
                               POWER OF ATTORNEY
 
   
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
    
 
   
<TABLE>
<CAPTION>
                      SIGNATURE                                    TITLE                    DATE
                      ---------                                    -----                    ----
<C>                                                    <S>                            <C>
 
                 /s/ BEN M. BRIGHAM                    President, Chief Executive     April 21, 1997
- -----------------------------------------------------    Officer and Chairman of the
                   Ben M. Brigham                        Board (principal executive
                                                         officer)
 
                /s/ ANNE L. BRIGHAM*                   Executive Vice President and   April 21, 1997
- -----------------------------------------------------    Director
                   Anne L. Brigham
 
                /s/ CRAIG M. FLEMING*                  Chief Financial Officer        April 21, 1997
- -----------------------------------------------------    (principal financial and
                  Craig M. Fleming                       accounting officer)
 
                  /s/ JON L. GLASS*                    Vice President -- Exploration  April 21, 1997
- -----------------------------------------------------    and Director
                    Jon L. Glass
 
                /s/ HAROLD D. CARTER*                  Consultant and Director        April 21, 1997
- -----------------------------------------------------
                  Harold D. Carter
 
                /s/ GARY J. MILAVEC*                   Director                       April 21, 1997
- -----------------------------------------------------
                   Gary J. Milavec
 
               /s/ ALEXIS M. CRANBERG*                 Director                       April 21, 1997
- -----------------------------------------------------
                 Alexis M. Cranberg
 
              /s/ STEPHEN P. REYNOLDS*                 Director                       April 21, 1997
- -----------------------------------------------------
                 Stephen P. Reynolds
 
               *By: /s/ BEN M. BRIGHAM
  ------------------------------------------------
                   Ben M. Brigham
                  Attorney-in-fact
</TABLE>
    
 
                                      II-8
<PAGE>   97
 
                               INDEX TO EXHIBITS
 
   
<TABLE>
<CAPTION>
  EXHIBIT
   NUMBER                            DESCRIPTION
  -------                            -----------
<C>          <S>                                                          <C>
   1++       -- Form of Underwriting Agreement.
   2.1+      -- Exchange Agreement.
   3.1+      -- Certificate of Incorporation.
   3.2       -- Composite Bylaws, as currently in effect.
   4.1       -- Form of Common Stock Certificate.
   5         -- Opinion of Thompson & Knight, A Professional Corporation.
  10.1+      -- Agreement of Limited Partnership, dated May 1, 1992,
                between Brigham Exploration Company and General Atlantic
                Partners III, L.P. as general partners, and Harold D.
                Carter and GAP-Brigham Partners, L.P. as limited
                partners.
  10.1.1+    -- Amendment No. 1 to Agreement of Limited Partnership of
                Brigham Oil & Gas, L.P., dated May 1, 1992, by and among
                Brigham Exploration Company, General Atlantic Partners
                III, L.P., GAP-Brigham Partners, L.P. and Harold D.
                Carter.
  10.1.2+    -- Amendment No. 2 to Agreement of Limited Partnership of
                Brigham Oil & Gas, L.P., dated September 30, 1994, by and
                among Brigham Exploration Company, General Atlantic
                Partners III, L.P., GAP-Brigham Partners, L.P., Harold D.
                Carter and the additional signatories thereto.
  10.1.3+    -- Amendment No. 3 to Agreement of Limited Partnership of
                Brigham Oil & Gas, L.P., dated August 24, 1995, by and
                among Brigham Exploration Company, General Atlantic
                Partners III, L.P., GAP-Brigham Partners, L.P., Harold D.
                Carter, Craig M. Fleming, David T. Brigham and Jon L.
                Glass.
  10.2+      -- Agreement of Limited Partnership of Venture Acquisitions,
                L.P., dated September 23, 1994, by and between Quest
                Resources, L.L.C. and RIMCO Energy, Inc. as general
                partners, and RIMCO Production Company, Inc., RIMCO
                Exploration Partners, L.P. I and RIMCO Exploration
                Partners, L.P. II, as limited partners.
  10.3+      -- Regulations of Quest Resources, L.L.C.
  10.4+      -- Management and Ownership Agreement, dated September 23,
                1994, by and among Brigham Oil & Gas, L.P., Brigham
                Exploration Company, General Atlantic Partners III, L.P.,
                Harold D. Carter, Ben M. Brigham and GAP-Brigham
                Partners, L.P.
  10.5*+     -- Employment Agreement, dated May 1, 1992, by and between
                Brigham Oil & Gas, L.P. and Ben M. Brigham.
  10.6*+     -- Consulting Agreement, dated May 2, 1995, by and between
                Brigham Oil & Gas, L.P. and Harold D. Carter.
  10.7*      -- Employment Agreement, by and between Brigham Exploration
                Company and Ben M. Brigham.
  10.8*      -- Form of Brigham Oil & Gas, L.P. Phantom Royalty Account
                Participating Agreement.
  10.9*      -- 1997 Incentive Plan of Brigham Exploration Company
  10.9.1*    -- Form of Option Agreement for certain executive officers.
  10.9.2*    -- Option Agreement dated as of March 4, 1997, by and
                between Brigham Exploration Company and Jon L. Glass.
</TABLE>
    
<PAGE>   98
   
<TABLE>
<CAPTION>
  EXHIBIT
   NUMBER                            DESCRIPTION
  -------                            -----------
<C>          <S>                                                          <C>
  10.10*+    -- Incentive Bonus Plan dated as of February 28, 1997 of
                Brigham, Inc. and Brigham Oil & Gas, L.P.
  10.11+     -- Note Purchase Agreement, dated August 24, 1995, by and
                among Brigham Oil & Gas, L.P., RIMCO Partners, L.P. II,
                RIMCO Partners, L.P. III and RIMCO Partners, L.P.
  10.11.1+   -- 5% Convertible Note Due September 1, 2002, dated August
                24, 1995, executed by Brigham Oil & Gas, L.P. in favor of
                RIMCO Partners, L.P. II in the principal sum of
                $5,584,000.
  10.11.2+   -- 5% Convertible Subordinated Note Due September 1, 2002,
                dated August 24, 1995, executed by Brigham Oil & Gas,
                L.P. in favor of RIMCO Partners, L.P. III in the
                principal sum of $2,800,000.
  10.11.3+   -- 5% Convertible Subordinated Note Due September 1, 2002,
                dated August 24, 1995, executed by Brigham Oil & Gas,
                L.P. in favor of RIMCO Partners, L.P. IV in the principal
                sum of $7,616,000.
  10.12+     -- Loan Agreement, dated April 1, 1996, by and between
                Brigham Oil & Gas, L.P. and Bank One, Texas, N.A.
  10.12.1+   -- Revolving Note, dated April 1, 1996, executed by Brigham
                Oil & Gas, L.P., in favor of Bank One, Texas, N.A. in the
                principle amount of $25,000,000.
  10.12.2+   -- Form of Mortgage, Security Agreement, Assignment of
                Production and Financing Statement for New Mexico, dated
                as of April 1, 1996, by Brigham Oil & Gas, L.P. and Bank
                One, Texas, N.A.
  10.12.3+   -- Form of Mortgage, Security Agreement, Assignment of
                Production and Financing Statement for Oklahoma, dated as
                of April 1, 1996, by Brigham Oil & Gas, L.P. and Bank
                One, Texas, N.A.
  10.12.4+   -- Form of Deed of Trust, Security Agreement, Assignment of
                Production and Financing Statement for Texas, dated as of
                April 1, 1996, by Brigham Oil & Gas, L.P. and Bank One,
                Texas, N.A.
  10.13+     -- Office Lease, dated May 17, 1993, by and between Sterling
                Plaza Ltd. and Brigham Oil & Gas, L.P.
  10.13.1+   -- First Amendment to Office Lease, dated April 8, 1994, by
                and between ZML-Sterling Plaza Limited Partnership by its
                agent, Equity Office Properties, Inc., and Brigham Oil &
                Gas, L.P.
  10.13.2+   -- Second Amendment to Office Lease, dated June 29, 1994, by
                and between ZML-Sterling Plaza Limited Partnership by its
                agent, Equity Office Properties, Inc., and Brigham Oil &
                Gas, L.P.
  10.13.3+   -- Third Amendment to Office Lease, dated December 30, 1996,
                by and between ZML-Sterling Plaza Limited Partnership by
                its agent, Equity Office Holdings, L.L.C., and Brigham
                Oil & Gas, L.P.
  10.13.4+   -- Modification and Ratification of Lease, dated April 1,
                1993.
  10.13.5+   -- Modification and Ratification of Lease, dated May 12,
                1993.
  10.14+     -- Two Bridgepoint Lease Agreement, dated September 30,
                1996, by and between Investors Life Insurance Company of
                North America and Brigham Oil & Gas, L.P.
  10.15+     -- Anadarko Basin Seismic Operations Agreement, dated
                February 15, 1996, by and between Brigham Oil & Gas, L.P.
                and Veritas Geophysical, Ltd.
  10.15.1+   -- Letter Amendment to Anadarko Basin Seismic Operations
                Agreement, dated June 10, 1996, between Brigham Oil &
                Gas, L.P. and Veritas Geophysical, Ltd.
</TABLE>
    
<PAGE>   99
 
   
<TABLE>
<CAPTION>
  EXHIBIT
  NUMBER                                       DESCRIPTION
  -------                                      -----------
<C>            <S>                                                                                         <C>
    10.16+     -- Expense Allocation and Participation Agreement, dated April 1, 1996, between Brigham
                  Oil & Gas, L.P. and Gasco Limited Partnership.
    10.16.1+   -- Amendment to Expense Allocation and Participation Agreement, dated October 21, 1996,
                  between Brigham Oil & Gas, L.P. and Gasco Limited Partnership.
    10.17+     -- Expense Allocation and Participation Agreement, dated April 1, 1996, between Brigham
                  Oil & Gas, L.P. and Middle Bay Oil Company, Inc.
    10.17.1+   -- Amendment to Expense Allocation and Participation Agreement, dated September 26, 1996,
                  between Brigham Oil & Gas, L.P. and Middle Bay Oil Company, Inc.
    10.17.2+   -- Letter Amendment to Expense Allocation and Participation Agreement, dated May 20, 1996,
                  between Brigham Oil & Gas, L.P. and Middle Bay Oil Company, Inc.
    10.18+     -- Anadarko Basin Joint Participation Agreement, dated May 1, 1996, by and among Stephens
                  Production Company and Brigham Oil & Gas, L.P.
    10.19+     -- Anadarko Basin Joint Participation Agreement, dated May 1, 1996, by and between Vintage
                  Petroleum, Inc. and Brigham Oil & Gas, L.P.
    10.20+     -- Processing Alliance Agreement, dated July 20, 1993, between Veritas Seismic Ltd. and
                  Brigham Oil & Gas, L.P.
    10.20.1+   -- Letter Amendment to Processing Alliance Agreement, dated November 3, 1994, between
                  Veritas Seismic Ltd. and Brigham Oil & Gas, L.P.
    10.21+     -- Agreement and Assignment of Interest, West Bradley Project, dated September 1, 1995, by
                  and between Aspect Resources Limited Liability Company and Brigham Oil & Gas, L.P.
    10.22      -- Agreement and Assignment of Interests in lands located in Grady County, Oklahoma, West
                  Bradley Project, dated December 1, 1995, by and between Aspect Resources Limited
                  Liability Company, Brigham Oil & Gas, L.P. and Venture Acquisitions, L.P.
    10.23+     -- Agreement and Assignment of Interests, West Bradley Project, dated December 1, 1995, by
                  and between Aspect Resources Limited Liability Company and Brigham Oil & Gas, L.P.
    10.24+     -- Geophysical Exploration Agreement, Hardeman Project, Hardeman and Wilbarger Counties,
                  Texas and Jackson County, Oklahoma, dated March 15, 1993 by and among General Atlantic
                  Resources, Inc., Maynard Oil Company, Ruja Muta Corporation, Tucker Scully Interests
                  Ltd., JHJ Exploration, Ltd., Cheyenne Petroleum Company, Antrim Resources, Inc., and
                  Brigham Oil & Gas, L.P.
    10.25+     -- Agreement and Partial Assignment of Interests in OK13-P Prospect Area, Jackson County,
                  Oklahoma (Hardeman Project), dated August 1, 1995, by and between Brigham Oil & Gas,
                  L.P. and Aspect Resources Limited Liability Company.
    10.26+     -- Agreement and Partial Assignment of Interests in Q140-E Prospect Area, Hardeman County,
                  Texas (Hardeman Project), dated August 1, 1995, by and between Brigham Oil & Gas, L.P.
                  and Aspect Resources Limited Liability Company.
    10.27+     -- Agreement and Partial Assignment of Interests in Hankins #1 Chappel Prospect Agreement,
                  Jackson County, Oklahoma (Hardeman Project), dated March 21, 1996, by and between
                  Brigham Oil & Gas, L.P., NGR, Ltd. and Aspect Resources Limited Liability Company.
</TABLE>
    
<PAGE>   100
 
   
<TABLE>
<CAPTION>
  EXHIBIT
   NUMBER                            DESCRIPTION
  -------                            -----------
<C>          <S>                                                          <C>
    10.28*     -- Form of Indemnity Agreement between the Registrant and each of its executive officers.
    10.29      -- Registration Rights Agreement dated February 26, 1997 by and among Brigham Exploration
                  Company, General Atlantic Partners III L.P., GAP-Brigham Partners, L.P., RIMCO
                  Partners, L.P. II, RIMCO Partners L.P. III, and RIMCO Partners, L.P. IV, Ben M.
                  Brigham, Anne L. Brigham, Harold D. Carter, Craig M. Fleming, David T. Brigham and Jon
                  L. Glass.
    10.30      -- 1997 Director Stock Option Plan.
    10.31      -- Form of Employee Stock Ownership Agreement.
    10.32      -- Unconditional Guaranty dated as of March 26, 1997, by Brigham Exploration Company for
                  the benefit of Bank One, Texas, National Association.
    10.33      -- Agreement and Assignment of Interest in Geophysical Exploration Agreement, Esperson
                  Dome Project, dated November 1, 1994, by and between Brigham Oil & Gas, L.P. and
                  Vaquero Gas Company.
    10.34      -- Geophysical Exploration Agreement, Southwest Danbury Project, Brazoria County, Texas,
                  dated as of July 1, 1996, by and among UNEXCO, Inc. and Brigham Oil & Gas, L.P.
    10.35      -- Geophysical Exploration Agreement, Welder Project, Duval County, Texas, dated as of
                  October 1, 1996, by and among UNEXCO, Inc. and Brigham Oil & Gas, L.P.
    10.36      -- Proposed Trade Structure, RIMCO/Tigre Project, Vermillion Parish, Louisiana, among
                  Brigham Oil & Gas, L.P., Tigre Energy Corporation and Resource Investors Management
                  Company
    10.36.1    -- Letter relating to Proposed Trade Structure, RIMCO/Tigre Project, dated January 31,
                  1997, from Resource Investors Management Company to Brigham Oil & Gas, L.P.
    10.37      -- Anadarko Basin Seismic Operations Agreement II, dated as of April 1, 1997, by and
                  between Brigham Oil & Gas, L.P.
    10.37.1    -- Letter Amendment to Anadarko Basin Seismic Operations Agreement II, dated March 20,
                  1997, between Brigham Oil & Gas, L.P. and Veritas DGC Land, Inc.
    11.1       -- Computation of Pro Forma Net Loss Per Common Share.
    21         -- Subsidiaries of the Registrant.
    23.1       -- Consent of Thompson & Knight, A Professional Corporation (included in Exhibit 5 above).
    23.2       -- Consent of Price Waterhouse LLP, independent accountants.
    23.3       -- Consent of Cawley, Gillespie & Associates, Inc., independent petroleum engineers.
    24.1       -- Powers of Attorney (included on the first signature page to this Registration
                  Statement).
    27+        -- Financial Data Schedule.
</TABLE>
    
 
- ---------------
 
   
 + Previously filed.
    
 
   
++ To be filed by amendment.
    
 
 * Management contract or compensatory plan.

<PAGE>   1





                                                                EXHIBIT 3.2





                                     BYLAWS


                                       OF


                          BRIGHAM EXPLORATION COMPANY



   
    

<PAGE>   2
                               TABLE OF CONTENTS

   
<TABLE>
         <S>              <C>                                                                                           <C>

ARTICLE I
       
         OFFICES  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   1
         Section 1.       Registered Office . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   1
         Section 2.       Other Offices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   1

ARTICLE II

         MEETINGS OF STOCKHOLDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   1
         Section 1.       Place of Meeting  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   1
         Section 2.       Annual Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   1
         Section 3.       Special Meetings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   2
         Section 4.       Notice of Meetings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   2
         Section 5.       Quorum  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   2
         Section 6.       Adjournments  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   2
         Section 7.       Order of Business . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   2
         Section 8.       List of Stockholders  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   3
         Section 9.       Voting  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   3
         Section 10.      Inspectors of Election  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   3

ARTICLE III

         BOARD OF DIRECTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   4
         Section 1.       General Powers  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   4
         Section 2.       Number, Qualification and Election  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   4
         Section 3.       Notification of Nominations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   4
         Section 4.       Quorum and Manner of Acting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   5
         Section 5.       Place of Meeting  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   5
         Section 6.       Regular Meetings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   5
         Section 7.       Special Meetings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   5
         Section 8.       Notice of Meetings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   5
         Section 9.       Rules and Regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   6
         Section 10.      Participation in Meeting by Means of Communication Equipment  . . . . . . . . . . . . . . .   6
         Section 11.      Action Without Meeting  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   6
         Section 12.      Resignations  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   6
         Section 13.      Removal of Directors  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   6
         Section 14.      Vacancies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   6
         Section 15.      Compensation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   6
         Section 16.      Advisory Directors  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   6

ARTICLE IV

         EXECUTIVE AND OTHER COMMITTEES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   7
         Section 1.       Executive Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   7
         Section 2.       Other Committees  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   7
         Section 3.       Procedure; Meetings; Quorum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   8
</TABLE>
    





                                      -i-
<PAGE>   3
   
<TABLE>
         <S>              <C>                                                                                          <C>

ARTICLE V

         OFFICERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   8
         Section 1.       Number; Term of Office  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   8
         Section 2.       Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
         Section 3.       Resignation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
         Section 4.       Vacancies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
         Section 5.       The President . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
         Section 6.       Chairman of the Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
         Section 7.       Vice Presidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
         Section 8.       Treasurer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
         Section 9.       Secretary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
         Section 10.      Controller  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
         Section 11.      Assistant Treasurers, Secretaries and Controllers . . . . . . . . . . . . . . . . . . . . .  10

ARTICLE VI

         INDEMNIFICATION OF DIRECTORS, OFFICERS, EMPLOYEES AND AGENTS . . . . . . . . . . . . . . . . . . . . . . . .  10
         Section 1.       Third Party Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
         Section 2.       Derivative Actions  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
         Section 3.       Determination of Indemnification  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 4.       Right to Indemnification  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 5.       Advancement of Expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 6.       Indemnification and Advancement of Expenses Not Exclusive . . . . . . . . . . . . . . . . .  11
         Section 7.       Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 8.       Definitions of Certain Terms  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 9.       Continuation and Successors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12
         Section 10.      Exclusive Jurisdiction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12

ARTICLE VII

         CAPITAL STOCK  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12
         Section 1.       Certificates for Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12
         Section 2.       Transfer of Shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12
         Section 3.       Address of Stockholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 4.       Lost, Destroyed and Mutilated Certificates  . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 5.       Regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 6.       Fixing Date for Determination of Stockholders of Record . . . . . . . . . . . . . . . . . .  13

ARTICLE VIII

         SEAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14

ARTICLE IX

         FISCAL YEAR  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
</TABLE>
    





                                      -ii-
<PAGE>   4

   
<TABLE>
         <S>                                                                                                           <C>

ARTICLE X

         WAIVER OF NOTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14

ARTICLE XI

         AMENDMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14

ARTICLE XII

         MISCELLANEOUS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
         Section 1.       Execution of Documents  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
         Section 2.       Deposits  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15
         Section 3.       Checks  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15
         Section 4.       Proxies in Respect of Stock or Other Securities of Other Corporations . . . . . . . . . . .  15
</TABLE>
    





                                     -iii-
<PAGE>   5
                                     BYLAWS

                                       OF

                          BRIGHAM EXPLORATION COMPANY


                                   ARTICLE I

                                    OFFICES

         Section 1.       Registered Office.  The registered office of Brigham
Exploration Company (hereinafter called the "Corporation") in the State of
Delaware shall be at Corporation Trust Center, 1209 Orange Street, in the City
of Wilmington, County of New Castle, 19801 and the registered agent in charge
thereof shall be The Corporation Trust Company.

         Section 2.       Other Offices.  The Corporation may also have an
office or offices, and keep the books and records of the Corporation, except as
may otherwise be required by law, at such other place or places, either within
or without the State of Delaware, as the Board of Directors may from time to
time determine or the business of the Corporation may require.


                                   ARTICLE II

                            MEETINGS OF STOCKHOLDERS

         Section 1.       Place of Meeting.  All meetings of the stockholders
of the Corporation shall be held at the office of the Corporation or at such
other places, within or without the State of Delaware, as may from time to time
be fixed by the Board of Directors, the Chairman of the Board or the President.

         Section 2.       Annual Meetings.  Annual meetings of the stockholders
of the Corporation for the election of directors and for the transaction of
such other business as may properly come before such meetings shall be held
during each calendar year on a date and at such hour as may be fixed by the
Board of Directors, the Chairman of the Board or the President.  Failure to
designate a time for the annual meeting or to hold the annual meeting at the
designated time shall not work a dissolution of the Corporation.

         In order for business to be properly brought before the meeting by a
stockholder, the business must be legally proper and written notice thereof
must have been filed with the Secretary of the Corporation not less than 60 nor
more than 120 days prior to the meeting.  Each such notice shall set forth: (a)
the name and address of the stockholder who intends to make the proposal as the
same appears in the Corporation's records; (b) the class and number of shares
of stock of the Corporation that are beneficially owned, directly or
indirectly, by such stockholder; and (c) a clear and concise statement of the
proposal and the stockholder's reasons for supporting it.

         The filing of a stockholder notice as required above shall not, in and
of itself, constitute the making of the proposal described therein.





                                      -1-
<PAGE>   6
         If the chairman of the meeting determines that any proposed business
has not been properly brought before the meeting, he shall declare such
business out of order; and such business shall not be conducted at the meeting.

         Section 3.       Special Meetings.  Except as otherwise required by
law and subject to the rights of the holders of any class or series of stock
having a preference over the Common Stock as to dividends or upon liquidation,
special meetings of the stockholders for any purpose or purposes may be called
only by (i) the Chairman of the Board, (ii) the President or (iii) a majority of
the entire Board of Directors. Only such business as is specified in the notice
of any special meeting of the stockholders shall come before such meeting.

         Section 4.       Notice of Meetings.  Except as otherwise provided by
law, written notice of each meeting of the stockholders, whether annual or
special, shall be given, either by personal delivery or by mail, not less than
10 nor more than 60 days before the date of the meeting to each stockholder of
record entitled to notice of the meeting.  If mailed, such notice shall be
deemed given when deposited in the United States mail, postage prepaid,
directed to the stockholder at such stockholder's address as it appears on the
records of the Corporation.  Each such notice shall state the place, date and
hour of the meeting, and the purpose or purposes for which the meeting is
called.  Notice of any meeting of stockholders shall not be required to be
given to any stockholder who shall attend such meeting in person or by proxy
without protesting, prior to or at the commencement of the meeting, the lack of
proper notice to such stockholder, or who shall waive notice thereof as
provided in Article X of these Bylaws.  Notice of adjournment of a meeting of
stockholders need not be given if the time and place to which it is adjourned
are announced at such meeting, unless the adjournment is for more than 30 days
or, after adjournment, a new record date is fixed for the adjourned meeting.

         Section 5.       Quorum.  Except as otherwise provided by law or by
the Certificate of Incorporation of the Corporation, the holders of a majority
of the votes entitled to be cast by the stockholders entitled to vote, which if
any vote is to be taken by classes shall mean the holders of a majority of the
votes entitled to be cast by the stockholders of each such class, present in
person or represented by proxy, shall constitute a quorum for the transaction
of business at any meeting of the stockholders.

         Section 6.       Adjournments.  In the absence of a quorum, the
holders of a majority of the votes present in person or represented by proxy,
may adjourn the meeting from time to time.  At any such adjourned meeting at
which a quorum may be present, any business may be transacted which might have
been transacted at the meeting as originally called.

         Section 7.       Order of Business.  At each meeting of the
stockholders, the Chairman of the Board, or, in the absence of the Chairman of
the Board, the President, shall act as chairman.  The order of business at each
such meeting shall be as determined by the chairman of the meeting.  The
chairman of the meeting shall have the right and authority to prescribe such
rules, regulations and procedures and to do all such acts and things as are
necessary or desirable for the proper conduct of the meeting, including,
without limitation, the establishment of procedures for the maintenance of
order and safety, limitations on the time allotted to questions or comments on
the affairs of the Corporation, restrictions on entry to such meeting after the
time prescribed for the commencement thereof, and the opening and closing of
the voting polls.  The chairman of the meeting shall announce at each such
meeting the date





                                      -2-
<PAGE>   7
and time of the opening and the closing of the voting polls for each matter
upon which the stockholders will vote at such meeting.

         Section 8.       List of Stockholders.  It shall be the duty of the
Secretary or other officer of the Corporation who has charge of the stock
ledger to prepare and make, at least 10 days before each meeting of the
stockholders, a complete list of the stockholders entitled to vote thereat,
arranged in alphabetical order, and showing the address of each stockholder and
the number of shares registered in such stockholder's name.  Such list shall be
produced and kept available at the times and places required by law.

         Section 9.       Voting.  Except as otherwise provided by law or by
the Certificate of Incorporation of the Corporation, each stockholder of record
of any class or series of stock having a preference over the Common Stock of
the Corporation as to dividends or upon liquidation shall be entitled at each
meeting of stockholders to such number of votes for each share of such stock as
may be fixed in the Certificate of Incorporation or in the resolution or
resolutions adopted by the Board of Directors providing for the issuance of
such stock, and each stockholder of record of Common Stock shall be entitled at
each meeting of stockholders to one vote for each share of such stock, in each
case, registered in such stockholder's name on the books of the Corporation:

                 (a)      on the date fixed pursuant to Section 6 of Article
         VII of these Bylaws as the record date for the determination of
         stockholders entitled to notice of and to vote at such meeting; or

                 (b)      if no such record date shall have been so fixed, then
         at the close of business on the day next preceding the date on which
         notice of such meeting is given, or, if notice is waived, at the close
         of business on the day next preceding the day on which the meeting is
         held.

         Each stockholder entitled to vote at any meeting of stockholders may
authorize not in excess of three persons to act for such stockholder by a proxy
signed by such stockholder or such stockholder's attorney-in-fact.  Any such
proxy shall be delivered to the secretary of such meeting at or prior to the
time designated for holding such meeting but, in any event, not later than the
time designated in the order of business for so delivering such proxies.  No
such proxy shall be voted or acted upon after three years from its date, unless
the proxy provides for a longer period.

   
      At each meeting of the stockholders, all corporate actions to be
taken by vote of the stockholders (except as otherwise required by law and
except as otherwise provided in the Certificate of Incorporation) shall be
authorized by a majority of the votes cast by the stockholders entitled to vote
thereon, present in person or represented by proxy. Where a separate vote by a
class or classes is required, the affirmative vote of the majority of shares of
such class or classes present in person or represented by proxy at the meeting
shall be the act of such class. 
    

         Unless required by law or determined by the chairman of the meeting to
be advisable, the vote on any matter, including the election of directors, need
not be by written ballot.  In the case of a vote by written ballot, each ballot
shall be signed by the stockholder voting, or by such stockholder's proxy, and
shall state the number of shares voted.

         Section 10.      Inspectors of Election.  Either the Board of
Directors or, in the absence of an appointment of inspectors by the Board, the
Chairman of the Board or the President shall, in advance of each meeting of the
stockholders, appoint one or more inspectors to act at such meeting and make a




                                      -3-

<PAGE>   8
written report thereof.  In connection with any such appointment, one or more
persons may, in the discretion of the body or person making such appointment,
be designated as alternate inspectors to replace any inspector who fails to
act.  If no inspector or alternate is able to act at any meeting of
stockholders, the chairman of such meeting shall appoint one or more inspectors
to act at such meeting.  Each such inspector shall perform such duties as are
required by law and as shall be specified by the Board, the Chairman of the
Board, the President or the chairman of the meeting.  Each such inspector,
before entering upon the discharge of his duties, shall take and sign an oath
faithfully to execute the duties of inspector with strict impartiality and
according to the best of his ability.  Inspectors need not be stockholders.  No
director or nominee for the office of director shall be appointed such an
inspector.


                                  ARTICLE III

                               BOARD OF DIRECTORS

         Section 1.       General Powers.  The business and affairs of the
Corporation shall be managed by or under the direction of the Board of
Directors, which may exercise all such powers of the Corporation and do all
such lawful acts and things as are not by law or by the Certificate of
Incorporation of the Corporation directed or required to be exercised or done
by the stockholders.

         Section 2.       Number, Qualification and Election.  Except as
otherwise provided in any resolution or resolutions adopted by the Board of
Directors pursuant to the provisions of Article FOURTH of the Certificate of
Incorporation of the Corporation relating to the rights of the holders of any
class or series of stock having a preference over the Common Stock as to
dividends or upon liquidation, the number of directors of the Corporation shall
be fixed from time to time by resolution adopted by vote of a majority of the
entire Board of Directors, provided that the number so fixed shall not be less
than five nor more than nine.

         The directors, other than those who may be elected by the holders of
shares of any class or series of stock having a preference over the Common
Stock as to dividends or upon liquidation pursuant to the terms of any
resolution or resolutions providing for the issuance of such stock adopted by
the Board, shall hold office until his successor is elected and qualified or
until his earlier resignation or removal.

         Each director shall be at least 21 years of age.  Directors need not
be stockholders of the Corporation.

         Subject to the rights of the holders of any class or series of stock
having a preference over the Common Stock as to dividends or upon liquidation,
at each annual meeting of the stockholders, all directors of the Corporation
shall be elected.

         In any election of directors, the persons receiving a plurality of the
votes cast, up to the number of directors to be elected in such election, shall
be deemed elected.

         Section 3.       Notification of Nominations.  Subject to the rights
of the holders of any class or series of stock having a preference over the
Common Stock as to dividends or upon liquidation, nominations for the election
of directors may be made by the Board of Directors or by any stockholder
entitled to vote for the election of directors.  Any stockholder entitled to
vote for the election of directors at a meeting may nominate persons for
election as directors only if written notice of such stockholder's intent to
make such nomination is given, either by personal delivery or by United States
mail, postage 



                                      -4-

<PAGE>   9
prepaid, to the Secretary of the Corporation not later than (i) with respect to
an election to be held at an annual meeting of stockholders, 90 days in advance
of such meeting, and (ii) with respect to an election to be held at a special
meeting of stockholders for the election of directors, the close of business on
the seventh day following the date on which notice of such meeting is first
given to stockholders.  Each such notice shall set forth:  (a) the name and
address of the stockholder who intends to make the nomination of the person or
persons to be nominated; (b) a representation that the stockholder is a holder
of record of stock of the Corporation entitled to vote at such meeting and
intends to appear in person or by proxy at the meeting to nominate the person
or persons specified in the notice; (c) a description of all arrangements or
understandings between the stockholder and each nominee and any other person or
persons (naming such person or persons) pursuant to which the nomination or
nominations are to be made by the stockholder; (d) such other information
regarding each nominee proposed by such stockholder as would have been required
to be included in a proxy statement filed pursuant to the proxy rules of the
Securities and Exchange Commission had each nominee been nominated, or intended
to be nominated, by the Board of Directors; and (e) the consent of each nominee
to serve as a director of the Corporation if so elected.  The chairman of the
meeting may refuse to acknowledge the nomination of any person not made in
compliance with the foregoing procedure.

         Section 4.       Quorum and Manner of Acting.  Except as otherwise
provided by law, the Certificate of Incorporation of the Corporation or these
Bylaws, a majority of the entire Board of Directors shall constitute a quorum
for the transaction of business at any meeting of the Board, and, except as so
provided, the vote of a majority of the directors present at any meeting at
which a quorum is present shall be the act of the Board.  In the absence of a
quorum, a majority of the directors present may adjourn the meeting to another
time and place.  At any adjourned meeting at which a quorum is present, any
business that might have been transacted at the meeting as originally called
may be transacted.

         Section 5.       Place of Meeting.  The Board of Directors may hold
its meetings at such place or places within or without the State of Delaware as
the Board may from time to time determine or as shall be specified or fixed in
the respective notices or waivers of notice thereof.

         Section 6.       Regular Meetings.  Regular meetings of the Board of
Directors shall be held at such times and places as the Board shall from time
to time by resolution determine.  If any day fixed for a regular meeting shall
be a legal holiday under the laws of the place where the meeting is to be held,
the meeting that would otherwise be held on that day shall be held at the same
hour on the next succeeding business day.

         Section 7.       Special Meetings.  Special meetings of the Board of
Directors shall be held whenever called by the Chairman of the Board or the
President or by a majority of the directors.

         Section 8.       Notice of Meetings.  Notice of regular meetings of
the Board of Directors or of any adjourned meeting thereof need not be given.
Notice of each special meeting of the Board shall be mailed or transmitted by
delivery service to each director, addressed to such director at such
director's residence or usual place of business, at least two days before the
day on which the meeting is to be held or shall be sent to such director at
such place by telegraph or facsimile telecommunication or be given personally
or by telephone, not later than the day before the meeting is to be held, but
notice need not be given to any director who shall, either before or after the
meeting, submit a signed waiver of such notice or who shall attend such meeting
without protesting, prior to or at its commencement, the lack of notice to such
director.  Every such notice shall state the time and place but need not state
the purpose of the meeting.




                                      -5-

<PAGE>   10

         Section 9.       Rules and Regulations.  The Board of Directors may
adopt such rules and regulations not inconsistent with the provisions of law,
the Certificate of Incorporation of the Corporation or these Bylaws for the
conduct of its meetings and management of the affairs of the Corporation as the
Board may deem proper.

         Section 10.      Participation in Meeting by Means of Communication
Equipment.  Any one or more members of the Board of Directors or any committee
thereof may participate in any meeting of the Board or of any such committee by
means of conference telephone or similar communications equipment by means of
which all persons participating in the meeting can hear each other, and such
participation in a meeting shall constitute presence in person at such meeting.

         Section 11.      Action Without Meeting.  Any action required or
permitted to be taken at any meeting of the Board of Directors or any committee
thereof may be taken without a meeting if all of the members of the Board or of
any such committee consent thereto in writing and the writing or writings are
filed with the minutes of proceedings of the Board or of such committee.

         Section 12.      Resignations.  Any director of the Corporation may at
any time resign by giving written notice to the Board of Directors, the
Chairman of the Board, the President or the Secretary of the Corporation.  Such
resignation shall take effect at the time specified therein or, if the time be
not specified, upon receipt thereof; and unless otherwise specified therein,
the acceptance of such resignation shall not be necessary to make it effective.

         Section 13.      Removal of Directors.  Any director or the entire
board of directors may be removed, with or without cause, by the holders of a
majority of the shares then entitled to vote at an election of directors.

         Section 14.      Vacancies.  Subject to the rights of the holders of
any class or series of stock having a preference over the Common Stock as to
dividends or upon liquidation, any vacancies on the Board of Directors and any
newly created directorship resulting from an increase in the authorized number
of directors, may be filled by election at an annual or special meeting of
stockholders called for that purpose or by the affirmative vote of a majority
of the remaining directors, though less than a quorum of the entire Board, and
the directors so chosen shall hold office until the next annual meeting of
stockholders and until their successors are duly elected and shall qualify,
unless sooner displaced.

         Section 15.      Compensation.  Each director who shall not at the
time also be a salaried officer or employee of the Corporation or any of its
subsidiaries (hereinafter referred to as an "outside director"), in
consideration of such person serving as a director, shall be entitled to
receive from the Corporation such amount per annum and such fees for attendance
at meetings of the Board of Directors or of
committees of the Board, or both, as the Board shall from time to time
determine.  In addition, each director, whether or not an outside director,
shall be entitled to receive from the Corporation reimbursement for the
reasonable expenses incurred by such person in connection with the performance
of such person's duties as a director.  Nothing contained in this Section 15
shall preclude any director from serving the Corporation or any of its
subsidiaries in any other capacity and receiving proper compensation therefor.

         Section 16.      Advisory Directors.   The Board of Directors may
appoint one or more advisory directors as it shall from time to time determine.
Each advisory director appointed shall hold office at the pleasure of the Board
of Directors.  An advisory director shall be entitled, but shall have no
obligation, to attend and be present at the meetings of the Board of Directors,
although a meeting of the 




                                      -6-

<PAGE>   11
Board of Directors may be held without notice to any advisory director and no
advisory director shall be considered in determining whether a quorum of the
Board of Directors is present.  An advisory director shall advise and counsel
the Board of Directors on the business and operations of the Corporation as
requested by the Board of Directors; however, an advisory director shall not be
entitled to vote on any matter presented to the Board of Directors.  An
advisory director, in consideration of such person serving as an advisory
director, shall be entitled to receive from the Corporation such fees for
attendance at meetings of the Board of Directors as the Board shall from time
to time determine.  In addition, an advisory director shall be entitled to
receive from the Corporation reimbursement for the reasonable expenses incurred
by such person in connection with the performance of such person's duties as an
advisory director.


                                   ARTICLE IV

                         EXECUTIVE AND OTHER COMMITTEES

         Section 1.       Executive Committee.  The Board of Directors may, by
resolution adopted by a majority of the entire Board, designate annually three
or more of its members to constitute members or alternate members of an
Executive Committee, which Committee shall have and may exercise, between
meetings of the Board, all the powers and authority of the Board in the
management of the business affairs of the Corporation, including, if such
Committee is so empowered and authorized by resolution adopted by a majority of
the entire Board, the power and authority to declare a dividend and to
authorize the issuance of stock, and may authorize the seal of the Corporation
to be affixed to all papers that may require it, except that the Executive
Committee shall not have such power or authority in reference to:

                 (a)      amending the Certificate of Incorporation of the
         Corporation;

                 (b)      adopting an agreement of merger or consolidation
         involving the Corporation;

                 (c)      recommending to the stockholders the sale, lease or
         exchange of all or substantially all of the property and assets of the
         Corporation;

                 (d)      recommending to the stockholders a dissolution of the
         Corporation or a revocation of a dissolution;

                 (e)      adopting, amending or repealing any Bylaw;

                 (f)      filling vacancies on the Board or on any committee of
         the Board, including the Executive Committee; or

                 (g)      amending or repealing any resolution of the Board
         which by its terms may be amended or repealed only by the Board.

The Board shall have power at any time to change the membership of the
Executive Committee, to fill all vacancies in it and to discharge it, either
with or without cause.

         Section 2.       Other Committees.  The Board of Directors may, by
resolution adopted by a majority of the entire Board, designate from among its
members one or more other committees, each of which shall, except as otherwise
prescribed by law, have such authority of the Board as may be specified 



                                      -7-

<PAGE>   12
in the resolution of the Board designating such committee.  A majority of all
the members of such committee may determine its action and fix the time and
place of its meetings, unless the Board shall otherwise provide.  The Board
shall have power at any time to change the membership of, to fill all vacancies
in and to discharge any such committee, either with or without cause.

         Section 3.       Procedure; Meetings; Quorum.  Regular meetings of the
Executive Committee or any other committee of the Board of Directors, of which
no notice shall be necessary, may be held at such times and places as shall be
fixed by resolution adopted by a majority of the members thereof.  Special
meetings of the Executive Committee or any other committee of the Board shall
be called at the request of any member thereof.  Notice of each special meeting
of the Executive Committee or any other committee of the Board shall be sent by
mail, delivery service, facsimile telecommunication, telegraph or telephone, or
be delivered personally to each member thereof not later than the day before
the day on which the meeting is to be held, but notice need not be given to any
member who shall, either before or after the meeting, submit a signed waiver of
such notice or who shall attend such meeting without protesting, prior to or at
its commencement, the lack of such notice to such member.  Any special meeting
of the Executive Committee or any other committee of the Board shall be a legal
meeting without any notice thereof having been given, if all the members
thereof shall be present thereat.  Notice of any adjourned meeting of any
committee of the Board need not be given.  The Executive Committee or any other
committee of the Board may adopt such rules and regulations not inconsistent
with the provisions of law, the Certificate of Incorporation of the Corporation
or these Bylaws for the conduct of its meetings as the Executive Committee or
any other committee of the Board may deem proper.  A majority of the Executive
Committee or any other committee of the Board shall constitute a quorum for the
transaction of business at any meeting, and the vote of a majority of the
members thereof present at any meeting at which a quorum is present shall be
the act of such committee.  The Executive Committee or any other committee of
the Board of Directors shall keep written minutes of its proceedings and shall
report on such proceedings to the Board.


                                   ARTICLE V

                                    OFFICERS

   
         Section 1.       Number; Term of Office.  The officers of the
Corporation shall be a Chairman of the Board, a President, one or more Vice
Presidents (one or more of which may be designated Executive Vice President and
one of which may be designated Chief Financial Officer), a Treasurer, a
Secretary, a Controller, and such other officers or agents with such titles and
such duties as the Board of Directors may from time to time determine, each to
have such authority, functions or duties as in these Bylaws provided or as the
Board may from time to time determine, and each to hold office for such term as
may be prescribed by the Board and until such person's successor shall have
been chosen and shall qualify, or until such person's death or resignation, or
until such person's removal in the manner hereinafter provided.  The Chairman
of the Board shall be elected from among the directors.  One person may hold
the offices and perform the duties of any two or more of said officers;
provided, however, that no officer shall execute, acknowledge or verify any
instrument in more than one capacity if such instrument is required by law, the
Certificate of Incorporation of the Corporation or these Bylaws to be executed,
acknowledged or verified by two or more officers.  The Board may from time to
time authorize any officer to appoint and remove any such other officers and
agents and to prescribe their powers and duties.  The Board may require any
officer or agent to give security for the faithful performance of such person's
duties.
    





                                      -8-

<PAGE>   13

         Section 2.       Removal.  Any officer may be removed, either with or
without cause, by the Board of Directors at any meeting thereof called for that
purpose, or, except in the case of any officer elected by the Board, by any
committee or superior officer upon whom such power may be conferred by the
Board.

         Section 3.       Resignation.  Any officer may resign at any time by
giving notice to the Board of Directors, the President or the Secretary of the
Corporation.  Any such resignation shall take effect at the date of receipt of
such notice or at any later date specified therein; and, unless otherwise
specified therein, the acceptance of such resignation shall not be necessary to
make it effective.

         Section 4.       Vacancies.  A vacancy in any office because of death,
resignation, removal or any other cause may be filled for the unexpired portion
of the term in the manner prescribed in these Bylaws for election to such
office.

         Section 5.       The President.  The President shall be the chief
executive officer of the Corporation and as such shall have general supervision
and direction of the business and affairs of the Corporation, subject to the
control of the Board of Directors.  The President shall, if present and in the
absence of the Chairman of the Board, preside at meetings of the stockholders,
meetings of the Board and meetings of the Executive Committee.  The President
shall perform such other duties as the Board may from time to time determine.
The President may sign and execute in the name of the Corporation deeds,
mortgages, bonds, contracts or other instruments authorized by the Board or any
committee thereof empowered to authorize the same.

         Section 6.       Chairman of the Board.  The Chairman of the Board
shall, if present, preside at meetings of the stockholders, meetings of the
Board and meetings of the Executive Committee.  The Chairman of the Board shall
counsel with and advise the President and perform such other duties as the
President or the Board or the Executive Committee may from time to time
determine.

         Section 7.       Vice Presidents.  Each Vice President shall have such
powers and duties as shall be prescribed by the President, the Chairman of the
Board or the Board of Directors.  Any Vice President may sign and execute in
the name of the Corporation deeds, mortgages, bonds, contracts or other
instruments authorized by the Board or any committee thereof empowered to
authorize the same.

         Section 8.       Treasurer.  The Treasurer shall perform all duties
incident to the office of Treasurer and such other duties as from time to time
may be assigned to the Treasurer by the President, the Chairman of the Board or
the Board of Directors.

         Section 9.       Secretary.  It shall be the duty of the Secretary to
act as secretary at all meetings of the Board of Directors, of the Executive
Committee and of the stockholders and to record the proceedings of such
meetings in a book or books to be kept for that purpose; the Secretary shall
see that all notices required to be given by the Corporation are duly given and
served; the Secretary shall be custodian of the seal of the Corporation and
shall affix the seal or cause it to be affixed to all certificates of stock of
the Corporation (unless the seal of the Corporation on such certificates shall
be a facsimile, as hereinafter provided) and to all documents, the execution of
which on behalf of the Corporation under its seal is duly authorized in
accordance with the provisions of these Bylaws. The Secretary shall have charge
of the stock ledger and also of the other books, records and papers of the
Corporation and shall see that the reports, statements and other documents
required by law are properly kept and filed; and the Secretary shall in general
perform all the duties incident to the office of Secretary and such other
duties   




                                      -9-

<PAGE>   14
as from time to time may be assigned to such person by the President, the
Chairman of the Board or the Board of Directors.

         Section 10.      Controller.  The Controller shall perform all of the
duties incident to the office of the Controller and such other duties as from
time to time may be assigned to such person by the President, the Chairman of
the Board or the Board of Directors.

         Section 11.      Assistant Treasurers, Secretaries and Controllers.
The Assistant Treasurers, the Assistant Secretaries and the Assistant
Controllers shall perform such duties as shall be assigned to them by the
Treasurer, Secretary or Controller, respectively, or by the President, the
Chairman of the Board or the Board of Directors.


                                   ARTICLE VI

          INDEMNIFICATION OF DIRECTORS, OFFICERS, EMPLOYEES AND AGENTS

         Section 1.       Third Party Actions.  The Corporation shall indemnify
any person who was or is a party or is threatened to be made a party to any
threatened, pending or completed action, suit or proceeding, whether civil,
criminal, administrative or investigative (other than an action by or in the
right of the Corporation), by reason of the fact that such person is or was a
director, officer, employee or agent  of the Corporation, or is or was serving
at the request of the Corporation as a director, officer, employee or agent  of
another corporation, partnership, joint venture, trust or other enterprise,
against expenses (including attorneys' fees), judgments, fines and amounts paid
in settlement actually and reasonably incurred by such person in connection
with such action, suit or proceeding if such person acted in good faith and in
a manner such person reasonably believed to be in or not opposed to the best
interests of the Corporation, and, with respect to any criminal action or
proceeding, had no reasonable cause to believe his or her conduct was unlawful.
The termination of any action, suit or proceeding by judgment, order,
settlement, conviction, or upon a plea of nolo contendere or its equivalent,
shall not, of itself, create a presumption that the person did not act in good
faith and in a manner which such person reasonably believed to be in or not
opposed to the best interests of the Corporation, and, with respect to any
criminal action or proceeding, had reasonable cause to believe that his or her
conduct was unlawful.

         Section 2.       Derivative Actions.  The Corporation shall indemnify
any person who was or is a party or is threatened to be made a party to any
threatened, pending or completed action or suit by or in the right of the
Corporation to procure a judgment in its favor by reason of the fact that such
person is or was a director, officer, employee or agent of the Corporation, or
is or was serving at the request of the Corporation as a director, officer,
employee or agent of another corporation, partnership, joint venture, trust or
other enterprise, against expenses (including attorneys' fees) actually and
reasonably incurred by such person in connection with the defense or settlement
of such action or suit if such person acted in good faith and in a manner such
person reasonably believed to be in or not opposed to the best interests of the
Corporation, except that no indemnification shall be made in respect of any
claim, issue or matter as to which such person shall have been adjudged to be
liable to the Corporation unless and only to the extent that the Court of
Chancery of Delaware or the court in which such action or suit was brought
shall determine upon application that, despite the adjudication of liability
but in view of all the circumstances of the case, such person is fairly and
reasonably entitled to indemnity for such expenses which the Court of Chancery
of Delaware or such other court shall deem proper.





                                      -10-

<PAGE>   15

         Section 3.       Determination of Indemnification.  Any
indemnification under Section 1 or 2 of this Article VI (unless ordered by a
court) shall be made by the Corporation only as authorized in the specific case
upon a determination that indemnification of the director, officer, employee or
agent is proper in the circumstances because such person has met the applicable
standard of conduct set forth in Section 1 or 2 of this Article VI.  Such
determination shall be made (i) by a majority vote of the directors who are not
parties to such action, suit or proceeding, even though less than a quorum, or
(ii) if there are no such directors, or if such directors so direct, by
independent legal counsel in a written opinion, or (iii) by the stockholders.

         Section 4.       Right to Indemnification.  Notwithstanding the other
provisions of this Article VI, to the extent that a director, officer, employee
or agent of the Corporation has been successful on the merits or otherwise in
defense of any action, suit or proceeding referred to in Section 1 or 2 of this
Article VI, or in defense of any claim, issue or matter therein, such person
shall be indemnified against expenses (including attorneys' fees) actually and
reasonably incurred by such person in connection therewith.

         Section 5.       Advancement of Expenses.  The Corporation shall pay
the expenses (including attorneys' fees) incurred in defending any civil,
criminal, administrative or investigative action, suit or proceeding in advance
of the final disposition of such action, suit or proceeding, provided, however,
that the payment of expenses incurred by a director, officer, employee or agent
in advance of the final disposition of the action, suit or proceeding shall be
made only upon receipt of an undertaking by or on behalf of the director,
officer, employee or agent to repay all amounts advanced if it should be
ultimately determined that such person is not entitled to be indemnified under
this Article VI or otherwise.

         Section 6.       Indemnification and Advancement of Expenses Not
Exclusive.  The indemnification and advancement of expenses provided by, or
granted pursuant to the other Sections of this Article VI shall not be deemed
exclusive of any other rights to which any person seeking indemnification may
be entitled under any law, agreement, vote of stockholders or disinterested
directors or otherwise, both as to action in such person's official capacity
and as to action in another capacity while holding such office.  All rights to
indemnification under this Article VI shall be deemed to be provided by a
contract between the Corporation and the director, officer, employee or agent
who served in such capacity at any time while these Bylaws and other relevant
provisions of the Delaware General Corporation Law and other applicable law, if
any, are in effect.  Any repeal or modification thereof shall not affect any
rights or obligations then existing.

         Section 7.       Insurance.  The Corporation may purchase and maintain
insurance on behalf of any person who is or was a director, officer, employee
or agent of the Corporation, or is or was serving at the request of the
Corporation as a director, officer, employee or agent of another corporation,
partnership, joint venture, trust or other enterprise, against any liability
asserted against such person and incurred by such person in any such capacity,
or arising out of such person's status as such, whether or not the Corporation
would have the power to indemnify such person against such liability under the
applicable provisions of the Delaware General Corporation Law.

         Section 8.       Definitions of Certain Terms.  For purposes of this
Article VI, references to "the Corporation" shall include, in addition to the
resulting corporation, any constituent corporation (including any constituent
of a constituent) absorbed in a consolidation or merger which, if its separate
existence had continued, would have had power and authority to indemnify its
directors, officers, employees or agents, so that any person who is or was a
director, officer, employee or agent of such constituent corporation, or is or
was serving at the request of such constituent corporation as a director,
officer, 




                                      -11-

<PAGE>   16
employee or agent of another corporation, partnership, joint venture, trust or
other enterprise, shall stand in the same position under the provisions of this
Article VI with respect to the resulting or surviving corporation as such
person would have with respect to such constituent corporation if its separate
existence had continued.

         For purposes of this Article VI, references to "other enterprise"
shall include employee benefit plans; references to "fines" shall include any
excise tax assessed on a person with respect to any employee benefit plan; and
references to "serving at the request of the Corporation" shall include any
service as a director, officer, employee or agent of the Corporation that
imposes duties on, or involves services by, such director, officer, employee or
agent with respect to an employee benefit plan, its participants or
beneficiaries; and a person who acted in good faith and in a manner such person
reasonably believed to be in the interest of the participants and beneficiaries
of an employee benefit plan shall be deemed to have acted in a manner "not
opposed to the best interests of the Corporation" as referred to in this
Article VI.

         Section 9.       Continuation and Successors.  The indemnification and
advancement of expenses provided by, or granted pursuant to, this Article VI
shall, unless otherwise provided when authorized or ratified, continue as to a
person who has ceased to be a director, officer, employee or agent and shall
inure to the benefit of the heirs, executors and administrators of such a
person.

         Section 10.      Exclusive Jurisdiction.  The Delaware Court of
Chancery is vested with exclusive jurisdiction to hear and determine all
actions for advancement of expenses or indemnification brought under this
Article VI or under any statute, agreement, vote of stockholders or
disinterested directors, or otherwise.  The Delaware Court of Chancery may
summarily determine the Corporation's obligation to advance expenses (including
attorneys' fees).


                                  ARTICLE VII

                                 CAPITAL STOCK

         Section 1.       Certificates for Shares.  Certificates representing
shares of stock of each class of the Corporation, whenever authorized by the
Board of Directors, shall be in such form as shall be approved by the Board.
The certificates representing shares of stock of each class shall be signed by,
or in the name of, the Corporation by the Chairman of the Board or the
President or a Vice President and by the Secretary or an Assistant Secretary or
the Treasurer or an Assistant Treasurer of the Corporation, and sealed with the
seal of the Corporation, which may be by a facsimile thereof.  Any or all such
signatures may be facsimiles if countersigned by a transfer agent or registrar.
Although any officer, transfer agent or registrar whose manual or facsimile
signature is affixed to such a certificate ceases to be such officer, transfer
agent or registrar before such certificate has been issued, it may nevertheless
be issued by the Corporation with the same effect as if such officer, transfer
agent or registrar were still such at the date of its issue.

         The stock ledger and blank share certificates shall be kept by the
Secretary or by a transfer agent or by a registrar or by any other officer or
agent designated by the Board.

         Section 2.       Transfer of Shares.  Transfer of shares of stock of
each class of the Corporation shall be made only on the books of the
Corporation by the holder thereof, or by such holder's attorney thereunto
authorized by a power of attorney duly executed and filed with the Secretary of
the Corporation or a transfer agent for such stock, if any, and on surrender of
the certificate or certificates for such shares 




                                      -12-

<PAGE>   17
properly endorsed or accompanied by a duly executed stock transfer power and
the payment of all taxes thereon.  The person in whose name shares stand on the
books of the Corporation shall be deemed the owner thereof for all purposes as
regards the Corporation; provided, however, that whenever any transfer of
shares shall be made for collateral security and not absolutely, and written
notice thereof shall be given to the Secretary or to such transfer agent, such
fact shall be stated in the entry of the transfer.  No transfer of shares shall
be valid as against the Corporation, its stockholders and creditors for any
purpose, except to render the transferee liable for the debts of the
Corporation to the extent provided by law, until it shall have been entered in
the stock records of the Corporation by an entry showing from and to whom
transferred.

         Section 3.       Address of Stockholders.  Each stockholder shall
designate to the Secretary or transfer agent of the Corporation an address at
which notices of meetings and all other corporate notices may be served or
mailed to such person, and, if any stockholder shall fail to designate such
address, corporate notices may be served upon such person by mail directed to
such person at such person's post office address, if any, as the same appears
on the share record books of the Corporation or at such person's last known
post office address.

         Section 4.       Lost, Destroyed and Mutilated Certificates.  The
holder of any share of stock of the Corporation shall immediately notify the
Corporation of any loss, theft, destruction or mutilation of the certificate
therefor; the Corporation may issue to such holder a new certificate or
certificates for shares, upon the surrender of the mutilated certificate or, in
the case of loss, theft or destruction of the certificate, upon satisfactory
proof of such loss, theft or destruction; the Board of Directors, or a
committee designated thereby, or the transfer agents and registrars for the
stock, may, in their discretion, require the owner of the lost, stolen or
destroyed certificate, or such person's legal representative, to give the
Corporation a bond in such sum and with such surety or sureties as they may
direct to indemnify the Corporation and said transfer agents and registrars
against any claim that may be made on account of the alleged loss, theft or
destruction of any such certificate or the issuance of such new certificate.

         Section 5.       Regulations.  The Board of Directors may make such
additional rules and regulations as it may deem expedient concerning the issue
and transfer of certificates representing shares of stock of each class of the
Corporation and may make such rules and take such action as it may deem
expedient concerning the issue of certificates in lieu of certificates claimed
to have been lost, destroyed, stolen or mutilated.

         Section 6.       Fixing Date for Determination of Stockholders of
Record.  In order that the Corporation may determine the stockholders entitled
to notice of or to vote at any meeting of stockholders or any adjournment
thereof, or entitled to receive payment of any dividend or other distribution
or allotment of any rights, or entitled to exercise any rights in respect of
any change, conversion or exchange of stock or for the purpose of any other
lawful action, the Board of Directors may fix a record date, which record date
shall not precede the date upon which the resolution fixing the record date is
adopted by the Board of Directors, and which record date shall not be more than
60 nor less than 10 days before the date of such meeting, nor more than 60 days
prior to any other action.  A determination of stockholders entitled to notice
of or to vote at a meeting of the stockholders shall apply to any adjournment
of the meeting; provided, however, that the Board of Directors may fix a new
record date for the adjourned meeting.





                                      -13-

<PAGE>   18


                                  ARTICLE VIII

                                      SEAL

         The Board of Directors may provide for a corporate seal bearing the
name of the Corporation in such form and bearing such other words or figures as
the Board of Directors may approve and adopt.  The seal may be used by causing
it or a facsimile thereof to be impressed or affixed or in any other manner
reproduced.


                                   ARTICLE IX

                                  FISCAL YEAR

         The fiscal year of the Corporation shall be fixed by resolution of the
Board of Directors.


                                   ARTICLE X

                                WAIVER OF NOTICE

         Whenever any notice whatsoever is required to be given by these
Bylaws, by the Certificate of Incorporation of the Corporation or by law, the
person entitled thereto may, either before or after the meeting or other matter
in respect of which such notice is to be given, waive such notice in writing,
which writing shall be filed with or entered upon the records of the meeting or
the records kept with respect to such other matter, as the case may be, and in
such event such notice need not be given to such person and such waiver shall
be deemed equivalent to such notice.


                                   ARTICLE XI

                                   AMENDMENTS

         Any Bylaw (including this Article XI) may be adopted, repealed,
altered or amended at any meeting of the Board of Directors by the affirmative
vote of a majority of the directors, provided that such proposed action in
respect thereof shall be stated in the notice of such meeting.  The
stockholders of the Corporation shall have the power to adopt, repeal, alter or
amend any provision of these Bylaws only to the extent and in the manner
provided in the Certificate of Incorporation of the Corporation.

                                  ARTICLE XII

                                 MISCELLANEOUS

         Section 1.       Execution of Documents.  The Board of Directors or
any committee thereof shall designate the officers, employees and agents of the
Corporation who shall have power to execute and deliver deeds, contracts,
mortgages, bonds, debentures, notes, checks, drafts and other orders for the
payment of money and other documents for and in the name of the Corporation and
may authorize such 



                                      -14-

<PAGE>   19
officers, employees and agents to delegate such power (including authority to
redelegate) by written instrument to other officers, employees or agents of the
Corporation.  Such delegation may be by resolution or otherwise and the
authority granted shall be general or confined to specific matters, all as the
Board or any such committee may determine.  In the absence of such designation
referred to in the first sentence of this Section 1, the officers of the
Corporation shall have such power so referred to, to the extent incident to the
normal performance of their duties.

         Section 2.       Deposits.  All funds of the Corporation not otherwise
employed shall be deposited from time to time to the credit of the Corporation
or otherwise as the Board of Directors or any committee thereof or any officer
of the Corporation to whom power in that respect shall have been delegated by
the Board or any such committee shall select.

         Section 3.       Checks.  All checks, drafts and other orders for the
payment of money out of the funds of the Corporation, and all notes or other
evidence of indebtedness of the Corporation, shall be signed on behalf of the
Corporation in such manner as shall from time to time be determined by
resolution of the Board of Directors or of any committee thereof.

         Section 4.       Proxies in Respect of Stock or Other Securities of
Other Corporations.  The Board of Directors or any committee thereof shall
designate the officers of the Corporation who shall have authority from time to
time to appoint an agent or agents of the Corporation to exercise in the name
and on behalf of the Corporation the powers and rights that the Corporation may
have as the holder of stock or other securities in any other corporation, and
to vote or consent in respect of such stock or securities; such designated
officers may instruct the person or persons so appointed as to the manner of
exercising such powers and rights; and such designated officers may execute or
cause to be executed in the name and on behalf of the Corporation and under its
corporate seal, or otherwise, such written proxies, powers of attorney or other
instruments as they may deem necessary or proper in order that the Corporation
may exercise its said powers and rights.





                                      -15-

<PAGE>   1
                                                                  EXHIBIT 4.1

   NUMBER                                                           SHARES
                                [BRIGHAM LOGO]
                                   BRIGHAM
                              EXPLORATON COMPANY

COMMON STOCK                                                    PAR VALUE $.01
                                                                   PER SHARE
                                               
   THIS CERTIFICATE IS TRANSFERABLE                           CUSIP 109178 10 3
IN NEW YORK, NEW YORK AND DALLAS, TEXAS                        SEE REVERSE FOR
                                                             CERTAIN DEFINITIONS

             INCORPORATED UNDER THE LAWS OF THE STATE OF DELAWARE
                   
This Certifies that


is the owner of

           FULLY PAID AND NON-ASSESSABLE SHARES OF THE COMMON STOCK,
                         PAR VALUE $.01 PER SHARE,  OF

                         BRIGHAM EXPLORATION COMPANY

(hereinafter referred to as the "Corporation"), transferable on the books of
the Corporation by the holder hereof in person or by duly authorized attorney
upon surrender of this Certificate properly endorsed. This Certificate and the
shares represented hereby are issued and shall be held subject to all of the
provisions of the Certificate of Incorporation, as amended from time to time,
of the Corporation (a copy of which Certificate is on file with the Transfer
Agent), to all of which the holder, by acceptance hereof, assents. This
Certificate is not valid until countersigned by the Transfer Agent and
registered by the Registrar.

         Witness the facsimile seal of the Corporation and the facsimile
signatures of its duly authorized officers.  


                                DATED:

                                COUNTERSIGNED AND REGISTERED: 
                                     AMERICAN STOCK TRANSFER & TRUST COMPANY
                                                    TRANSFER AGENT AND REGISTRAR

                                BY

                                                            AUTHORIZED SIGNATURE

                               [CORPORATE SEAL]


/s/ BEN M. BRIGHAM          /s/ ANNE L. BRIGHAM

PRESIDENT, CHIEF            SECRETARY      
EXECUTIVE OFFICER AND 
CHAIRMAN OF THE BOARD

<PAGE>   2
                         BRIGHAM EXPLORATION COMPANY

         The Corporation will furnish without charge to each stockholder who so
requests a statement of the powers, designations, preferences and relative,
participating, optional or other special rights of each class of stock or
series thereof which the Corporation is authorized to issue and the
qualifications, limitations or restrictions of such preferences and/or rights.
Any such request is to be addressed to the Secretary of the Corporation at its
principal place of business or to the Transfer Agent.

         The following abbreviations, when used in the inscription on the face
of this certificate, shall be construed as though they were written out in full
according to applicable laws or regulations:

         TEN COM -        as tenants in common
         TEN ENT -        as tenants by the entireties
         JT TEN  -        as joint tenants with right
                          of survivorship and not as
                          tenants in common

         UNIF GIFT MIN ACT  - ________  Custodian ________
                                (Cust)              (Minor)
                          Under Uniform Gifts to Minors
                          Act _______________________
                                    (State)

   Additional abbreviations may also be used though not in the above list.

                                  ASSIGNMENT

For Value Received,                             hereby sell, assign and 
                   ----------------------------- 
transfer unto

PLEASE INSERT SOCIAL SECURITY OR OTHER
   IDENTIFYING NUMBER OF ASSIGNEE

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

- -------------------------------------------------------------------------------
PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING POSTAL ZIP CODE, OF
ASSIGNEE

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

- -------------------------------------------------------------------------------
                                                                         Shares
- -------------------------------------------------------------------------       
of the Common Stock represented by the within Certificate, and do hereby
irrevocably constitute and appoint
                                                                       Attorney
- -----------------------------------------------------------------------         
to register the transfer of the said shares of Common Stock on the books of the
within-named Corporation, with full power of substitution in the premises.  


Dated 
     -----------------------------
                                     X
                                      -----------------------------------------
             NOTICE:                                (SIGNATURE)
THE SIGNATURE(S) TO THIS ASSIGNMENT
MUST CORRESPOND WITH THE NAME(S)     X
AS WRITTEN UPON THE FACE OF THE       -----------------------------------------
CERTIFICATE WITHOUT ALTERATION                      (SIGNATURE)
OR ANY CHANGE WHATEVER.

- -------------------------------------------------------------------------------
THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE GUARANTOR INSTITUTION
(BANKS, STOCKBROKERS, SAVINGS AND LOAN ASSOCIATIONS AND CREDIT UNIONS WITH
MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE PROGRAM), PURSUANT TO S.E.C. RULE
17Ad-15.
- -------------------------------------------------------------------------------
SIGNATURE(S) GUARANTEED BY:


<PAGE>   1
                                                                      EXHIBIT 5

(214) 969-1700

                                 April 21, 1997


Brigham Exploration Company
5949 Sherry Lane
Suite 1616
Dallas, Texas 75224

Ladies and Gentlemen:

       We have acted as counsel for Brigham Exploration Company, a Delaware
corporation (the "Company"), in connection with the preparation of the Company's
Registration Statement on Form S-1 (Registration No. 333-22491), as amended (the
"Registration Statement"), filed with the Securities and Exchange Commission
under the Securities Act of 1933, as amended, relating to the proposed offering
of 3,000,000 shares (the "Shares") of the Company's common stock, par value $.01
per share (the "Common Stock"), together with 450,000 additional shares (the
"Additional Shares") of Common Stock (including 95,238 shares being offered by
stockholders of the Company) subject to the underwriters' over-allotment option
as described in the Registration Statement.

       In connection with the foregoing, we have examined the originals or
copies, certified or otherwise authenticated to our satisfaction, of the
Registration Statement and such corporate records of the Company, certificates
of public officials and of officers of the Company, and other agreements,
instruments and documents as we have deemed necessary as a basis for the
opinions hereinafter expressed.  Where facts material to the opinions
hereinafter expressed were not independently established by us, we have relied
upon the statements of officers of the Company, where we deemed such reliance
appropriate under the circumstances.

       Based upon the foregoing and in reliance thereon, and subject to the
assumptions and qualifications hereinafter specified, it is our opinion that:

       1.     The Company is a corporation duly incorporated and validly
existing in good standing under the laws of the State of Delaware.

       2.     Upon (a) the taking of action by the duly authorized Pricing
Committee of the Board of Directors of the Company to determine the price at
which the Shares and Additional Shares are to be sold under the Underwriting
Agreement and (b) the sale of the Shares and the Additional Shares in
accordance with the terms of the Underwriting Agreement for the price so
determined, the Shares and any Additional Shares will be duly authorized by all
necessary corporate action on the part of the Company, validly issued, fully
paid and nonassessable.

       We hereby consent to the filing of this opinion as Exhibit 5 to the
Registration Statement and to the reference to us under the caption "Legal
Matters" in the prospectus forming a part of the Registration Statement.  In
giving this consent, we do not thereby admit that we are within the category of
persons whose consent is required under Section 7 of the Securities Act or the
rules or regulations of the Commission thereunder.


                                         Respectfully submitted,           
                                                                           
                                         THOMPSON & KNIGHT,                
                                         A Professional Corporation        
                                                                           
                                                                           
                                                                           
                                         By:   /s/  JOE DANNENMAIER         
                                            ------------------------------ 
                                            Joe Dannenmaier, Attorney      
                                         
                                         

<PAGE>   1
                                                                    EXHIBIT 10.7




                              EMPLOYMENT AGREEMENT

         THIS EMPLOYMENT AGREEMENT (this "AGREEMENT") is made between Brigham
Exploration Company, a Delaware corporation (the "COMPANY"), and Ben M. Brigham
("EMPLOYEE");

                              W I T N E S S E T H:

         WHEREAS, the Company has been recently created and organized to serve
as the holding company of Brigham Oil & Gas, L.P., a Delaware limited
partnership ("PARTNERSHIP") and Brigham, Inc., a Texas corporation ("GENERAL
PARTNER") in connection with a reorganization in which the Company will acquire
all of the limited partnership interests of the Partnership and all of the
outstanding shares of the capital stock of the General Partner;

         WHEREAS, Employee has been employed by the Partnership pursuant to an
Employment Agreement with the Partnership (the "PARTNERSHIP EMPLOYMENT
AGREEMENT");

         WHEREAS, the Company desires to employ Employee effective as of the
date on which the Company completes an initial public offering of shares of its
Common Stock (a "PUBLIC OFFERING"), and Employee desires to be employed by the
Company, subject to and upon the terms and conditions contained herein;

         NOW, THEREFORE, in consideration of the mutual promises contained
herein, the parties, intending to be legally bound, agree as follows:

         1.      Effective Date; Termination of Partnership Employment
Agreement.  This Agreement shall become effective as of the date on which the
Company successfully completes the Public Offering (the "EFFECTIVE DATE").  The
Partnership Employment Agreement shall terminate and be of no further force and
effect as of the Effective Date.

         2.      Employment and Duties.  Subject to the terms hereof, the
Company agrees to employ Employee to render full-time services to the Company
as President and Chief Executive Officer of the Company.  Employee shall have
such duties as are customarily associated with such position, together with
such other duties as may be assigned to Employee from time to time by the Board
of Directors of the Company.  Employee agrees to devote his full time and
attention to the performance and fulfillment of such duties, functions and
responsibilities as are necessary to discharge such duties, functions and
responsibilities, except for service for civic, charitable or non-profit
organizations and other non-competitive endeavors not interfering with his
duties hereunder.

         3.      Base Compensation.

         (a)     Salary.  The Company shall pay Employee for his services under
this Agreement a base annual salary of $275,000 (before Federal and state
withholdings).  Employee shall be eligible for additional increases in his
annual base salary, not less frequently than once each fiscal year of the
Company, in such amounts as shall be determined by the Board of Directors of
the Company.  The base salary shall be payable
<PAGE>   2
semi-monthly or in such other installments as shall be consistent with the
Company's general payroll practices.

         (b)     Bonus.  In addition to his annual base salary, Employee shall
be entitled to an annual cash bonus in an amount, not to exceed seventy-five
percent (75%) of Employee's then-current annual base salary, two-thirds of
which is to be determined by reference to the Company's satisfaction of certain
performance-based criteria established by the Board of Directors of the Company
by November 30 of the preceding year and one-third of which shall be determined
at the Board's discretion.

         4.      Fringe Benefits.  During the term hereof Employee shall be
entitled to participate in any benefit programs and incentive plans applicable
to all employees or to executive employees of the Company on the same basis as
such benefits and plans are customarily made available by the Company from time
to time, including without limitation all employee retirement, insurance,
vacation, sick leave, long-term disability and other benefit programs, and
grants of rights or options to acquire equity interests or other awards
provided for under the Company's incentive plans, as such benefits and plans
may be modified, amended or terminated from time to time.  In addition,
Employee shall receive a Petroleum Club membership at the expense of the
Company at all times during the term of this Agreement.

         5.      Business Expenses.  Employee shall be reimbursed by the
Company for expenses reasonably paid or incurred by him in connection with the
performance of his duties hereunder upon presentation of expense statements,
receipts or vouchers or such other supporting information reasonably evidencing
such expenses.

         6.      Term.  The term of Employee's employment by the Company
hereunder shall initially be for a period of five (5) years commencing on the
Effective Date of this Agreement.  Beginning on the second anniversary of the
Effective Date of this Agreement, and on each subsequent anniversary thereof
(each such anniversary being referred to as an "Extension Date"), the term of
this Agreement shall be extended for an additional one year period, unless
either party provides written notice to the other prior to an Extension Date
that the term of this Agreement shall not be extended.  It is the express
intent of both parties to this Agreement that the provisions of this Section 6
are intended to ensure that upon notice of an election not to extend the term
of this Agreement, the remaining term of this Agreement will at all times be
not less than three (3) years.

         7.      Termination.  Employee's employment with the Company shall
terminate upon the first to occur of the (i) expiration of the term of this
Agreement (as extended pursuant to Section 6 hereof), (ii) death of Employee,
(iii) disability of Employee, but only upon compliance with the provisions of
Section 9 hereof, (iv) termination of Employee for Cause (as defined below),
(v) termination by Employee pursuant to Section 11 hereof, or (vi) written
consent of all parties to this Agreement.


         8.      Death of Employee.  The employment of Employee hereunder shall
cease on the date of his death.  The Company will purchase life insurance on
the life of Employee in


                                      2
<PAGE>   3
an amount mutually agreeable to the Company and Employee, the benefits of which
will be payable to Employee's beneficiary (as defined below).  Employee's
"beneficiary" is the person or persons (who may be designated concurrently,
successively or contingently) designated by Employee in his last effective
writing filed with the Company prior to his death, or if Employee shall have
failed to make an effective designation, Employee's beneficiary is his spouse,
if living at the time of each payment, and otherwise his surviving children.
Employee shall assist the Company in procuring such insurance by submitting to
such examinations and by signing such applications and other instruments as may
be reasonable and as may be required by the insurance carriers to which
application is made for any such insurance.  Employee represents that, to the
best of his knowledge, he is currently insurable at standard premium rates for
life insurance policies.

         9.      Disability of Employee.  If, as a result of Employee's
incapacity due to physical or mental illness, Employee shall have been absent
from his duties hereunder on a full-time basis for the entire period of six
consecutive months, and within thirty (30) days after written notice of
termination is given (which may occur before or after the end of such six-month
period) shall not have returned to the performance of his duties hereunder on a
full-time basis, employment of Employee hereunder shall cease.

         The Company shall purchase disability insurance to cover such a
contingency with coverage and benefits mutually agreeable to the Company and
Employee.  Employee shall assist the Company in procuring such insurance by
submitting to such examinations and by signing such applications and other
instruments as may be reasonable and as may be required by the insurance
carriers to which application is made for any such insurance.  Employee
represents that, to the best of his knowledge, he is currently insurable at
standard premium rates for life insurance policies.  During any period prior to
termination during which Employee fails to perform his duties hereunder as a
result of incapacity due to physical or mental illness ("disability period"),
Employee shall continue to receive his full salary at the rate then in effect
for such period until his employment terminates pursuant to this Section 9.

         If employment of Employee hereunder terminates because of Employee's
incapacity, Employee (or, in the event of his legal incapacity, a
court-appointed guardian for his benefit) shall receive those benefits payable
under the disability policy or policies (purchased in compliance with the
foregoing provisions) in effect at such time.

         10.     Termination for Cause.  The Company may terminate Employee's
employment hereunder for Cause.  For purposes of this Agreement, the Company
shall have "Cause" to terminate Employee's employment hereunder upon (A) the
willful and continued failure by Employee to substantially perform his duties
hereunder (other than any such failure resulting from Employee's incapacity due
to physical or mental illness or infirmity), after demand for substantial
performance is delivered by the Company that specifically identifies the manner
in which the Company believes Employee has not substantially performed his
duties or (B) the willful engaging by Employee in misconduct which is
materially injurious to the Company, monetarily or otherwise.  For purposes of
this section, no act, or failure to act, on Employee's part shall be considered
"willful" unless done, or omitted to be done, by him not in good faith and
without reasonable belief that his action or omission was in or not opposed to
the best interest of the Company.  Notwithstanding the foregoing, Employee
shall not be





                                       3
<PAGE>   4
deemed to have been terminated for Cause without (i) reasonable notice to
Employee setting forth the reasons for the Company's intention to terminate for
Cause, (ii) an opportunity for Employee, together with his counsel, to be heard
before the Board of Directors of the Company, and (iii) delivery to Employee of
a Notice of Termination as defined in Section 12 hereof from the Board of
Directors, finding that in the good faith opinion of such Board of Directors
that Employee was guilty of conduct set forth above in clause (A) or (B) of the
preceding sentence, and specifying the particulars thereof in detail.

         11.     Termination by Employee.  Employee may terminate his
employment hereunder (i) for Good Reason, or (ii) for any other reason upon
providing at least 30 days advance written notice.

         For purposes of this Agreement, "Good Reason" shall mean (A) a failure
by the Company to comply with any material provision of this Agreement which
has not been cured within thirty (30) working days after notice of such
noncompliance has been given by Employee to the Company, (B) any purported
termination of Employee's employment which is not effected pursuant to a valid
Notice of Termination satisfying the requirements of Section 12 hereof (and for
purposes of this Agreement no such purported termination shall be effective),
or (C) a material reduction or diminution of Employee's position, titles,
offices, responsibilities or status with the Company without Cause and without
Employee's express written consent.

         An election by Employee to terminate for Good Reason shall not be
deemed a voluntary termination of employment by Employee for the purpose of
this Agreement or any plan or practice of the Company.

         12.     Notice of Termination.  Any termination of Employee's
employment by the Company or by Employee pursuant to Sections 9, 10 or 11 shall
be communicated by written Notice of Termination to the other party hereto.
For purposes of this Agreement, a "Notice of Termination" shall mean a notice
which shall indicate the specific termination provisions in this Agreement
relied upon and shall set forth in reasonable detail the facts and
circumstances claimed or provide a basis for termination of Employee's
employment under the provision so indicated.

         13.     Termination of Employment for Cause or Without Good Reason.
If Employee shall voluntarily terminate his employment other than for Good
Reason or if the Company shall terminate Employee's employment for Cause, then
upon such termination all rights, benefits and compensation of Employee under
this Agreement shall immediately terminate, except that equity options, if any,
shall continue to be governed in accordance with their terms.  The rights and
remedies of the Company as set forth in this Section 13, in case of termination
of employment by the Company for Cause, shall be cumulative with and shall be
in addition to (i) any and all other relief available to the Company for breach
by Employee of any other provision of this Agreement, and (ii) any and all
other general or equitable relief to which the Company may be entitled by
reason of such breach.

         14.     Other Termination of Employment.  If Employee shall terminate
his employment for Good Reason under Section 11 hereof or if the employment of
Employee





                                       4
<PAGE>   5
hereunder is terminated under any circumstances other than those set forth in
Sections 8, 9, 10 or 13 hereof, then (i) within 30 days following such
termination, the Company shall pay to Employee a sum equal to (A) the amount of
Employee's annual base salary (as in effect at the time of termination) that
Employee would have received during the remainder of Employee's employment term
hereunder, plus (B) an amount equal to the average annual bonus received by
Employee pursuant to Section 3(b) hereof during the immediately preceding two
(2) years, multiplied by the number of years (with portions of a year expressed
as a fraction) in the remainder of Employee's employment term hereunder, (ii)
Employee shall be entitled to continue to participate in all benefit programs
and incentive plans as provided in Section 4 of this Agreement during a period
equal to the remainder of Employee's employment term hereunder, and (iii) all
restricted stock, options or other rights with respect to equity interests in
the Company and/or its affiliates granted to Employee on or before such date of
termination shall immediately vest as of the date of such termination; provided
that, the Company shall also pay to Employee those amounts provided in Sections
8 and 9 pursuant to the terms thereof.

         15.     Confidentiality: Ownership of Patentable Inventions.

         (a)     Employee will maintain the confidentiality of, and will not
disclose without the Company's express consent, any and all proprietary or
confidential information of the Company.  The provisions of this section will
be deemed to encompass any and all confidential or proprietary information of
the Company that was obtained by Employee since the commencement of Employee's
employment with the Partnership.  This section will continue after, and will
not be deemed to be extinguished or terminated by, the termination of this
Agreement or of Employee's employment by the Company.  For purposes of this
section "proprietary or confidential information" of the Company does not
include (i) information that is or becomes generally available to the public
other than as a result of disclosure by Employee in breach of this Agreement,
(ii) information that was or is available to Employee on a non-confidential
basis, (iii) any non-patentable information that is or was conceived, created
or independently developed by Employee, or (iv) information that is disclosed
by Employee to others on behalf of the Company or to further the business
opportunities or best interests of the Company.

         (b)     Employee agrees that any patentable invention, design or
process made, invented or discovered by Employee in the course of his
employment hereunder shall be the property of the Company and Employee shall
execute and deliver all documents necessary and proper to make all such
patentable inventions, designs or processes the property of the Company.

         16.     Non-Competition.

         (a)     Employee agrees that during the term of this Agreement he will
not, directly or indirectly, for Employee's own account or for the benefit of
any other person or party engage or become, without the prior consent of the
Company, an owner, director, manager, officer, partner, operator, employee or
agent of, or render services to or invest in, any business or enterprise
competing with the primary business of the Company.





                                       5
<PAGE>   6
         (b)     In addition to the agreement in Section 16(a), for a period of
three years after the term of this Agreement Employee agrees not to compete
with the Company with respect to any prospect established with respect to
Company properties owned at the time of termination of this Agreement, or any
other specific matter or opportunity, which was specifically identified by the
Company to Employee in writing as of the date of such termination.

         Notwithstanding the foregoing, nothing in this Agreement shall
prohibit Employee from being a passive investor in (i) any Fortune 500
companies, or (ii) any other business or enterprise (A) not in direct
competition with the business of the Company and (B) not an entity which is a
party to an exploration agreement with the Company.  Provided, however, that
with respect to any investment in a business or enterprise engaged in the oil
and gas industry (other than any Fortune 500 companies), Employee shall obtain
the prior consent of the Board of Directors of the Company, which consent shall
not be unreasonably withheld.

         If Employee intentionally breaches any provisions of Section 15 or
this Section 16 (collectively the "Restrictive Covenants") in a material way,
the Company shall have the right to have the Restrictive Covenants specifically
enforced by any court having equity jurisdiction it being acknowledged and
agreed that any such breach will cause irreparable injury to the Company and
that money damages will not provide adequate remedy to the Company.  The
Company's right of specific performance hereunder shall be independent of, and
in addition to, any other rights and remedies available to the Company under
law or in equity.

         If any court determines that any of the Restrictive Covenants or any
part thereof is invalid or unenforceable, the remainder of the Restrictive
Covenants shall not thereby be affected and shall be given full effect, without
regard to the invalid portions.  If any court determines that any of the
Restrictive Covenants, or any part thereof, is unenforceable because of the
duration or geographic scope of such provision, such court shall have the power
to reduce the duration or geographical scope of such provision, as the case may
be and, in its reduced form, such provision shall then be enforceable and shall
be enforced.

         17.     Miscellaneous.  (a)  Notices.  Any notice or communication
required or permitted hereunder shall be given in writing and shall be (i) sent
by first class registered or certified United States mail, postage prepaid,
(ii) sent by overnight or express mail or expedited delivery service, (iii)
delivered by hand or (iv) transmitted by facsimile transmission, to the address
or fax number for the party as set forth opposite such party's name on the
signature page hereof, or to such other address or to the attention of such
other person as hereafter shall be designated in writing by the applicable
party in accordance herewith.  Any such notice or communication shall be deemed
to have been given as of the date of first attempted delivery at the address or
fax number and in the manner provided above.

         (b)     Successors and Assigns.  This Agreement is personal in nature
and neither of the parties hereto shall, without the consent of the other,
assign or transfer this Agreement or any rights or obligations hereunder;
provided, however, that in the event of a merger,





                                       6
<PAGE>   7
consolidation or transfer or sale of all or substantially all of the assets of
the Company, this Agreement shall be binding upon the successor to the
Company's business and assets.

         (c)     Interpretation.  When the context in which words are used in
this Agreement indicates that such is the intent, words in the singular number
shall include the plural and vice versa, and the words in masculine gender
shall include the feminine and neuter genders and vice versa.

         (d)     Severability.  Every provision in this Agreement is intended
to be severable.  In the event that any provision of this Agreement shall be
held to be invalid, the same shall not affect in any respect whatsoever the
validity of the remaining provisions of this Agreement.

         (e)     Captions.  Any section or paragraph titles or captions
contained in this Agreement are for convenience only and shall not be deemed a
part of the context of this Agreement.

         (f)     Entire Agreement.  This Agreement together with the
Partnership Agreement contains the entire understanding and agreement between
the parties and supersedes any prior written or oral agreements between them
respecting the subject matter contained herein.  There are no representations,
agreements, arrangements or understandings, oral or written, between and among
the parties hereto relating to the subject matter of this Agreement which are
not fully expressed herein or therein.

         (g)     No Waiver.  The failure of any party to insist upon strict
performance of a covenant hereunder or of any obligation hereunder,
irrespective of the length of time for which such failure continues, shall not
be a waiver of such party's right to demand strict compliance in the future.
No consent or waiver, express or implied, to or of any breach or default in the
performance of any obligation hereunder shall constitute a consent or waiver to
or of any other breach or default in the performance of the same or any
obligation hereunder.

         (h)     Amendment.  This Agreement may be changed, modified or amended
only by an instrument in writing duly executed by all of the parties hereto.
Any such amendment shall be effective as of such date as may be determined by
the parties hereto.

         (i)     Enforcement.  The Company may enforce this Agreement pursuant
to the provisions of the Agreement of Limited Partnership of the Partnership,
provided that in the event of a dispute, either General Partner of the Company
shall have the right to enforce the provisions hereof.

         (j)     Choice of Law.  THIS AGREEMENT AND THE RIGHTS AND OBLIGATIONS
OF THE PARTIES HEREUNDER SHALL BE GOVERNED BY TEXAS LAW.





                                       7
<PAGE>   8
         IN WITNESS WHEREOF, the parties have executed this Agreement or caused
the same to be executed by their duly authorized corporate officers, all as of
the day and year first above written.


"Employee"
   
                                        /s/ BEN M. BRIGHAM
                                        ------------------------------
                                        Ben M. Brigham
    





"Company"                               Brigham Exploration Company


   
                                        By: /s/ CRAIG M. FLEMING
                                           ---------------------------
                                        Name: Craig M. Fleming
                                             -------------------------
                                        Title: Vice President - 
                                               Finance and Treasurer
    




                                       8

<PAGE>   1
                                                                    EXHIBIT 10.8


                            BRIGHAM OIL & GAS, L.P.
                          PHANTOM ROYALTY ACCOUNT PLAN
                            PARTICIPATION AGREEMENT


         THIS AGREEMENT, made by and between BRIGHAM OIL & GAS, L.P., a
Delaware limited partnership (the "Company") and [see Schedule I attached]
("Employee"),

                                WITNESSETH THAT:

         WHEREAS, the Company has established the Brigham Oil & Gas, L.P.
Phantom Royalty Account Plan (the "Plan") to provide a performance incentive
for the employees of the Company who are designated by the President of the
Company as eligible to become Participants under the Plan and who elect to
become such Participants; and

         WHEREAS, the President of the Company desires to designate Employee as
an employee of the Company eligible to become a Participant under the Plan with
respect to the Phantom Royalty Account to be established thereunder for the
Plan Year indicated in paragraph 2 below, and Employee desires to become such a
Participant;

         NOW, THEREFORE, in consideration of the premises and the mutual
covenants herein contained, the parties hereto do hereby agree as follows:

         1.      Definitions.  Unless the context clearly indicates otherwise,
the words and phrases used in this Agreement shall have the meanings assigned
to them under the provisions of the Plan.

         2.      Participant and Account Percentage Designations.  The
President hereby designates Employee to be a Participant in the Phantom Royalty
Account to be established under the Plan for the 1996 Plan Year, and further
designates that Employee shall have an Account Percentage of ____________
percent (_____%) in such Phantom Royalty Account.

         3.      Terms of Participation.  Employee hereby (i) acknowledges that
Employee has reviewed a copy of the Plan, (ii) voluntarily elects to become a
Participant in the Plan, and (iii) agrees to be bound by the terms and
provisions of the Plan and this Agreement.  Employee further acknowledges that
Employee understands that:

                 (a)      upon the termination of Employee's employment with
         the Company for any reason, Employee's Account Percentage in each
         Phantom Royalty Account established under the Plan will terminate and
         Employee will cease participating in the Plan;





<PAGE>   2
                 (b)      the Company has the right and power in its absolute
         discretion to sell, exchange or otherwise dispose of all or any
         portion of its interest in any Company Well;

                 (c)      the President of the Company has the right and power
         at any time and from time to time to amend the Plan, in whole or in
         part, and at any time to terminate the Plan; and

                 (d)      the establishment of the Plan and the execution of
         this Agreement do not enlarge or otherwise affect the terms of
         Employee's employment with the Company, and the Company may terminate
         the employment of Employee at will and as freely and with the same
         effect as if the Plan had not been established and this Agreement had
         not been executed.

         4.      Confidentiality.  Employee hereby acknowledges that the
Company's trade secrets and other confidential or proprietary information, as
they may exist from time to time, are valuable, special and unique assets of
the Company's business, access to and knowledge of which are essential to the
performance of Employee's duties as an employee of the Company.  Employee
agrees that Employee will hold in strict confidence and will not directly or
indirectly disclose or reveal to any person, or use for Employee's own personal
benefit or for the benefit of anyone else, any trade secrets or other
confidential or proprietary information of any kind (including but not limited
to compensation data, partner lists, financial information, pending projects
and proposals information, proprietary processes, research and development
strategy information, scientific data, technological data and technological
prototypes, regardless of whether acquired, learned, obtained or developed by
Employee alone or in conjunction with others) belonging to or concerning the
Company or any of its affiliates, participants, partners, customers or clients,
except (i) with the prior written consent of the President of the Company, (ii)
in the course of the proper performance of Employee's duties as an employee of
the Company, or (iii) as required by applicable law or legal process.  The
provisions of this paragraph 4 shall continue in effect notwithstanding the
termination of Employee's employment with the Company for any reason.

         5.      Noncompetition.  During the period of Employee's employment
with the Company and for a period of one year thereafter, Employee agrees that
Employee will not directly or indirectly engage or participate in, on
Employee's own behalf or for anyone else, whether as a director, officer,
shareholder, member, partner, employee, consultant, agent, representative,
proprietor, associate, investor or otherwise, any business or activity which is
competitive with the business of the Company or any of its affiliates in any
geographical area in the continental United States, or in the offshore area
within the portion of the





                                      -2-
<PAGE>   3
Gulf of Mexico over which the United States or any State thereof asserts
jurisdiction, which is within one-half (1/2) mile of lands (i) in which the
Company has a mineral property interest (including but not limited to a mineral
lease, overriding royalty interest, production payment, net profits interest,
or mineral fee interest) or right, license or authority to conduct or direct
exploratory activities (including but not limited to seismic, geophysical and
geochemical activities) as of the date of Employee's termination of employment
with the Company, or (ii) which are part of an area of mutual interest
designated by the Company as of the date of Employee's termination of
employment with the Company.  The foregoing restrictions shall not apply,
however, to Employee's ownership of or dealings with respect to any securities
of any corporation or other entity whose equity securities are actively traded
on any recognized stock exchange or in the over-the-counter market so long as
Employee's holdings in such corporation or other entity do not exceed five
percent (5%) of the outstanding equity securities of any class in such
corporation or other entity.  The provisions of this paragraph 5 shall continue
in effect notwithstanding the termination of Employee's employment with the
Company for any reason.

         6.      This Agreement shall be binding upon and inure to the benefit
of Employee and his beneficiaries, devisees, heirs and legal representatives,
and the Company and its successors and assigns.

         IN WITNESS WHEREOF, this Agreement has been executed this _____ day of
_________________________, 19___.

                                         BRIGHAM OIL & GAS, L.P.



                                         By                                    
                                           ------------------------------------
                                           President


                                                                               
                                         --------------------------------------
                                         [See Schedule I attached]





                                      -3-
<PAGE>   4
                                   Schedule I

Jon L. Glass

Craig M. Fleming

David T. Brigham

A. Lance Langford



                                      -4-

<PAGE>   1
                                                                   EXHIBIT 10.9




                              1997 INCENTIVE PLAN

                                       OF

                          BRIGHAM EXPLORATION COMPANY


                 1.       Plan.  This 1997 Incentive Plan of Brigham
Exploration Company (the "Plan") was adopted by the Board of Directors of
Brigham Exploration Company (the "Company") to reward certain key employees of
the Company and its consolidated subsidiaries by enabling them to acquire
shares of Common Stock, par value $.01 per share, of the Company and/or to be
compensated for individual performances.

                 2.       Objectives.  The Plan is designed to attract and
retain key employees of the Company and its Subsidiaries (as hereinafter
defined), to encourage the sense of proprietorship of such employees and to
stimulate the active interest of such persons in the development and financial
success of the Company and its Subsidiaries.  These objectives are to be
accomplished by making Awards (as hereinafter defined) under this Plan and
thereby providing Participants (as hereinafter defined) with a proprietary
interest in the growth and performance of the Company and its Subsidiaries.

                 3.       Definitions.  As used herein, the terms set forth
below shall have the following respective meanings:

                 "Authorized Officer" means the Chairman of the Board or the
Chief Executive Officer of the Company (or any other senior officer of the
Company to whom either of them shall delegate the authority to execute any
Award Agreement).

                 "Award" means the grant of any Option, SAR, Stock Award, Cash
Award or Performance Award, whether granted singly, in combination or in
tandem, to a Participant pursuant to such applicable terms, conditions and
limitations as the Committee may establish in order to fulfill the objectives
of the Plan.

                 "Award Agreement" means a written agreement between the
Company and a Participant setting forth the terms, conditions and limitations
applicable to an Award.

                 "Board" means the Board of Directors of the Company.

                 "Cash Award" means an award denominated in cash.

                 "Code" means the Internal Revenue Code of 1986, as amended
from time to time.

                 "Committee" means such committee of the Board as is designated
by the Board to administer the Plan.

                 "Common Stock" means the Common Stock, par value $.01 per
share, of the Company.
<PAGE>   2
                 "Company" means Brigham Exploration Company, a Delaware
corporation.

                 "Dividend Equivalents" means, with respect to shares of
Restricted Stock that are to be issued at the end of the Restriction Period, an
amount equal to all dividends and other distributions (or the economic
equivalent thereof) that are payable to stockholders of record during the
Restriction Period on a like number of shares of Common Stock.

                 "Effective Date" has the meaning set forth in paragraph 18
hereof.

                 "Employee" means an employee of the Company or any of its
Subsidiaries.

                 "Fair Market Value" of a share of Common Stock means, as of a
particular date, (i) if shares of Common Stock are listed on a national
securities exchange, the mean between the highest and lowest sales price per
share of Common Stock on the consolidated transaction reporting system for the
principal national securities exchange on which shares of Common Stock are
listed on that date, or, if there shall have been no such sale so reported on
that date, on the last preceding date on which such a sale was so reported,
(ii) if shares of Common Stock are not so listed but are quoted on the Nasdaq
National Market, the mean between the highest and lowest sales price per share
of Common Stock reported by the Nasdaq National Market on that date, or, if
there shall have been no such sale so reported on that date, on the last
preceding date on which such a sale was so reported, (iii) if the Common Stock
is not so listed or quoted, the mean between the closing bid and asked price on
that date, or, if there are no quotations available for such date, on the last
preceding date on which such quotations shall be available, as reported by the
Nasdaq National Market, or, if not reported by the Nasdaq National Market, by
the National Quotation Bureau Incorporated or (iv) if shares of Common Stock
are not publicly traded, the most recent value determined in good faith by the
Committee for such purpose.

                 "Incentive Option" means an Option that is intended to comply
with the requirements set forth in Section 422 of the Code.

                 "Nonqualified Stock Option" means an Option that is not an
Incentive Option.

                 "Option" means a right to purchase a specified number of
shares of Common Stock at a specified price.

                 "Participant" means an Employee to whom an Award has been made
under this Plan.

                 "Performance Award" means an award made pursuant to this Plan
to a Participant that is subject to the attainment of one or more Performance
Goals.

                 "Performance Goal" means a standard established by the
Committee to determine in whole or in part whether a Performance Award shall be
earned.





                                      -2-
<PAGE>   3
                 "Restricted Stock" means any Common Stock that is restricted
or subject to forfeiture provisions.

                 "Restriction Period" means a period of time beginning as of
the date upon which an Award of Restricted Stock is made pursuant to this Plan
and ending as of the date upon which the Common Stock subject to such Award is
no longer restricted or subject to forfeiture provisions.

                 "SAR" means a right to receive a payment, in cash or Common
Stock, equal to the excess of the Fair Market Value or other specified
valuation of a specified number of shares of Common Stock on the date the right
is exercised over a specified strike price, in each case, as determined by the
Committee.

                 "Stock Award" means an award in the form of shares of Common
Stock or units denominated in shares of Common Stock.

                 "Subsidiary" means (i) in the case of a corporation, any
corporation in which the Company directly or indirectly owns shares
representing more than 50% of the combined voting power of the shares of all
classes or series of capital stock of such corporation which have the right to
vote generally on matters submitted to a vote of the stockholders of such
corporation and (ii) in the case of a partnership or other business entity not
organized as a corporation, any such business entity of which the Company
directly or indirectly owns more than 50% of the voting, capital or profits
interests (whether in the form of partnership interests, membership interests
or otherwise).

                 4.       Eligibility.  Key Employees eligible for Awards under
this Plan are those who hold positions of responsibility and whose performance,
in the judgment of the Committee, can have a significant effect on the success
of the Company and its Subsidiaries.

                 5.       Common Stock Available for Awards.  Subject to the
provisions of paragraph 14 hereof, there shall be available for Awards under
this Plan granted wholly or partly in Common Stock (including rights or options
that may be exercised for or settled in Common Stock) an aggregate of 1,588,169
shares of Common Stock.  The number of shares of Common Stock that are the
subject of Awards under this Plan, that are forfeited or terminated, expire
unexercised, are settled in cash in lieu of Common Stock or in a manner such
that all or some of the shares covered by an Award are not issued to a
Participant or are exchanged for Awards that do not involve Common Stock, shall
again immediately become available for Awards hereunder.  The Committee may
from time to time adopt and observe such procedures concerning the counting of
shares against the Plan maximum as it may deem appropriate.  The Board and the
appropriate officers of the Company shall from time to time take whatever
actions are necessary to file any required documents with governmental
authorities, stock exchanges and transaction reporting systems to ensure that
shares of Common Stock are available for issuance pursuant to Awards.





                                      -3-
<PAGE>   4
                 6.       Administration.

                 (a)      This Plan shall be administered by the Committee.

                 (b)      Subject to the provisions hereof, the Committee shall
         have full and exclusive power and authority to administer this Plan
         and to take all actions that are specifically contemplated hereby or
         are necessary or appropriate in connection with the administration
         hereof.  The Committee shall also have full and exclusive power to
         interpret this Plan and to adopt such rules, regulations and
         guidelines for carrying out this Plan as it may deem necessary or
         proper, all of which powers shall be exercised in the best interests
         of the Company and in keeping with the objectives of this Plan.  The
         Committee may, in its discretion, provide for the extension of the
         exercisability of an Award, accelerate the vesting or exercisability
         of an Award, eliminate or make less restrictive any restrictions
         contained in an Award, waive any restrictions or other provision of
         this Plan or an Award or otherwise amend or modify an Award in any
         manner that is either (i) not adverse to the Participant to whom such
         Award was granted or (ii) consented to by such Participant. The
         Committee may correct any defect or supply any omission or reconcile
         any inconsistency in this Plan or in any Award in the manner and to
         the extent the Committee deems necessary or desirable to further the
         Plan purposes.  Any decision of the Committee in the interpretation
         and administration of this Plan shall lie within its sole and absolute
         discretion and shall be final, conclusive and binding on all parties
         concerned.

                 (c)      No member of the Committee or officer of the Company
         shall be liable for anything done by him or her, by any member of the
         Committee or by any officer of the Company in connection with the
         performance of any duties under this Plan, except for his or her own
         willful misconduct or as expressly provided by statute.

                 7.       Delegation of Authority.  The Committee may delegate
to the Chief Executive Officer and to other senior officers of the Company its
duties under this Plan pursuant to such conditions or limitations as the
Committee may establish.

                 8.       Awards.  The Committee shall determine the type or
types of Awards to be made under this Plan and shall designate from time to
time the Employees who are to be the recipients of such Awards.  The Committee
shall review and consider the recommendations of the President of the Company
as to such Awards.  Awards shall become effective only upon and after approval
by the Committee.  Each Award may be embodied in an Award Agreement, which
shall contain such terms, conditions and limitations as shall be determined by
the Committee in its sole discretion and shall be signed by the Participant to
whom the Award is made and by an Authorized Officer for and on behalf of the
Company.  Awards may consist of those listed in this paragraph 8 hereof and may
be granted singly, in combination or in tandem.  Awards may also be made in
combination or in tandem with, in replacement of, or as alternatives to, grants
or rights under this Plan or any other employee plan of the Company or any of
its Subsidiaries, including the plan of any acquired entity.  Any provision of
this Plan to the contrary notwithstanding, the maximum number of shares of
Common Stock for which Options and SARs may be granted under the Plan to any
one Employee during a calendar year





                                      -4-
<PAGE>   5
is 500,000.  An Award may provide for the grant or issuance of additional,
replacement or alternative Awards upon the occurrence of specified events,
including the exercise of the original Award granted to a Participant.  All or
part of an Award may be subject to conditions established by the Committee,
which may include, but are not limited to, continuous service with the Company
and its Subsidiaries, achievement of specific business objectives, increases in
specified indices, attainment of specified growth rates and other comparable
measurements of performance.  Upon the termination of employment by a
Participant, any unexercised, deferred, unvested or unpaid Awards shall be
treated as set forth in the applicable Award Agreement.

                 (a)      Stock Option.  An Award may be in the form of an
         Option.  An Option awarded pursuant to this Plan may consist of an
         Incentive Option or a Nonqualified Option.  The price at which shares
         of Common Stock may be purchased upon the exercise of any Incentive
         Option shall be not less than the Fair Market Value of the Common
         Stock on the date of grant, except that with respect to Incentive
         Options granted to any Participant who at the time of such grant owns
         stock possessing more than 10 percent of the total combined voting
         power of all classes of stock of the Company, the exercise price shall
         be not less than 110 percent of the Fair Market Value of the Common
         Stock on the date of grant and such Incentive Option must not be
         exercisable after the expiration of five years from the date such
         option is granted.  The price at which shares of Common Stock may be
         purchased upon the exercise of a Nonqualified Option shall be such
         amount as shall be determined by the Committee, but not less than the
         par value of the Common Stock on the date of grant.  The maximum
         number of shares of Common Stock with respect to which any Option may
         be granted to an Employee hereunder is the number of shares available
         for Awards, pursuant to paragraph 5 hereof, at the time such Option is
         granted.  Subject to the foregoing provisions, the terms, conditions
         and limitations applicable to any Options awarded pursuant to this
         Plan, including the term of any Options and the date or dates upon
         which they become exercisable, shall be determined by the Committee.

                 (b)      Stock Appreciation Right.  An Award may be in the
         form of an SAR.  The terms, conditions and limitations applicable to
         any SARs awarded pursuant to this Plan, including the term of any SARs
         and the date or dates upon which they become exercisable, shall be
         determined by the Committee.

                 (c)      Stock Award.  An Award may be in the form of a Stock
         Award.  The terms, conditions and limitations applicable to any Stock
         Awards granted pursuant to this Plan shall be determined by the
         Committee.

                 (d)      Cash Award.  An Award may be in the form of a Cash
         Award.  The terms, conditions and limitations applicable to any Cash
         Awards granted pursuant to this Plan shall be determined by the
         Committee.

                 (e)      Performance Award.  Without limiting the type or
         number of Awards that may be made under the other provisions of this
         Plan, an Award may be in the form of a Performance Award.  A
         Performance Award shall be paid, vested or otherwise





                                      -5-
<PAGE>   6
         deliverable solely on account of the attainment of one or more
         pre-established, objective Performance Goals established by the
         Committee.


                 9.       Payment of Awards.

                 (a)      General.  Payment of Awards may be made in the form
         of cash or Common Stock, or a combination thereof, and may include
         such restrictions as the Committee shall determine, including, in the
         case of Common Stock, restrictions on transfer and forfeiture
         provisions.  If payment of an Award is made in the form of Restricted
         Stock, the Award Agreement relating to such shares shall specify
         whether they are to be issued at the beginning or end of the
         Restriction Period.  In the event that shares of Restricted Stock are
         to be issued at the beginning of the Restriction Period, the
         certificates evidencing such shares (to the extent that such shares
         are so evidenced) shall contain appropriate legends and restrictions
         that describe the terms and conditions of the restrictions applicable
         thereto.  In the event that shares of Restricted Stock are to be
         issued at the end of the Restriction Period, the right to receive such
         shares shall be evidenced by book entry registration or in such other
         manner as the Committee may determine.

                 (b)      Dividends and Interest.  Rights to dividends or
         Dividend Equivalents may be extended to and made part of any Award
         consisting of shares of Common Stock or units denominated in shares of
         Common Stock, subject to such terms, conditions and restrictions as
         the Committee may establish.  The Committee may also establish rules
         and procedures for the crediting of interest on deferred cash payments
         and Dividend Equivalents for Awards consisting of shares of Common
         Stock or units denominated in shares of Common Stock.

                 (c)      Substitution of Awards.  At the discretion of the
         Committee, a Participant may be offered an election to substitute an
         Award for another Award or Awards of the same or different type.

                 10.      Stock Option Exercise.  The price at which shares of
Common Stock may be purchased under an Option shall be paid in full at the time
of exercise in cash or, if elected by the optionee and to the extent permitted
by the optionee's Award Agreement, the optionee may purchase such shares by
means of tendering Common Stock or surrendering another Award, including
Restricted Stock, valued at Fair Market Value on the date of exercise, or any
combination thereof.  The Committee shall determine acceptable methods for
Participants to tender Common Stock or other Awards.  The Committee may provide
for procedures to permit the exercise or purchase of such Awards by use of the
proceeds to be received from the sale of Common Stock issuable pursuant to an
Award.  Unless otherwise provided in the applicable Award Agreement, in the
event shares of Restricted Stock are tendered as consideration for the exercise
of an Option, a number of the shares issued upon the exercise of the Option,
equal to the number of shares of Restricted Stock used as consideration
therefor, shall be subject to the same restrictions as the Restricted Stock so
submitted as well as any additional restrictions that may be imposed by the
Committee.  In addition, the Committee, at its sole discretion, may





                                      -6-
<PAGE>   7
provide for loans, on either a short-term or demand basis, from the Company to
a Participant to permit the payment of the exercise price of an Option.


                 11.      Tax Withholding.  The Company shall have the right to
deduct applicable taxes from any Award payment and withhold, at the time of
delivery or vesting of cash or shares of Common Stock under this Plan, an
appropriate amount of cash or number of shares of Common Stock or a combination
thereof for payment of taxes required by law or to take such other action as
may be necessary in the opinion of the Company to satisfy all obligations for
withholding of such taxes, including, withholding from other amounts payable to
or with respect to the Participant by the Company.  The Committee may also
permit withholding to be satisfied by the transfer to the Company of shares of
Common Stock theretofore owned by the holder of the Award with respect to which
withholding is required.  If shares of Common Stock are used to satisfy tax
withholding, such shares shall be valued based on the Fair Market Value when
the tax withholding is required to be made.  The Committee may provide for
loans, on either a short-term or demand basis, from the Company to a
Participant to permit the payment of taxes required by law.

                 12.      Amendment, Modification, Suspension or Termination.
The Board may amend, modify, suspend or terminate this Plan for the purpose of
meeting or addressing any changes in legal requirements or for any other
purpose permitted by law, except that no amendment or alteration that would
adversely affect the rights of any Participant under any Award previously
granted to such Participant shall be made without the consent of such
Participant.

                 13.      Assignability.  The Committee may prescribe and
include in applicable Award Agreements restrictions on transfer.  Any attempted
assignment of an Award or any other benefit under this Plan in violation of the
terms in an Award Agreement pursuant to this paragraph 13 shall be null and
void.

                 14.      Adjustments.

                 (a)      The existence of outstanding Awards shall not affect
         in any manner the right or power of the Company or its stockholders to
         make or authorize any or all adjustments, recapitalizations,
         reorganizations or other changes in the capital stock of the Company
         or its business or any merger or consolidation of the Company, or any
         issue of bonds, debentures, preferred or prior preference stock
         (whether or not such issue is prior to, on a parity with or junior to
         the Common Stock) or the dissolution or liquidation of the Company, or
         any sale or transfer of all or any part of its assets or business, or
         any other corporate act or proceeding of any kind, whether or not of a
         character similar to that of the acts or proceedings enumerated above.

                 (b)      In the event of any subdivision or consolidation of
         outstanding shares of Common Stock, declaration of a dividend payable
         in shares of Common Stock or other stock split, then (i) the number of
         shares of Common Stock reserved under this Plan, (ii) the number of
         shares of Common Stock covered by outstanding Awards in the form of





                                      -7-
<PAGE>   8
         Common Stock or units denominated in Common Stock, (iii) the exercise
         or other price in respect of such Awards and (iv) the appropriate Fair
         Market Value and other price determinations for such Awards shall each
         be proportionately and equitably adjusted by the Board to reflect such
         transaction.  In the event of any other recapitalization or capital
         reorganization of the Company, any consolidation or merger of the
         Company with another corporation or entity, the adoption by the
         Company of any plan of exchange affecting the Common Stock or any
         distribution to holders of Common Stock of securities or property
         (other than normal cash dividends or dividends payable in Common
         Stock), the Board shall make appropriate and equatable adjustments to
         (i) the number of shares of Common Stock covered by Awards in the form
         of Common Stock or units denominated in Common Stock, (ii) the
         exercise or other price in respect of such Awards and (iii) the
         appropriate Fair Market Value and other price determinations for such
         Awards, to give effect to such transaction; provided that such
         adjustments shall only be such as are necessary to maintain the
         proportionate interest of the holders of the Awards and preserve,
         without exceeding, the value of such Awards.  In the event of a
         corporate merger, consolidation, acquisition of property or stock,
         separation, reorganization or liquidation, the Board shall be
         authorized to issue or assume Awards by means of substitution of new
         Awards, as appropriate, for previously issued Awards or to assume
         previously issued Awards as part of such adjustment.

                 15.      Restrictions.  No Common Stock or other form of
payment shall be issued with respect to any Award unless the Company shall be
satisfied based on the advice of its counsel that such issuance will be in
compliance with applicable federal and state securities laws.  Certificates
evidencing shares of Common Stock delivered under this Plan (to the extent that
such shares are so evidenced) may be subject to such stop transfer orders and
other restrictions as the Committee may deem advisable under the rules,
regulations and other requirements of the Securities and Exchange Commission,
any securities exchange or transaction reporting system upon which the Common
Stock is then listed or to which it is admitted for quotation and any
applicable federal or state securities law.  The Committee may cause a legend
or legends to be placed upon such certificates (if any) to make appropriate
reference to such restrictions.

                 16.      Unfunded Plan.  Insofar as it provides for Awards of
cash, Common Stock or rights thereto, this Plan shall be unfunded.  Although
bookkeeping accounts may be established with respect to Participants who are
entitled to cash, Common Stock or rights thereto under this Plan, any such
accounts shall be used merely as a bookkeeping convenience.  The Company shall
not be required to segregate any assets that may at any time be represented by
cash, Common Stock or rights thereto, nor shall this Plan be construed as
providing for such segregation, nor shall the Company, the Board, the Committee
or any officer or other employee of the Company be deemed to be a trustee of
any cash, Common Stock or rights thereto to be granted under this Plan.  Any
liability or obligation of the Company to any Participant with respect to an
Award of cash, Common Stock or rights thereto under this Plan shall be based
solely upon any contractual obligations that may be created by this Plan and
any Award Agreement, and no such liability or obligation of the Company shall
be deemed to be secured by any pledge or other encumbrance on any property of
the Company.  None of the Company,  the Board, the Committee or any other
officer or other employee of the Company shall be





                                      -8-
<PAGE>   9
required to give any security or bond for the performance of any obligation
that may be created by this Plan.

                 17.      Governing Law.  This Plan and all determinations made
and actions taken pursuant hereto, to the extent not otherwise governed by
mandatory provisions of the Code or the securities laws of the United States,
shall be governed by and construed in accordance with the laws of the State of
Delaware.


                 18.      Effectiveness.  This Plan shall be effective as of
February 26, 1997, (the "Effective Date"), the date on which it was approved by
the Board of Directors of the Company.  Notwithstanding the foregoing, the
ability of the Company to issue any Incentive Options under this Plan is
expressly conditioned upon the approval of the Plan by the holders of a
majority of shares of Common Stock before the first anniversary of the
Effective Date.  If the Stockholders of the Company should fail to so approve
this Plan prior to such date, the Company's ability to issue Incentive Options
under this Plan shall terminate and cease to be of any further force or effect
and any and all grants of Incentive Options hereunder shall be null and void.






                                      -9-

<PAGE>   1





                                                                  EXHIBIT 10.9.1
                                OPTION AGREEMENT

   
    

               1997 Incentive Plan of Brigham Exploration Company
                          (Non-Qualified Stock Option)

         This Option Agreement ("Agreement"), made and entered into as of March
4, 1997, is by and between Brigham Exploration Company, a Delaware corporation
(the "Company"), and [See Schedule I attached hereto] (the "Optionee").

                                  WITNESSETH:

         WHEREAS, the 1997 Incentive Plan of Brigham Exploration Company
("Plan") was adopted by the Company, effective as of February 27, 1997 ("Plan
Date"), for certain employees of the Company and its Subsidiaries;

         WHEREAS, the Optionee is eligible to participate in the Plan and the
Committee has approved the grant to Optionee of an option to purchase shares of
Common Stock, par value $.01 per share, of the Company ("Shares") pursuant to
the Plan and upon the terms set forth herein;

         NOW, THEREFORE, in consideration of the premises and of the mutual
covenants and agreements hereinafter set forth, the Company and Optionee hereby
agree as follows:

         1.      Certain Definitions.  Terms used in this Agreement and not
otherwise defined shall have the respective meanings assigned to such terms in
the Plan; and the following terms shall have the following meanings:

                 "Companies" means the Company and any of its Subsidiaries.

                 "Expiration Date" means 6:00 P.M., Austin, Texas time, on
March 4, 2004.

         2.      Grant of Option.  Subject to the terms, conditions and
provisions of the Plan and those hereinafter set forth, the Company hereby
irrevocably grants to the Optionee a Nonqualified Stock Option (the "Option")
to purchase [See Schedule I attached hereto] Shares, subject to adjustment in
accordance with the provisions of Section 7 of this Agreement.

         3.      Option Price.  The price to be paid by Optionee to the Company
for each Share purchased pursuant to the exercise of this Option ("Option
Price") shall be $5.00 per share; provided, however, that the Option Price
shall be subject to adjustment in accordance with the provisions of Section 7
of this Agreement.

         4.      Vesting of Right to Exercise Option.

         (a)     Except as otherwise provided in this Agreement, the right to
exercise this Option shall vest as to 30% of the total Shares which may be
purchased hereunder (rounded to the nearest whole share) on March 4, 1998,
shall vest with respect to an additional 20% of the total
<PAGE>   2
Shares which may be purchased hereunder (rounded to the nearest whole share) on
March 4, 1999, shall vest with respect to an additional 16.66% of the total
Shares which may be purchased hereunder (rounded to the nearest whole share) on
March 4, 2000, shall vest with respect to an additional 16.67% of the total
Shares which may be purchased hereunder (rounded to the nearest whole share) on
March 4, 2001, and shall be fully vested on March 4, 2002.  From and after each
date of vesting, Optionee may exercise this Option, subject to the terms and
conditions set forth herein, to purchase all or any portion of the Shares for
which Optionee's rights have vested.

         (b)     To the extent Optionee does not purchase all or any part of
the Shares at the times this Option becomes exercisable, the Optionee has the
right cumulatively thereafter to purchase any Shares not so purchased and such
right shall continue until this Option terminates or expires.

         (c)     If Optionee's employment by the Companies is terminated on
account of fraud or dishonesty or other acts which the Board has determined are
materially detrimental to the interests of the Company, the Option shall
automatically terminate as of the date of such termination and this Option,
including any portion which has vested, shall be forfeited.

         (d)     If Optionee's employment by the Companies terminates
voluntarily by Optionee or by action of the Companies for reasons other than as
specified in subsection (c), this Option may be exercised, but only (i) within
90 days after such termination (if otherwise prior to the date of expiration of
this Option), and not thereafter, and (ii) to purchase the number of Shares, if
any, that could be purchased upon exercise of this Option at the date of
termination of Optionee's employment.

         (e)     In the event of Optionee's death or disability, this Option
shall remain outstanding and may be exercised by the person who acquires this
Option by will or the laws of descent and distribution, or by Optionee, as the
case may be, but only (i) within the one-year period following the date of
death or disability (if otherwise prior to the date of expiration of this
Option), and not thereafter, and (ii) to purchase the number of Shares that
could be purchased upon exercise of this Option at the time of such death or
disability.

         (f)     For purposes of subsection (d) and (e), if this Option shall
not have fully vested as of the date of termination of Optionee's employment by
the Company (but not in the case of a voluntary termination by Optionee) or as
of the date of the Optionee's death or disability, then a ratable portion of
the number of Shares which would have become purchasable upon the next vesting
date shall be deemed to have vested as of the date of such termination (or
death or disability), determined by multiplying the number of Shares that vest
on the next vesting date by a fraction with a numerator equal to the number of
full months which have then elapsed since the last vesting date and a
denominator of 12, and rounding to the closest whole number.




                                      -2-
<PAGE>   3
         5.      Restrictions on Exercise.  The right to exercise the Option
shall be subject to the following restrictions:

         (a)     Vesting.  Optionee shall have no right to exercise this Option
to purchase any Shares for which Optionee's rights have not yet vested in
accordance with Section 4.

         (b)     No Fractional Shares.  The Option may be exercised only with
respect to full Shares.

         (c)     Compliance with Law.  The Option may not be exercised in whole
or in part, and no Shares shall be issued nor certificates representing such
Shares (if any) delivered pursuant to any exercise of the Option, if any
requisite approval or consent of any governmental authority of any kind having
jurisdiction over the exercise of options or the issuance and sale of Shares
shall not have been obtained or if such exercise or issuance would violate any
applicable law.

         (d)     Exercise by Optionee.  The Option shall only be exercisable by
the Optionee and by any transferee who has received such Option pursuant to
Section 4(e).

         6.      Exercise of Option.

         (a)     Subject to the other terms and provisions of this Agreement,
the Option shall be exercisable by written notice timely given to the Company
by the Optionee (the "Exercise Notice"), which notice (i) shall state the
number of Shares that the Optionee then desires to purchase, and (ii) shall be
accompanied by payment in full of the Option Price for each of such Shares.
Unless the Company and Optionee shall have made mutually acceptable alternative
arrangements, payment of the Option Price shall be made in cash or by surrender
of Shares owned by the Optionee (the "Payment Shares"), the aggregate Fair
Market Value of which shall be credited against the Option Price.

         (b)     The Company's obligation to issue and transfer Shares upon the
exercise of this Option shall be conditioned on Optionee's payment to the
Company of an amount in cash equal to applicable withholding taxes, if any, due
in connection with the exercise of this Option; provided, however, that with
the consent of the Company, Optionee may satisfy any tax withholding obligation
in connection with the exercise of this Option by (i) surrendering Shares owned
by the Optionee to the Company or (ii) having the Company withhold from Shares
otherwise deliverable to Optionee upon exercise of this Option.  Any Shares
surrendered or withheld to satisfy Optionee's tax withholding obligation shall
be valued at Fair Market Value as of the date of surrender or withholding of
such Shares.

         7.      Recapitalization or Reorganization; Adjustments.

         (a)     The existence of this Option shall not affect in any way the
right or power of the Company to make or authorize any adjustment,
recapitalization, reorganization or other change in the Company's capital
structure or its business, any merger or consolidation of the Company, any
issuance of additional securities by the Company with priority over Shares or
otherwise affecting Shares or the rights thereof, the dissolution or
liquidation of the Company or any sale, lease, exchange or other disposition of
all or any part of its assets or business or any other corporate act or
proceeding.





                                      -3-
<PAGE>   4
         (b)     If as a result of any merger or acquisition transaction
involving the Company or any transaction involving the issuance or redemption
of equity interests in the Company, more than fifty percent (50%) of such
equity interests is owned by parties other than those listed on Exhibit A
attached hereto (such event is referred to herein as a "Fundamental Change"),
then immediately before the consummation of the Fundamental Change, any portion
of the Option which has not then vested shall become vested, so that the
Optionee shall have an opportunity to exercise the Option prior to the
consummation of the Fundamental Change.  The Company shall provide to Optionee
at least 30 days' notice of any pending Fundamental Change during which period
Optionee may elect to exercise the Option effective immediately before
consummation of such Fundamental Change.

         (c)     If the Company subdivides its outstanding Shares into a
greater number of Shares, the Option Price in effect immediately prior to such
subdivision shall be proportionately reduced, and the number of Shares then
subject to the Option shall be proportionately increased.  Conversely, if the
outstanding number of Shares of the Company are combined into a smaller number
of Shares, the Option Price in effect immediately prior to such combination
shall be proportionately increased, and the number of Shares then subject to
the Option shall be proportionately reduced.

         8.      Termination of Option.  Unless terminated earlier pursuant to
Section 4 hereof, this Option shall terminate upon the first to occur of the
(i) the Expiration Date, or (ii) the date on which Optionee purchases, or in
writing surrenders his right to purchase, all Shares or other securities then
subject to the Option.

         9.      Restriction on Transfer of Option.  The Option may not be
sold, assigned, hypothecated or transferred, except by will or by the laws of
descent and distribution.  Any attempted transfer of the Option in violation of
this provision shall be void and of no effect whatsoever.

         10.     Rights as a Shareholder.  Optionee shall have no rights as a
shareholder of the Company with respect to any Shares covered by the Option
until the exercise of the Option.

         11.     Additional Documents.  The Company and the Optionee will, upon
request of the other party, promptly execute and deliver all additional
documents, and take all such further action, reasonably deemed by such party to
be necessary, appropriate or desirable to complete and evidence the sale,
assignment and transfer of the Shares pursuant to this Agreement.

         12.     Representations, Warranties and Covenants of Optionee.

         (a)     The Optionee acknowledges that the Option has not been
registered under the Securities Act of 1933 or applicable state securities laws
on the grounds that the issuance of the Option is exempt from registration
under one or more provisions of each of such acts.  The Optionee further
understands that in determining the availability and applicability of such
exemptions and in executing and delivering this Agreement and issuing and
delivering any Shares upon exercise of the Option, the Company has relied and
will rely upon the representations, warranties and covenants made by the
Optionee herein and in any other documents which he may hereafter deliver to
the Company.  Accordingly, the Optionee represents and warrants to and
covenants and agrees with the Company that the Optionee is





                                      -4-
<PAGE>   5
acquiring and will hold the Option for his own account for investment and not
with a view to any sale or distribution of all or any part thereof.

         (b)     The Optionee agrees (i) that the certificates representing the
Shares or other securities purchased under this Option may bear such legend or
legends as the Company deems appropriate in order to assure compliance with
applicable securities laws, (ii) that the Company may refuse to register the
transfer of the Shares or other securities purchased under this Option on the
transfer records of the Company unless the Company is provided with an opinion
of counsel in form and substance satisfactory to the Company confirming that
such proposed transfer would not constitute a violation of any applicable
securities laws, and (iii) that the Company may give related instructions to
its transfer agent, if any, to stop registration of the transfer of the Shares
or other securities purchased under this Option.

         (c)     Optionee acknowledges that the value of the Option over its
life will be speculative and uncertain, that there is no market for the Option
and it is unlikely that any market will develop, and consequently, the Optionee
may ultimately realize no value from the Option.

         13.     Notices.  All notices required or permitted to be given
hereunder shall be in writing and shall be deemed to have been given on the
earlier of the date of receipt by the party to whom the notice is given or five
(5) days after being mailed by certified or registered United States mail,
postage prepaid, addressed to the appropriate party at the address shown beside
such party's signature below or at such other address as such party shall have
theretofore designated by written notice given to the other party.

         14.     Entirety and Modification.  This Agreement contains the entire
agreement between the parties hereto with respect to the subject matter hereof
and supersedes any and all prior agreements, whether written or oral, between
such parties relating to such subject matter.  No modification, alteration,
amendment or supplement to this Agreement shall be valid or effective unless
the same is in writing and signed by the party against whom it is sought to be
enforced.

         15.     Severability.  If any provision of this Agreement is held to
be unenforceable, this Agreement shall be considered divisible, and such
provision shall be deemed inoperative to the extent it is unenforceable, and in
all other respects this Agreement shall remain in full force and effect;
provided, however, that if any such provision may be made enforceable by
limitation thereof, then such provision shall be deemed to be so limited and
shall be enforceable to the maximum extent permitted by applicable law.

         16.     Gender.  Words used in this Agreement which refer to Optionee
and denote the male gender shall also be deemed to include the female gender or
the neuter gender when appropriate.

         17.     Headings.  The headings of the various sections and
subsections of this Agreement have been inserted for convenient reference only
and shall not be construed to enlarge, diminish or otherwise change the express
provisions hereof.

         18.     GOVERNING LAW.  THIS AGREEMENT SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF





                                      -5-
<PAGE>   6
DELAWARE (REGARDLESS OF THE LAWS THAT MIGHT OTHERWISE GOVERN UNDER APPLICABLE
DELAWARE PRINCIPLES OF CONFLICTS OF LAW).

         19.     Counterparts.  This Agreement may be signed in counterparts,
each of which shall be deemed an original and all of which shall constitute one
and the same agreement.

         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first set forth above.

                                    BRIGHAM EXPLORATION COMPANY


5949 Sherry Lane
Suite 1616
Dallas, Texas  75225                By                                        
                                    ------------------------------------------
                                      Anne L. Brigham, Executive Vice President

                                    OPTIONEE

5949 Sherry Lane
Suite 1616
Dallas, Texas  75225                
                                    -------------------------------------------
                                    [See Schedule I attached hereto]





                                      -6-
<PAGE>   7
                                   EXHIBIT A



BRIGHAM EXPLORATION COMPANY, A Delaware corporation

BRIGHAM OIL & GAS, L.P., A Delaware limited partnership

BRIGHAM, INC. (f/k/a Brigham Exploration Company), a Texas corporation

GENERAL ATLANTIC PARTNERS III, L.P., a Delaware limited partnership

GAP-BRIGHAM PARTNERS, L.P., a Delaware limited partnership

BEN M. BRIGHAM

ANNE L. BRIGHAM

HAROLD D. CARTER

RIMCO PARTNERS, L.P. II

RIMCO PARTNERS, L.P. III

RIMCO PARTNERS, L.P. IV





                                      -7-
<PAGE>   8
                                   SCHEDULE I


<TABLE>
<CAPTION>
                                                                             Number of Shares
                 Name                                                        Subject to Option
                 ----                                                        -----------------
                 <S>                                                         <C>

                 David T. Brigham                                            69,445

                 Craig M. Fleming                                            69,445

                 Jon L. Glass                                                69,445
</TABLE>





                                      -8-

<PAGE>   1




                                                                  EXHIBIT 10.9.2
                                OPTION AGREEMENT

               1997 Incentive Plan of Brigham Exploration Company
                          (Non-Qualified Stock Option)

         This Option Agreement ("Agreement"), made and entered into as of March
4, 1997, is by and between Brigham Exploration Company, a Delaware corporation
(the "Company"), and Jon L. Glass (the "Optionee").

                                  WITNESSETH:

         WHEREAS, the 1997 Incentive Plan of Brigham Exploration Company
("Plan") was adopted by the Company, effective as of February 27, 1997 ("Plan
Date"), for certain employees of the Company and its Subsidiaries;

         WHEREAS, the Optionee is eligible to participate in the Plan and the
Committee has approved the grant to Optionee of an option to purchase shares of
Common Stock, par value $.01 per share, of the Company ("Shares") pursuant to
the Plan and upon the terms set forth herein;

         NOW, THEREFORE, in consideration of the premises and of the mutual
covenants and agreements hereinafter set forth, the Company and Optionee hereby
agree as follows:

         1.      Certain Definitions.  Terms used in this Agreement and not
otherwise defined shall have the respective meanings assigned to such terms in
the Plan; and the following terms shall have the following meanings:

                 "Companies" means the Company and any of its Subsidiaries.

                 "Expiration Date" means 6:00 P.M., Austin, Texas time, on July
1, 2004.

         2.      Grant of Option.  Subject to the terms, conditions and
provisions of the Plan and those hereinafter set forth, the Company hereby
irrevocably grants to the Optionee a Nonqualified Stock Option (the "Option")
to purchase 138,889 Shares, subject to adjustment in accordance with the
provisions of Section 7 of this Agreement.

         3.      Option Price.  The price to be paid by Optionee to the Company
for each Share purchased pursuant to the exercise of this Option ("Option
Price") shall be $5.00 per share; provided, however, that the Option Price
shall be subject to adjustment in accordance with the provisions of Section 7
of this Agreement.
<PAGE>   2
         4.      Vesting of Right to Exercise Option.

         (a)     Except as otherwise provided in this Agreement, the right to
exercise this Option shall vest as to 30% of the total Shares which may be
purchased hereunder (rounded to the nearest whole share) on July 1, 1998, shall
vest with respect to an additional 20% of the total Shares which may be
purchased hereunder (rounded to the nearest whole share) on July 1, 1999, shall
vest with respect to an additional 16.66% of the total Shares which may be
purchased hereunder (rounded to the nearest whole share) on July 1, 2000, shall
vest with respect to an additional 16.67% of the total Shares which may be
purchased hereunder (rounded to the nearest whole share) on July 1, 2001, and
shall be fully vested on July 1, 2002.  From and after each date of vesting,
Optionee may exercise this Option, subject to the terms and conditions set
forth herein, to purchase all or any portion of the Shares for which Optionee's
rights have vested.

         (b)     To the extent Optionee does not purchase all or any part of
the Shares at the times this Option becomes exercisable, the Optionee has the
right cumulatively thereafter to purchase any Shares not so purchased and such
right shall continue until this Option terminates or expires.

         (c)     If Optionee's employment by the Companies is terminated on
account of fraud or dishonesty or other acts which the Board has determined are
materially detrimental to the interests of the Company, the Option shall
automatically terminate as of the date of such termination and this Option,
including any portion which has vested, shall be forfeited.

         (d)     If Optionee's employment by the Companies terminates
voluntarily by Optionee or by action of the Companies for reasons other than as
specified in subsection (c), this Option may be exercised, but only (i) within
90 days after such termination (if otherwise prior to the date of expiration of
this Option), and not thereafter, and (ii) to purchase the number of Shares, if
any, that could be purchased upon exercise of this Option at the date of
termination of Optionee's employment.

         (e)     In the event of Optionee's death or disability, this Option
shall remain outstanding and may be exercised by the person who acquires this
Option by will or the laws of descent and distribution, or by Optionee, as the
case may be, but only (i) within the one-year period following the date of
death or disability (if otherwise prior to the date of expiration of this
Option), and not thereafter, and (ii) to purchase the number of Shares that
could be purchased upon exercise of this Option at the time of such death or
disability.

         (f)     For purposes of subsection (d) and (e), if this Option shall
not have fully vested as of the date of termination of Optionee's employment by
the Company (but not in the case of a voluntary termination by Optionee) or as
of the date of the Optionee's death or disability, then a ratable portion of
the number of Shares which would have become purchasable upon the next vesting
date shall be deemed to have vested as of the date of such termination (or
death or disability), determined by multiplying the number of Shares that vest
on the next vesting date by a fraction with a numerator equal to the number of
full months which have then elapsed since the last vesting date and a
denominator of 12, and rounding to the closest whole number.





                                      -2-
<PAGE>   3
         (g)     Any provision of this Agreement to the contrary
notwithstanding, this Option shall automatically terminate and be of no further
force or effect if Optionee fails to relocate his permanent residence and
family to Austin, Texas at such time in 1997 as the Company may prescribe.
Satisfaction of this requirement shall be determined by the Chief Executive
Officer of the Company.

         5.      Restrictions on Exercise.  The right to exercise the Option
shall be subject to the following restrictions:

         (a)     Vesting.  Optionee shall have no right to exercise this Option
to purchase any Shares for which Optionee's rights have not yet vested in
accordance with Section 4.

         (b)     No Fractional Shares.  The Option may be exercised only with
respect to full Shares.

         (c)     Compliance with Law.  The Option may not be exercised in whole
or in part, and no Shares shall be issued nor certificates representing such
Shares (if any) delivered pursuant to any exercise of the Option, if any
requisite approval or consent of any governmental authority of any kind having
jurisdiction over the exercise of options or the issuance and sale of Shares
shall not have been obtained or if such exercise or issuance would violate any
applicable law.

         (d)     Exercise by Optionee.  The Option shall only be exercisable by
the Optionee and by any transferee who has received such Option pursuant to
Section 4(e).

         6.      Exercise of Option.

         (a)     Subject to the other terms and provisions of this Agreement,
the Option shall be exercisable by written notice timely given to the Company
by the Optionee (the "Exercise Notice"), which notice (i) shall state the
number of Shares that the Optionee then desires to purchase, and (ii) shall be
accompanied by payment in full of the Option Price for each of such Shares.
Unless the Company and Optionee shall have made mutually acceptable alternative
arrangements, payment of the Option Price shall be made in cash or by surrender
of Shares owned by the Optionee (the "Payment Shares"), the aggregate Fair
Market Value of which shall be credited against the Option Price.

         (b)     The Company's obligation to issue and transfer Shares upon the
exercise of this Option shall be conditioned on Optionee's payment to the
Company of an amount in cash equal to applicable withholding taxes, if any, due
in connection with the exercise of this Option; provided, however, that with
the consent of the Company, Optionee may satisfy any tax withholding obligation
in connection with the exercise of this Option by (i) surrendering Shares owned
by the Optionee to the Company or (ii) having the Company withhold from Shares
otherwise deliverable to Optionee upon exercise of this Option.  Any Shares
surrendered or withheld to satisfy Optionee's tax withholding obligation shall
be valued at Fair Market Value as of the date of surrender or withholding of
such Shares.





                                      -3-
<PAGE>   4
         7.      Recapitalization or Reorganization; Adjustments.

         (a)     The existence of this Option shall not affect in any way the
right or power of the Company to make or authorize any adjustment,
recapitalization, reorganization or other change in the Company's capital
structure or its business, any merger or consolidation of the Company, any
issuance of additional securities by the Company with priority over Shares or
otherwise affecting Shares or the rights thereof, the dissolution or
liquidation of the Company or any sale, lease, exchange or other disposition of
all or any part of its assets or business or any other corporate act or
proceeding.

         (b)     If as a result of any merger or acquisition transaction
involving the Company or any transaction involving the issuance or redemption
of equity interests in the Company, more than fifty percent (50%) of such
equity interests is owned by parties other than those listed on Exhibit A
attached hereto (such event is referred to herein as a "Fundamental Change"),
then immediately before the consummation of the Fundamental Change, any portion
of the Option which has not then vested shall become vested, so that the
Optionee shall have an opportunity to exercise the Option prior to the
consummation of the Fundamental Change.  The Company shall provide to Optionee
at least 30 days' notice of any pending Fundamental Change during which period
Optionee may elect to exercise the Option effective immediately before
consummation of such Fundamental Change.

         (c)     If the Company subdivides its outstanding Shares into a
greater number of Shares, the Option Price in effect immediately prior to such
subdivision shall be proportionately reduced, and the number of Shares then
subject to the Option shall be proportionately increased.  Conversely, if the
outstanding number of Shares of the Company are combined into a smaller number
of Shares, the Option Price in effect immediately prior to such combination
shall be proportionately increased, and the number of Shares then subject to
the Option shall be proportionately reduced.

         8.      Termination of Option.  Unless terminated earlier pursuant to
Section 4 hereof, this Option shall terminate upon the first to occur of the
(i) the Expiration Date, or (ii) the date on which Optionee purchases, or in
writing surrenders his right to purchase, all Shares or other securities then
subject to the Option.

         9.      Restriction on Transfer of Option.  The Option may not be
sold, assigned, hypothecated or transferred, except by will or by the laws of
descent and distribution.  Any attempted transfer of the Option in violation of
this provision shall be void and of no effect whatsoever.

         10.     Rights as a Shareholder.  Optionee shall have no rights as a
shareholder of the Company with respect to any Shares covered by the Option
until the exercise of the Option.

         11.     Additional Documents.  The Company and the Optionee will, upon
request of the other party, promptly execute and deliver all additional
documents, and take all such further action, reasonably deemed by such party to
be necessary, appropriate or desirable to complete and evidence the sale,
assignment and transfer of the Shares pursuant to this Agreement.





                                      -4-
<PAGE>   5
         12.     Representations, Warranties and Covenants of Optionee.

         (a)     The Optionee acknowledges that the Option has not been
registered under the Securities Act of 1933 or applicable state securities laws
on the grounds that the issuance of the Option is exempt from registration
under one or more provisions of each of such acts.  The Optionee further
understands that in determining the availability and applicability of such
exemptions and in executing and delivering this Agreement and issuing and
delivering any Shares upon exercise of the Option, the Company has relied and
will rely upon the representations, warranties and covenants made by the
Optionee herein and in any other documents which he may hereafter deliver to
the Company.  Accordingly, the Optionee represents and warrants to and
covenants and agrees with the Company that the Optionee is acquiring and will
hold the Option for his own account for investment and not with a view to any
sale or distribution of all or any part thereof.

         (b)     The Optionee agrees (i) that the certificates representing the
Shares or other securities purchased under this Option may bear such legend or
legends as the Company deems appropriate in order to assure compliance with
applicable securities laws, (ii) that the Company may refuse to register the
transfer of the Shares or other securities purchased under this Option on the
transfer records of the Company unless the Company is provided with an opinion
of counsel in form and substance satisfactory to the Company confirming that
such proposed transfer would not constitute a violation of any applicable
securities laws, and (iii) that the Company may give related instructions to
its transfer agent, if any, to stop registration of the transfer of the Shares
or other securities purchased under this Option.

         (c)     Optionee acknowledges that the value of the Option over its
life will be speculative and uncertain, that there is no market for the Option
and it is unlikely that any market will develop, and consequently, the Optionee
may ultimately realize no value from the Option.

         13.     Notices.  All notices required or permitted to be given
hereunder shall be in writing and shall be deemed to have been given on the
earlier of the date of receipt by the party to whom the notice is given or five
(5) days after being mailed by certified or registered United States mail,
postage prepaid, addressed to the appropriate party at the address shown beside
such party's signature below or at such other address as such party shall have
theretofore designated by written notice given to the other party.

         14.     Entirety and Modification.  This Agreement contains the entire
agreement between the parties hereto with respect to the subject matter hereof
and supersedes any and all prior agreements, whether written or oral, between
such parties relating to such subject matter.  No modification, alteration,
amendment or supplement to this Agreement shall be valid or effective unless
the same is in writing and signed by the party against whom it is sought to be
enforced.

         15.     Severability.  If any provision of this Agreement is held to
be unenforceable, this Agreement shall be considered divisible, and such
provision shall be deemed inoperative to the extent it is unenforceable, and in
all other respects this Agreement shall remain in full force and effect;
provided, however, that if any such provision may be made enforceable by





                                      -5-
<PAGE>   6
limitation thereof, then such provision shall be deemed to be so limited and
shall be enforceable to the maximum extent permitted by applicable law.

         16.     Gender.  Words used in this Agreement which refer to Optionee
and denote the male gender shall also be deemed to include the female gender or
the neuter gender when appropriate.

         17.     Headings.  The headings of the various sections and
subsections of this Agreement have been inserted for convenient reference only
and shall not be construed to enlarge, diminish or otherwise change the express
provisions hereof.

         18.     GOVERNING LAW.  THIS AGREEMENT SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE (REGARDLESS OF
THE LAWS THAT MIGHT OTHERWISE GOVERN UNDER APPLICABLE DELAWARE PRINCIPLES OF
CONFLICTS OF LAW).

         19.     Counterparts.  This Agreement may be signed in counterparts,
each of which shall be deemed an original and all of which shall constitute one
and the same agreement.

         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first set forth above.

<TABLE>
<S>                                        <C>
                                           BRIGHAM EXPLORATION COMPANY


5949 Sherry Lane
Suite 1616
Dallas, Texas  75225                       By /s/ Anne L. Brigham                      
                                             ------------------------------------------
                                              Anne L. Brigham, Executive Vice President

                                           OPTIONEE

5949 Sherry Lane
Suite 1616
Dallas, Texas  75225                       /s/ Jon L. Glass                            
                                           --------------------------------------------
                                           Jon L. Glass
</TABLE>





                                      -6-
<PAGE>   7
                                   EXHIBIT A



BRIGHAM EXPLORATION COMPANY, A Delaware corporation

BRIGHAM OIL & GAS, L.P., A Delaware limited partnership

BRIGHAM, INC. (f/k/a Brigham Exploration Company), a Texas corporation

GENERAL ATLANTIC PARTNERS III, L.P., a Delaware limited partnership

GAP-BRIGHAM PARTNERS, L.P., a Delaware limited partnership

BEN M. BRIGHAM

ANNE L. BRIGHAM

HAROLD D. CARTER

RIMCO PARTNERS, L.P. II

RIMCO PARTNERS, L.P. III

RIMCO PARTNERS, L.P. IV





                                      -7-

<PAGE>   1
                                                                   EXHIBIT 10.22


                          AGREEMENT AND ASSIGNMENT OF
                          INTEREST IN LANDS LOCATED IN
                             GRADY COUNTY, OKLAHOMA


       This Agreement and Assignment of Interest in Lands Located in  Grady
County, Oklahoma (hereinafter referred to as the "Assignment") is made and
entered into effective as of the 1st day of December, 1995, by and between
ASPECT RESOURCES LIMITED LIABILITY COMPANY ("Aspect"), BRIGHAM OIL & GAS, L.P.
("BOG") and VENTURE ACQUISITIONS, L.P.  (Aspect, BOG and Venture are sometimes
individually referred to herein as a "Party" and collectively referred to
herein as the "Parties").

                              W I T N E S S E T H:

       WHEREAS, BOG and Aspect entered into that certain Agreement and Partial
Assignment of Interests located in the West Bradley Project, Grady County,
Oklahoma, dated September 1, 1995 (hereinafter referred to as the "West Bradley
Agreement") under which Aspect assigned BOG interests under the Geophysical
Agreement (as such term is defined in the West Bradley Agreement),  the Ward
Agreement (as such term is defined in the West Bradley Agreement) and the Quest
3-D Exploration Agreement (as such term is defined in the West Bradley
Agreement) (the Geophysical Agreement, the Ward Agreement and the Quest 3-D
Exploration Agreement being sometimes collectively referred to herein  as the
"Agreements"); and

       WHEREAS, OXY USA Inc. ("OXY") has proposed the acquisition of producing
properties and oil and gas leasehold from Oxley Petroleum Company in its letter
dated November 20, 1995 which is attached hereto as Exhibit A (hereinafter
referred to as the OXY Acquisition"); and

       WHEREAS, under the terms of the Agreements Aspect and BOG have the right
to participate in the OXY Acquisition; and

       WHEREAS, Aspect and BOG have elected to participate in the OXY
Acquisition; and

       WHEREAS, Aspect and BOG have agreed to assign Venture all of their
interest and right to participate in the OXY Acquisition;

       NOW, THEREFORE, for and in consideration of the mutual covenants
contained herein and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Parties hereto agree as
follows:


                                   ARTICLE I.
                              TERMS OF ASSIGNMENT

       Section 1.1.  Assignment.  For good and valuable consideration, the
receipt and sufficiency of which is hereby acknowledged, Aspect and BOG hereby
grant, bargain, sell, assign and convey to Venture all of their right, title
and interest in the OXY Acquisition.  Aspect and BOG agree to execute any other
instruments or documentation which may be reasonably necessary to effectuate
the conveyance to Venture of all of their right, title and interest in the OXY
Acquisition.

       Section 1.2.  Subject to Terms of the Agreements.  Venture recognizes
and agrees that its interests in the OXY Acquisition shall be subject to the
terms and provisions of the Agreements.  However, anything to the contrary set
forth in the West Bradley Agreement notwithstanding, the Parties agree that the
Back-In Interest (as such term is defined in the West Bradley Agreement) shall
not apply to or burden Venture's interests in any oil and/or gas wells that are
the subject of the OXY Acquisition, including without limitation, any
production which may be obtained from such existing oil and/or gas wells.  In
addition, any costs, expenses or revenues received by Venture and related to
any oil and/or gas wells that are the subject of the OXY Acquisition shall not
be included in the determination as to the occurrence of Payout (as such term
if defined in the West Bradley Agreement) under the West Bradley Agreement.  In
the event that any new wells are drilled on the leases that are the subject of
the OXY Acquisition, Venture's interest in such new wells and the production
which may be obtained therefrom shall be burdened with the Back-In Interests
and all
<PAGE>   2
costs, expenses and revenues related to such new wells shall be included in the
determination as to the occurrence of Payout under the West Bradley Agreement.

       Section 1.3.  Venture Responsibility for Costs and Liabilities Related
to the OXY Acquisition.  Venture hereby agrees to assume and be responsible
for, and indemnify and hold BOG and Aspect harmless from, all costs, expenses
and liabilities related to the OXY Acquisition.


                                  ARTICLE II.
                        SEISMIC DATA AND INTERPRETATIONS

       Section 2.1.  Program Data and Interpretations.  The Parties agree that
Venture shall have access to the seismic data and interpretations which are
generated by BOG pursuant to the terms of the West Bradley Agreement; however,
VENTURE UNDERSTANDS AND AGREES THAT BOG AND ASPECT MAKE NO REPRESENTATIONS OR
WARRANTIES OF ANY KIND AS TO THE PROGRAM DATA OR INTERPRETATIONS THAT ARE
PROVIDED TO VENTURE, INCLUDING WITHOUT LIMITATION, THEIR FITNESS FOR A
PARTICULAR PURPOSE, MERCHANTABILITY OR ACCURACY, AND BOG AND ASPECT HEREBY
DISCLAIM ANY AND ALL SUCH REPRESENTATIONS OR WARRANTIES, AND ANY USE OF THE
SEISMIC DATA OR INTERPRETATIONS BY VENTURE, OR ANY ACTION TAKEN BY VENTURE
SHALL BE BASED SOLELY ON VENTURE'S OWN JUDGMENT, AND BOG, ASPECT AND THEIR
OFFICERS, EMPLOYEES, SUCCESSORS AND ASSIGNS, SHALL NOT BE LIABLE OR RESPONSIBLE
TO VENTURE FOR ANY LOSS, COST, DAMAGES, OR EXPENSE WHATSOEVER, INCLUDING
INCIDENTAL OR CONSEQUENTIAL DAMAGES, INCURRED OR SUSTAINED AS A RESULT OF THE
USE OF OR RELIANCE UPON THE PROGRAM DATA OR INTERPRETATIONS, REGARDLESS OF
WHETHER OR NOT SUCH LOSS, COST, DAMAGE OR EXPENSE IS FOUND TO RESULT IN WHOLE
OR IN PART FROM THE SOLE OR CONCURRENT NEGLIGENCE OR OTHER FAULT OF BOG, ASPECT
OR ANY OF THEIR OFFICERS, AGENTS OR EMPLOYEES.

       Section 2.2.  No Charge for BOG's Services.  Venture shall not be
required to reimburse BOG for any costs that are incurred by BOG in
interpreting the seismic data which has resulted from the Geophysical Program
conducted pursuant to the terms of the Agreements.


                                  ARTICLE III.
                                 MISCELLANEOUS

       Section 3.1.  Entirety of Agreement.  This Assignment contains the
entire understanding and agreement of the Parties with respect to the subject
matter hereof and supersedes all prior agreements, understandings,
negotiations, and discussions among the Parties with respect to such subject
matter.

       Section 3.2.  Assignment.  This Assignment shall be binding upon and
inure to the benefit of the Parties hereto and their respective successors and
their respective assigns of rights hereunder; provided, however, that the
conveyance or assignment instrument vesting such assignee with all or part of
such interests must expressly provide that the assignment or conveyance is made
subject to the terms and conditions contained in this Assignment.

       Section 3.3.  Counterparts.  This Assignment may be executed in multiple
counterparts, each of which shall be binding upon the signing Party or Parties
thereto as fully as if all Parties had executed one instrument, and all of such
counterparts shall constitute one and the same instrument.  If counterparts of
this Assignment are executed, the signatures of the Parties, as affixed hereto,
may be combined in and treated and given effect for all purposes as a single
instrument.





Agreement and Assignment of
Interests in Lands Located in
Grady County, Oklahoma
                                       2
<PAGE>   3
       IN WITNESS WHEREOF this Assignment is executed by the Parties on the
dates set forth opposite their respective signatures below but is effective for
all purposes as of the date first set forth above.


Address:                                 BRIGHAM OIL & GAS, L.P.,
       5949 Sherry Lane, Suite 1616      by Brigham Exploration Company,
       Dallas, Texas  75225              its Managing General Partner
       (214) 360-9182
       Fax:  (214) 360-9825
                                         By:                                    
                                            ------------------------------------
                                            Ben M. Brigham, President / CEO



Address:                                 ASPECT RESOURCES LIMITED
                                         LIABILITY COMPANY
       535 16th Street
       Suite 820
       Denver, Colorado  80202
       (303) 573-7011
       Fax:  (303) 573-7340              By:                                    
                                            ------------------------------------
                                         (name printed)                         
                                                       -------------------------
                                         Its:                                   
                                             -----------------------------------



Address:                                 VENTURE ACQUISITIONS, L.P.
       5949 Sherry Lane, Suite 1616
       Dallas, Texas  75225              By:  QUEST RESOURCES, L.L.C.
       (214) 360-9269                    Its:  Managing General Partner
       Fax:  (214) 360-9825

                                         by:                                    
                                            ------------------------------------
                                         (name printed)                         
                                                       -------------------------
                                         its:                                   
                                             -----------------------------------

                                         and
                                         By:  RIMCO ENERGY, INC.
                                         Its:  General Partner


                                         by:                                    
                                            ------------------------------------
                                         (name printed)                         
                                                       -------------------------
                                         its:                                   
                                             -----------------------------------





Agreement and Assignment of
Interests in Lands Located in
Grady County, Oklahoma
                                       3

<PAGE>   1


                                                                   EXHIBIT 10.28
                              INDEMNITY AGREEMENT


         This Agreement made and entered into as of this 4th day of March,
1997, by and between Brigham Exploration Company, a Delaware corporation (the
"Company"), and [See Schedule I attached] ("Indemnitee"), who is currently
serving the Company in the capacity of a director and/or officer thereof;

                              W I T N E S S E T H:

         WHEREAS, the Company and Indemnitee recognize that the interpretation
of ambiguous statutes, regulations and court opinions and of the Certificate of
Incorporation and Bylaws of the Company, and the vagaries of public policy, are
too uncertain to provide the directors and officers of the Company with
adequate or reliable advance knowledge or guidance with respect to the legal
risks and potential liabilities to which they become personally exposed as a
result of performing their duties in good faith for the Company; and

         WHEREAS, the Company and the Indemnitee are aware that highly
experienced and capable persons are often reluctant to serve as directors or
officers of a corporation unless they are protected to the fullest extent
permitted by law by comprehensive insurance or indemnification, especially
since the legal risks and potential liabilities, and the very threat thereof,
associated with lawsuits filed against the officers and directors of a
corporation, and the resultant substantial time, expense, harassment, ridicule,
abuse and anxiety spent and endured in defending against such lawsuits, whether
or not meritorious, bear no reasonable or logical relationship to the amount of
compensation received by the directors or officers from the corporation; and

         WHEREAS, Section 145 of the General Corporation Law of the State of
Delaware, which sets forth certain provisions relating to the mandatory and
permissive indemnification of, and advancement of expenses to, officers and
directors (among others) of a Delaware corporation by such corporation, is
specifically not exclusive of other rights to which those indemnified
thereunder may be entitled under any bylaw, agreement, vote of stockholders or
disinterested directors or otherwise, and, thus, does not by itself limit the
extent to which the Company may indemnify persons serving as its officers and
directors (among others); and

         WHEREAS, after due consideration and investigation of the terms and
provisions of this Agreement and the various other options available to the
Company and the Indemnitee in lieu thereof, the board of directors of the
Company has determined that the following Agreement is not only reasonable and
prudent but necessary to promote and ensure the best interests of the Company
and its stockholders; and

         WHEREAS, the Company desires to have Indemnitee serve or continue to
serve as an officer and/or director of the Company, free from undue concern for
unpredictable, inappropriate or unreasonable legal risks and personal
liabilities by reason of his acting in good faith in the performance of his
duty to the Company; and Indemnitee desires to serve, or to continue to serve
(provided that he is furnished the indemnity provided for hereinafter), in
either or both of such capacities;
<PAGE>   2
         NOW, THEREFORE, in consideration of the premises and the mutual
agreements herein set forth and for other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the Company and
Indemnitee, intending to be legally bound, do hereby agree as follows:

         1.      Agreement to Serve.  Indemnitee agrees to serve or continue to
serve as director and/or officer of the Company, at the will of the Company or
under separate contract, if such exists, for so long as he is duly elected or
appointed and qualified in accordance with the provisions of the Bylaws of the
Company or until such time as he tenders his resignation in writing.

         2.      Definitions.  As used in this Agreement:

                 (a)      The term "Proceeding" shall mean any action, suit or
         proceeding, whether civil, criminal, administrative, arbitrative or
         investigative, any appeal in such an action, suit or proceeding, and
         any inquiry or investigation that could lead to such an action, suit
         or proceeding, except one initiated by Indemnitee to enforce his
         rights under this Agreement.

                 (b)      The term "Expenses" includes, without limitation, all
         reasonable attorneys' fees, retainers, court costs, transcript costs,
         fees of experts, witness fees, travel expenses, duplicating costs,
         printing and binding costs, telephone charges, postage, delivery
         service fees and all other disbursements or expenses of the types
         customarily incurred in connection with prosecuting, defending,
         preparing to prosecute or defend, investigating, or being or preparing
         to be a witness in a Proceeding.

                 (c)      References to "other enterprise" shall include
         employee benefit plans; references to "fines" shall include any (i)
         excise taxes assessed with respect to any employee benefit plan and
         (ii) penalties; references to "serving at the request of the Company"
         shall include any service as a director, officer, employee or agent of
         the Company which imposes duties on, or involves services by, such
         director, officer, employee or agent with respect to an employee
         benefit plan, its participants or beneficiaries; and a person who acts
         in good faith and in a manner he reasonably believes to be in the
         interest of the participants and beneficiaries of an employee benefit
         plan shall be deemed to have acted in a manner "not opposed to the
         best interests of the Company" as referred to in this Agreement.

         3.      Indemnity in Third Party Proceedings.  The Company shall
indemnify Indemnitee in accordance with the provisions of this Section 3 if
Indemnitee is a party to or is threatened to be made a party to or otherwise
involved in any threatened, pending or completed Proceeding (other than a
Proceeding by or in the right of the Company to procure a judgment in its
favor) by reason of the fact that Indemnitee is or was a director and/or
officer of the Company, or is or was serving at the request of the Company as a
director, officer, employee or agent of another corporation, partnership, joint
venture, trust or other enterprise, against all Expenses, judgments, fines and
amounts paid in settlement actually and reasonably incurred by Indemnitee in
connection with such Proceeding, provided it is determined pursuant to Section
7 of this



                                      -2-
<PAGE>   3
Agreement or by the court having jurisdiction in the matter, that Indemnitee
acted in good faith and in a manner that he reasonably believed to be in or not
opposed to the best interests of the Company, and, with respect to any criminal
Proceeding, had no reasonable cause to believe his conduct was unlawful.  The
termination of any Proceeding by judgment, order, settlement or conviction, or
upon a plea of nolo contendere or its equivalent, shall not, of itself, create
a presumption that Indemnitee did not act in good faith and in a manner that he
reasonably believed to be in or not opposed to the best interests of the
Company, and, with respect to any criminal Proceeding, had reasonable cause to
believe that his conduct was unlawful.

         4.      Indemnity in Proceedings By or In the Right of the Company.
The Company shall indemnify Indemnitee in accordance with the provisions of
this Section 4 if Indemnitee is a party to or is threatened to be made a party
to or otherwise involved in any threatened, pending or completed Proceeding by
or in the right of the Company to procure a judgment in its favor by reason of
the fact that Indemnitee is or was a director and/or officer of the Company, or
is or was serving at the request of the Company as a director, officer,
employee or agent of another corporation, partnership, joint venture, trust or
other enterprise, against all Expenses actually and reasonably incurred by
Indemnitee in connection with the defense, settlement or other disposition of
such Proceeding, but only if he acted in good faith and in a manner that he
reasonably believed to be in or not opposed to the best interests of the
Company, except that no indemnification shall be made under this Section 4 in
respect of any claim, issue or matter as to which Indemnitee shall have been
adjudged to be liable to the Company unless and only to the extent that the
Delaware Court of Chancery or the court in which such Proceeding was brought
shall determine upon application that, despite the adjudication of liability
but in view of all the circumstances of the case, Indemnitee is fairly and
reasonably entitled to indemnity for such Expenses as the Delaware Court of
Chancery or such other court shall deem proper.

         5.      Indemnification for Expenses of Successful Party.
Notwithstanding any other provision of this Agreement to the contrary, to the
extent that Indemnitee has been successful on the merits or otherwise in
defense of any Proceeding referred to in Sections 3 and/or 4 of this Agreement,
or in defense of any claim, issue or matter therein, including dismissal
without prejudice, Indemnitee shall be indemnified against all Expenses
actually and reasonably incurred by Indemnitee in connection therewith.

         6.      Advances of Expenses.  The Expenses incurred by Indemnitee
pursuant to Sections 3 and/or 4 of this Agreement in connection with any
Proceeding shall, at the written request of the Indemnitee, be paid by the
Company in advance of the final disposition of such Proceeding upon receipt by
the Company of an undertaking by or on behalf of Indemnitee ("Indemnitee's
Undertaking") to repay such amount to the extent that it is ultimately
determined that Indemnitee is not entitled to be indemnified by the Company.
The request for advancement of Expenses by Indemnitee and the undertaking to
repay of Indemnitee, which need not be secured, shall be substantially in the
form of Exhibit A to this Agreement.





                                      -3-
<PAGE>   4
         7.      Right of Indemnitee to Indemnification or Advancement of
Expenses Upon Application; Procedure Upon Application.

                 (a)      Any indemnification under Sections 3 and/or 4 of this
         Agreement shall be made no later than 45 days after receipt by the
         Company of the written request of Indemnitee, unless a determination
         is made within said 45-day period by (i) a majority vote of the
         directors of the Company who are not parties to the involved
         Proceeding, even though less than a quorum, or (ii) independent legal
         counsel in a written opinion (which counsel shall be appointed if
         there are no such directors or if such directors so direct), that the
         Indemnitee has not met the applicable standards for indemnification
         set forth in Section 3 or 4, as the case may be.

                 (b)      Any advancement of Expenses under Section 6 of this
         Agreement shall be made no later than 10 days after receipt by the
         Company of Indemnitee's Undertaking.

                 (c)      In any action to establish or enforce the right of
         indemnification or to receive advancement of Expenses as provided in
         this Agreement, the burden of proving that indemnification or
         advancement of Expenses is not appropriate shall be on the Company.
         Neither the failure of the Company (including its board of directors
         or independent legal counsel) to have made a determination prior to
         the commencement of such action that indemnification or advancement of
         Expenses is proper in the circumstances because Indemnitee has met the
         applicable standard of conduct, nor an actual determination by the
         Company (including its board of directors or independent legal
         counsel) that Indemnitee has not met such applicable standard of
         conduct, shall be a defense to the action or create a presumption that
         Indemnitee has not met the applicable standard of conduct.  Expenses
         incurred by Indemnitee in connection with successfully establishing or
         enforcing his right of indemnification or to receive advancement of
         Expenses, in whole or in part, under this Agreement shall also be
         indemnified by the Company.

         8.      Indemnification and Advancement of Expenses Under this
Agreement Not Exclusive.  The rights of indemnification and to receive
advancement of Expenses as provided by this Agreement shall not be deemed
exclusive of any other rights to which Indemnitee may be entitled under the
Certificate of Incorporation or Bylaws of the Company, any other agreement, any
vote of stockholders or disinterested directors, the General Corporation Law of
the State of Delaware, or otherwise, both as to action in his official capacity
and as to action in another capacity while holding such office.

         9.      Partial Indemnification.  If Indemnitee is entitled under any
provision of this Agreement to indemnification or to receive advancement by the
Company for some or a portion of the Expenses, judgments, fines or amounts paid
in settlement actually and reasonably incurred by Indemnitee in the
investigation, defense, appeal, settlement or other disposition of any
Proceeding but not, however, for the total amount thereof, the Company shall
nevertheless indemnify Indemnitee for the portion thereof to which Indemnitee
is entitled.





                                      -4-
<PAGE>   5
         10.     Rights Continued.  The rights of indemnification and to
receive advancement of Expenses as provided by this Agreement shall continue as
to Indemnitee even though Indemnitee may have ceased to be a director or
officer of the Company and shall inure to the benefit of Indemnitee's personal
or legal representatives, executors, administrators, successors, heirs,
distributees, devisees and legatees.

         11.     No Construction as an Employment Agreement or Any Other
Commitment.  Nothing contained in this Agreement shall be construed as giving
Indemnitee any right to be retained in the employ of the Company or any of its
subsidiaries, if Indemnitee currently serves as an officer of the Company, or
to be renominated as a director of the Company, if Indemnitee currently serves
as a director of the Company.

         12.     Liability Insurance.  To the extent the Company maintains an
insurance policy or policies providing directors' and officers' liability
insurance, Indemnitee shall be covered by such policy or policies in accordance
with its or their terms, to the maximum extent of the coverage available for
any director or officer of the Company under such policy or policies.

         13.     No Duplication of Payments.  The Company shall not be liable
under this Agreement to make any payment of amounts otherwise indemnifiable
under this Agreement if, and to the extent that, Indemnitee has otherwise
actually received such payment under any contract, agreement or insurance
policy, the Certificate of Incorporation or Bylaws of the Company, or
otherwise.

         14.     Subrogation.  In the event of payment under this Agreement,
the Company shall be subrogated to the extent of such payment to all the rights
of recovery of Indemnitee, who shall execute all papers required and shall do
everything that may be necessary to secure such rights, including without
limitation the execution of such documents as may be necessary to enable the
Company effectively to bring suit to enforce such rights.

         15.     Exceptions.  Notwithstanding any other provision in this
Agreement, the Company shall not be obligated pursuant to the terms of this
Agreement, to indemnify or advance Expenses to the Indemnitee with respect to
any Proceeding, or any claim therein, (i)  brought or made by Indemnitee
against the Company, or (ii) in which final judgment is rendered against the
Indemnitee for an accounting of profits made from the purchase and sale or the
sale and purchase by Indemnitee of securities of the Company pursuant to the
provisions of Section 16(b) of the Securities Exchange Act of 1934, as amended,
or similar provisions of any federal, state or local statute.

         16.     Notices.  Any notice or other communication required or
permitted to be given or made to the Company or Indemnitee pursuant to this
Agreement shall be given or made in writing by depositing the same in the
United States mail, with postage thereon prepaid, addressed to the person to
whom such notice or communication is directed at the address of such person on
the records of the Company, and such notice or communication shall be deemed
given or made at the time when the same shall be so deposited in the United
States mail.  Any such notice or communication to the Company shall be
addressed to the Secretary of the Company.





                                      -5-
<PAGE>   6
         17.     Contractual Rights.  The right to be indemnified or to receive
advancement of Expenses under this Agreement (i) is a contract right based upon
good and valuable consideration, pursuant to which Indemnitee may sue, (ii) is
and is intended to be retroactive and shall be available as to events occurring
prior to the date of this Agreement and (iii) shall continue after any
rescission or restrictive modification of this Agreement as to events occurring
prior thereto.

         18.     Severability.  If any provision or provisions of this
Agreement shall be held to be invalid, illegal or unenforceable for any reason
whatsoever, the validity, legality and enforceability of the remaining
provisions shall not in any way be affected or impaired thereby; and, to the
fullest extent possible, the provisions of this Agreement shall be construed so
as to give effect to the intent manifested by the provisions held invalid,
illegal or unenforceable.

         19.     Successors; Binding Agreement.  The Company shall require any
successor to all or substantially all of the business and/or assets of the
Company (whether direct or indirect, by purchase, merger, consolidation or
otherwise), by agreement in form and substance reasonably satisfactory to
Indemnitee, to expressly assume and agree to perform this Agreement in the same
manner and to the same extent that the Company would be required to perform if
no such succession had taken place.  As used in this Agreement, "Company" shall
mean the Company as hereinbefore defined and any successor to its business
and/or assets as aforesaid which executes and delivers the agreement provided
for in this Section 19 or which otherwise becomes bound by the terms and
provisions of this Agreement by operation of law.

         20.     Counterparts, Modification, Headings, Gender.

                 (a)      This Agreement may be executed in any number of
         counterparts, each of which shall constitute one and the same
         instrument, and either party hereto may execute this Agreement by
         signing any such counterpart.

                 (b)      No provisions of this Agreement may be modified,
         waived or discharged unless such waiver, modification or discharge is
         agreed to in writing and signed by Indemnitee and an appropriate
         officer of the Company.  No waiver by any party at any time of any
         breach by any other party of, or compliance with, any condition or
         provision of this Agreement to be performed by any other party shall
         be deemed a waiver of similar or dissimilar provisions or conditions
         at the same time or at any prior or subsequent time.

                 (c)      Section headings are not to be considered part of
         this Agreement, are solely for convenience of reference, and shall not
         affect the meaning or interpretation of this Agreement or any
         provision set forth herein.

                 (d)      Pronouns in masculine, feminine and neuter genders
         shall be construed to include any other gender, and words in the
         singular form shall be construed to include the plural and vice versa,
         unless the context otherwise requires.





                                      -6-
<PAGE>   7
         21.     Assignability.  This Agreement shall not be assignable by
either party without the consent of the other.

         22.      Exclusive Jurisdiction; Governing Law.  The Company and
Indemnitee agree that all disputes in any way relating to or arising under this
Agreement, including, without limitation, any action for advancement of
Expenses or indemnification, shall be litigated, if at all, exclusively in the
Delaware Court of Chancery, and, if necessary, the corresponding appellate
courts.  This Agreement shall be governed by and construed and enforced in
accordance with the laws of the State of Delaware applicable to contracts made
and to be performed in such state without giving effect to the principles of
conflicts of laws.  The Company and Indemnitee expressly submit themselves to
the personal jurisdiction of the State of Delaware.

         23.     Termination.

                 (a)      This Agreement shall terminate upon the mutual
         agreement of the parties that this Agreement shall terminate or upon
         the death of Indemnitee or the resignation, retirement, removal or
         replacement of Indemnitee from all of his positions as a director
         and/or officer of the Company.

                 (b)      The termination of this Agreement shall not
         terminate:

                          (i)     the Company's liability for claims or actions
                          against Indemnitee arising out of or related to acts,
                          omissions, occurrences, facts or circumstances
                          occurring or alleged to have occurred prior to such
                          termination; or

                          (ii)    the applicability of the terms and conditions
                          of this Agreement to such claims or actions.





                                      -7-
<PAGE>   8
         IN WITNESS WHEREOF, the Company and Indemnitee have executed this
Agreement as of the date and year first above written.




                                BRIGHAM EXPLORATION COMPANY


                                By:                            
                                         ----------------------------------
                                         Anne L. Brigham
                                         Executive Vice President



                                INDEMNITEE


                                                                         
                                -------------------------------------------
                                [See Schedule I attached]





                                      -8-
<PAGE>   9
                                                                       EXHIBIT A

                            INDEMNITEE'S UNDERTAKING

                               ___________, 19__


Brigham Exploration Company
6300 Bridgepoint Parkway
Building 2, Suite 500
Austin, Texas 78730

         Re:  Indemnity Agreement

Ladies and Gentlemen:

         Reference is made to the Indemnity Agreement dated as of March 4,
1997, by and between Brigham Exploration, Inc. and the undersigned Indemnitee,
and particularly to Section 6 thereof relating to advance payment by the
Company of certain Expenses incurred by the undersigned Indemnitee.
Capitalized terms used and not otherwise defined in this Indemnitee's
Undertaking shall have the respective meanings ascribed to such terms in the
Agreement.

         The undersigned Indemnitee has incurred Expenses pursuant to Section 3
and/or 4 of the Agreement in connection with a Proceeding.  The types and
amounts of Expenses are itemized on Attachment I to this Indemnitee's
Undertaking.  The undersigned Indemnitee hereby requests that the total amount
of these Expenses (the "Advanced Amount") be paid by the Company in advance of
the final disposition of such Proceeding in accordance with the Agreement.

         The undersigned Indemnitee hereby agrees to repay the Advanced Amount
to the Company to the extent that it is ultimately determined that the
undersigned Indemnitee is not entitled to be indemnified by the Company.  This
agreement of Indemnitee to repay shall be unsecured.

                                                 Very truly yours,



                                                 ______________________________
                                                 [See Schedule I attached]
<PAGE>   10
                                ATTACHMENT I TO
                            INDEMNITEE'S UNDERTAKING

                                 ITEMIZATION OF
                         TYPES AND AMOUNTS OF EXPENSES


         Attached hereto are receipts, statements or invoices for the following
qualifying Expenses which Indemnitee represents have been incurred by
Indemnitee in connection with a Proceeding:




<TABLE>
<CAPTION>
- -----------------------------------------------------------------------------------
                           TYPE                                     AMOUNT
- -----------------------------------------------------------------------------------
 <S>                 <C>                                        <C>
  1.
- -----------------------------------------------------------------------------------

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

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

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

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

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

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

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

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

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

                     Total Advanced Amount                         ============
- -----------------------------------------------------------------------------------

</TABLE>
<PAGE>   11
                                   Schedule I


Name


Ben M. Brigham

Anne L. Brigham

Jon L. Glass

Craig M. Fleming

David T. Brigham

A. Lance Langford

Harold D. Carter

Alexis M. Cranberg





                                      -11-

<PAGE>   1
                                                                 EXHIBIT 10.29

                         REGISTRATION RIGHTS AGREEMENT

         THIS REGISTRATION RIGHTS AGREEMENT (this "Agreement"), dated February
26, 1997 and effective as of the Effective Date (defined below), is made by and
among BRIGHAM EXPLORATION COMPANY, a Delaware corporation ("COMPANY"), GENERAL
ATLANTIC PARTNERS III, L.P., a Delaware limited partnership ("GAP"),
GAP-BRIGHAM PARTNERS, L.P., a Delaware limited partnership ("GBP")
(collectively, GAP and GBP and their respective successors and assigns are
referred to as the "GAP PARTIES"), RIMCO PARTNERS, L.P. II ("RPII"), RIMCO
PARTNERS, L.P. III ("RPIII") and RIMCO PARTNERS, L.P. IV ("RPIV")(collectively,
RPII, RPIII and RPIV and their respective successors and assigns are referred
to as "RIMCO") BEN M. BRIGHAM ("BMB"), ANNE L. BRIGHAM ("ALB") (collectively,
BMB and ALB and their respective successors and assigns are referred to as the
"BRIGHAMS") and HAROLD D. CARTER ("HDC"), CRAIG M. FLEMING ("CMF"), DAVID T.
BRIGHAM ("DTB") and JON L. GLASS ("JLG")(collectively, HDC, CMF, DTB and JLG
and their respective successors and assigns are referred to herein as the
"OTHER BRIGHAM PARTIES") (collectively, the GAP Parties, RIMCO, the Brighams
and the Other Brigham Parties are referred to herein as "OWNERS").

         Capitalized terms used herein which are not otherwise defined shall
have the meanings set forth for such terms in Section 3.

                 1.       Background. The Owners own, directly or indirectly,
or have the right to acquire interests in Brigham Oil & Gas, L.P. ("PARTNERSHIP
INTERESTS"). The Agreement of Limited Partnership, as amended (the "PARTNERSHIP
AGREEMENT") of Brigham Oil & Gas, L.P. (the "PARTNERSHIP") provides that the
Owners shall have certain registration rights with respect to the Partnership
Interests or in the event of a conversion of the Partnership to corporate form,
any capital stock into or for which the Partnership Interests are converted or
exchanged. The Company and the Owners are parties to that certain Exchange
Agreement dated as of February 26, 1997 (the "EXCHANGE AGREEMENT"), pursuant to
which the Owners will exchange Partnership Interests (or securities convertible
into Partnership Interests) and the stock of the general partner of the
Partnership for shares of the Company's common stock, par value $.01 per share
(the "COMPANY COMMON STOCK"), as more fully described in the Exchange Agreement
(the "PROPOSED EXCHANGE"). The parties hereto desire to enter into this
Agreement in order to give effect to the registration rights of the Owners
under the Partnership Agreement by granting to the Owners registration rights
with respect to the Company Common Stock. The execution and delivery of this
Agreement is a condition to the consummation of the Proposed Exchange. This
Agreement shall be effective as of the date of the closing of the Proposed
Exchange (the "EFFECTIVE DATE").

                 2.       Registration under Securities Act.

                 2.1. Incidental Registration. If the Company at any time after
the Initial Registration Date proposes to register any Transfer of its
Registrable Securities under the Securities Act for its own account or for the
account of a security holder (other than a registration relating to employee
benefit plans, the acquisition of another company or business, an exchange
offer solely for already outstanding securities of the Company, or a
registration on a form that
<PAGE>   2
does not require substantially the same information that would be required in a
registration statement covering a Transfer of Registrable Securities held by an
Owner), the Company will each such time give prompt written notice to all
holders of Registrable Securities (herein collectively called the "PROSPECTIVE
SELLERS") of its intention to do so. Upon the written notification by any
Prospective Seller of an intention to register a Transfer of Registrable
Securities under this Section 2.1 (stating the intended method of Transfer of
such Registrable Securities by such Prospective Seller and the number of
Registrable Securities to be transferred), given within twenty (20) days after
receipt of any such notice from the Company, the Company will cause such
intended Transfer of all Registrable Securities of which any such Prospective
Sellers shall have given such notice to be registered under the Securities Act.
The Company shall have the right to reduce or eliminate Registrable Securities
of a Prospective Seller to be included pursuant to exercise of its incidental
rights under this Section 2.1 in an underwritten offering by the Company if, in
the good faith opinion of the managing underwriter, supported by written
reasons therefor, the inclusion of such shares would raise a substantial doubt
as to whether the proposed offering could be successfully consummated. Any
reduction of Registrable Securities to be included in an incidental
registration pursuant to the immediately preceding sentence shall be made pro
rata among the Prospective Sellers thereof requesting such incidental
registration on the basis of the percentage of the Registrable Securities of
the Company held by the holders of Registrable Securities which have requested
that such securities be included; provided, a Demand Holder requiring
registration pursuant to Section 2.2 of this Agreement shall not be subject to
the foregoing reduction. The Company shall include in such a registration all
of the Registrable Securities requested by the Prospective Sellers to be
included in such registration that are not eliminated from such registration by
the underwriters. In the case of an underwritten public offering by the
Company, each Prospective Seller participating in such incidental registration
shall, if requested by the managing underwriter, agree not to Transfer any
securities of the Company held by such Prospective Seller to any person other
than such underwriter for a period of up to thirty (30) days following the
effective date of the registration statement relating to such offering or such
longer period as may be reasonably requested by such underwriter, but in no
event to exceed ninety (90) days, and the Company hereby covenants that it
will, thereafter, take whatever actions (including amendment of its
registration statement) as shall be reasonably necessary to enable such
Prospective Seller to register a Transfer of any such securities at such time.

                 2.2. Required Registration. Subject to the provisions of
Section 2.3, whenever the Company shall be requested by a Demand Holder to
effect the registration under the Securities Act of any specified Transfer of
Registrable Securities, which right may not be exercised prior to the Initial
Registration Date, the Company shall promptly give written notice of such
proposed registration to all Prospective Sellers and thereupon shall, as
expeditiously as possible, use its best efforts to effect the registration
under the Securities Act of any such Transfer of Registrable Securities which
any Prospective Seller has requested to be registered. If the Company shall
notify Prospective Sellers within five business days of the Company's receipt
of a registration request hereunder that the Company has in good faith
determined that the filing of such a registration statement at that time would
interfere with a material financing or acquisition then contemplated by the
Company and specifies in writing the manner and extent





                                       2
<PAGE>   3
to which such registration would so interfere, the Company shall have the right
to delay for a period of not more than ninety (90) days a registration of a
Transfer of Registrable Securities pursuant to the request of Prospective
Sellers under this Section 2.2. If for any reason (other than the requested
withdrawal of such registration statement by such Prospective Sellers or other
action or inaction of the Prospective Seller) any registration statement filed
with the Commission with respect to securities which the Company is required to
register under this Section 2.2 shall not be declared effective by the
Commission and remain effective for a period of at least 90 days, such
attempted registration shall not constitute a registration under this Section
2.2. The Company may register a Transfer on the least expensive form available.
The Company may permit certain third parties incidental rights subordinate to
the Prospective Sellers' rights in a registration under this Section 2.2,
provided that any shares to be included pursuant to such incidental rights may
be reduced or eliminated if in the good faith opinion of the Prospective
Sellers or their managing underwriter, if any, the inclusion of such shares
would raise a substantial doubt as to whether the proposed offering could be
consummated successfully. Any expenses required to be paid by the Prospective
Sellers with respect to any such registration shall be borne on a pro rata
basis by any third parties registering a transfer or transfers of stock
pursuant to the same registration.

                 2.3. Certain Limitations. The Brighams shall not have the
right to require a registration under Section 2.2 prior to the expiration of
one year from the date hereof. The GAP Parties, RIMCO and the Brighams shall
each have the right to initiate one registration pursuant to Section 2.2 (an
aggregate of three (3) registrations for all of the Demand Holders); provided
that, if after having effected three (3) registrations pursuant to Section 2.2,
any Registrable Securities requested to be included therein by a Demand Holder
shall not have been disposed of in accordance with such registration
statements, the Company shall be required to effect one, but no more than one,
additional registration at the request of any one or more Demand Holders
pursuant to Section 2.2 (an "ADDITIONAL REQUIRED REGISTRATION"). In addition,
the Company shall not be required to effect a registration pursuant to Section
2.2 unless the Registrable Securities to be included in such registration,
including those of all Prospective Sellers joining in such proposed sale, have
an estimated aggregate offering price to the public of at least $3,000,000. The
Prospective Sellers shall not have the right to participate in a registration
under Section 2.1 unless the Prospective Sellers provide to the Company a
written opinion of counsel, in substance and authorship acceptable to the
Company, that such Prospective Sellers may make such Transfer of all of their
Registrable Securities (if applicable) in a public sale which will be in
compliance with all applicable securities laws. All registration rights granted
in this Agreement shall expire ten (10) years after the completion of the first
public offering by the Company.

                 2.4. Registration Procedures. If and whenever the Company is
required by the provisions of this Agreement to effect the registration of any
Transfer of Registrable Securities under the Securities Act, the Company will,
as expeditiously as possible, and at its expense,

                 (a)      prepare and file with the Commission a registration
         statement with respect to such Transfer and use its best efforts to
         cause such registration statement to become





                                       3
<PAGE>   4
         and remain effective for a period of at least one hundred eighty (180)
         days or until the Prospective Sellers have completed the distribution
         described in the registration statement relating thereto, whichever
         occurs first;

                 (b)      prepare and file with the Commission such amendments
         and supplements to such registration statement and the prospectus used
         in connection therewith as may be necessary to keep such registration
         statement effective, and to comply with the provisions of the
         Securities Act with respect to the Transfer of all securities covered
         by such registration statement, for a period of at least one hundred
         eighty (180) days or until the Prospective Sellers have completed the
         distribution described in the registration statement relating thereto,
         whichever occurs first;

                 (c)      furnish to each Prospective Seller who has requested
         to use such registration statement such numbers of copies of a summary
         prospectus or other prospectus, including a preliminary prospectus, in
         conformity with the requirements of the Securities Act, and such other
         documents, as such Prospective Seller may reasonably request in order
         to facilitate its intended Transfer of the Registrable Securities
         owned by such Prospective Seller and covered by such registration
         statement;

                 (d)      register or qualify the securities covered by such
         registration statement under such other securities or blue sky laws of
         such jurisdictions as each Prospective Seller shall reasonably
         request, and do any and all other acts and things which may be
         necessary or advisable to enable such Prospective Seller to consummate
         the public sale or other disposition in such jurisdictions of the
         Registrable Securities owned by such Prospective Seller and covered by
         such registration statement;

                 (e)      promptly upon becoming aware of such, notify each
         Prospective Seller who has requested to use such registration
         statement and each underwriter, at any time when a prospectus relating
         thereto is required to be delivered under the Securities Act, of the
         happening of any event as a result of which the prospectus contained
         in such registration statement, as then in effect, includes an untrue
         statement of a material fact or omits to state any material fact
         required to be stated therein or necessary to make the statements
         therein not misleading in the light of the circumstances then existing

                 (f)      furnish to the Prospective Sellers whose intended
         Transfers are registered a signed copy of an opinion of counsel for
         the Company, in substance and authorship acceptable to such
         Prospective Sellers, to the effect that: (i) a registration statement
         covering such Transfers of Registrable Securities has been filed with
         the Commission under the Securities Act and has been made effective by
         order of the Commission, (ii) such registration statement and the
         prospectus contained therein and any amendments or supplements thereto
         (other than the financial statements and other financial and
         statistical data included therein, as to which an expert has rendered
         an opinion) comply as to form in all material respects with the
         requirements of the Securities Act, and nothing has come to such
         counsel's attention which would cause him to believe that the
         registration





                                       4
<PAGE>   5
         statement or such prospectus contains any untrue statement of a
         material fact or omits to state a material fact required to be stated
         therein or necessary to make the statements therein (in the case of
         such prospectus, in the light of the circumstances under which they
         were made) not misleading, (iii) such counsel knows of no legal or
         governmental proceedings required to be described in such prospectus
         which are not described as required, nor of any contract or documents
         of a character required to be described in such registration statement
         or such prospectus or to be filed as an exhibit to such registration
         statement or to be incorporated by reference therein which is not
         described and filed as required, (iv) a prospectus meeting the
         requirements of the Securities Act is available for delivery, (v) to
         the best of such counsel's knowledge, no stop order has been issued by
         the Commission suspending the effectiveness of such registration
         statement, and no proceedings for the issuance of such a stop order
         are threatened or contemplated, and (vi) the applicable provisions of
         the securities or blue sky laws of each state or jurisdiction in which
         the Company shall be required, pursuant to clause (d) of this Section
         2.4, to register or qualify such intended Transfers or the Registrable
         Securities to be so transferred, have been complied with, assuming the
         accuracy and completeness of the information furnished to such counsel
         with respect to each filing relating to such laws; it being understood
         that such counsel may rely, as to all factual matters and financial
         data treated therein, on certificates of the Company (copies of which
         shall be delivered to such Prospective Sellers), and as to all
         questions of the laws of each jurisdiction in which the Company shall
         be so required to register or qualify such intended Transfers or the
         Registrable Securities to be so transferred, on an examination of the
         securities laws of such jurisdiction and of the published rules and
         regulations (if any) of the authorities administering such laws, as
         reported in accepted unofficial publications and/or on an opinion of
         counsel from such jurisdiction acceptable to such Prospective Sellers,
         copies of which opinions shall be delivered to such Prospective
         Sellers; provided, however, that the opinion of counsel for the
         Company required by this Section 2.4(f) need not contain the opinion
         required by this subsection (vi) in those situations in which the
         underwriter's counsel provides such an opinion upon which the
         Prospective Sellers are entitled to rely;

                 (g)      otherwise comply with all applicable rules and
         regulations of the Commission under the Securities Act, the Exchange
         Act and otherwise, and make available to its security holders, as soon
         as reasonably practicable, an earnings statement covering the period
         of at least twelve months, but not more than eighteen months,
         beginning with the first month after the effective date of the
         registration statement, which earnings statement shall satisfy the
         provisions of Section 11(a) of the Securities Act; and

                 (h)      use its best efforts to list such securities on any
         securities exchange on which any shares of Registrable Securities of
         the Company are then listed.

                 2.5. Expenses; Limitations on Registration.

         (a)     All expenses incurred by the Company in complying with
Sections 2.1 and 2.2, including, without limitation, all registration and
filing fees, printing expenses, fees and





                                       5
<PAGE>   6
disbursements of counsel for the Company, fees and disbursements of accountants
and auditors of the Company with respect to quarterly and annual financial
statements of the Company, and expenses of complying with the securities or
blue sky laws of any jurisdictions pursuant to Section 2.4, shall be paid by
the Company; provided that commissions, fees and expenses of the underwriter
allocable to the securities to be registered for the Prospective Sellers and
costs of separate counsel shall be borne pro rata by the Prospective Sellers.

         (b)     It shall be a condition precedent to the obligation of the
Company to take any action pursuant to this Agreement in respect of any
Transfer of Registrable Securities which is to be registered at the request of
any Prospective Seller that such Prospective Seller furnish to the Company such
written information regarding the securities held by such Prospective Seller
and the intended method of disposition thereof as the Company shall reasonably
request and as shall be required in connection with the action to be taken by
the Company.

                 2.6. Indemnification.

         (a)     In the event of any registration of any Transfer of
Registrable Securities under the Securities Act pursuant to this Agreement, the
Company shall indemnify and hold harmless each Prospective Seller of such
securities, its directors, partners and officers, each underwriter and each
other person who participates in the offering of such securities and each other
person, if any, who controls such Prospective Seller or such participating
person within the meaning of the Securities Act, against any losses, claims,
damages, expenses or liabilities, joint or several, to which such Prospective
Seller or any such director, partner or officer or participating person or
controlling person may become subject under the Securities Act or otherwise,
insofar as such losses, claims, damages, expenses or liabilities (or actions in
respect thereof) arise out of or are based upon (i) any alleged untrue
statement of any material fact contained, on the effective date thereof, in any
registration statement under which such Transfer of Registrable Securities was
registered under the Securities Act, any preliminary prospectus or final
prospectus contained therein, or any amendment or supplement thereto, or (ii)
any alleged omission to state therein a material fact required to be stated
therein or necessary to make the statements therein not misleading, and shall
reimburse such Prospective Seller or such director, partner, officer,
underwriter or participating person or controlling person for any legal or any
other expenses incurred by such Prospective Seller or such director, partner,
officer, underwriter or participating person or controlling person in
connection with investigating or defending any such loss, claim, damage,
liability or action; provided, however, that the Company shall not be liable
hereunder in any such case to the extent that any such loss, claim, damage or
liability arises out of or is based upon any alleged untrue statement or
alleged omission made in such registration statement, preliminary prospectus,
prospectus, or amendment or supplement in reliance upon and in conformity with
written information furnished to the Company through an instrument duly
executed by such Prospective Seller specifically for use in connection
therewith. Such indemnity shall remain in full force and effect regardless of
any investigation made by or on behalf of such Prospective Seller or such
director, partner, officer, underwriter or participating person or controlling
person, and shall survive any Transfer of such Registrable Securities by such
Prospective Seller.





                                       6
<PAGE>   7
         (b)     Each Prospective Seller shall indemnify and hold harmless each
other Prospective Seller, the Company, its directors, partners and officers,
each underwriter and each other person who participates in the offering of
Registrable Securities, and each other person, if any, who controls the Company
within the meaning of the Securities Act, against any losses, claims, damages,
expenses or liabilities, joint or several, to which the Company or any such
director, partner or officer or any such controlling person or Prospective
Seller may become subject under the Securities Act or otherwise, insofar as
such losses, claims, damages or liabilities (or actions in respect thereof)
arise out of or are based upon:

                 (i)      any alleged untrue statement of any material fact
         contained, on the effective date thereof, in any registration
         statement under which a Transfer of Registrable Securities was
         registered under the Securities Act at the request of such Prospective
         Seller, any preliminary prospectus or final prospectus contained
         therein, or any amendment or supplement thereto, or

                 (ii)     any 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 such alleged untrue statement or alleged omission was
         made in such registration statement, preliminary prospectus, final
         prospectus, amendment or supplement in reliance upon and in conformity
         with written information furnished to the Company through an
         instrument duly executed by such indemnifying Prospective Seller
         specifically for use in connection therewith, and shall reimburse the
         Company or such director, officer, controlling person or Prospective
         Seller for any legal or any other expenses reasonably incurred in
         connection with investigating or defending any such loss, claim,
         damage, liability or action.

         (c)     Promptly after receipt by an indemnified party hereunder of
notice of the commencement of any action, such indemnified party shall, if a
claim in respect hereof is to be made against the indemnifying party hereunder,
notify the indemnifying party in writing thereof, but the failure so to notify
the indemnifying party shall not relieve it from any liability which it may
have to any indemnified party hereunder. In any proceeding in which
indemnification is sought pursuant to Section 2.6(a) and (b) above, the
indemnifying party may (i) participate at its own expense in the defense or,
(ii) if it so elects, jointly with any other indemnifying party similarly
notified, assume the defense of any suit or administrative or other proceeding
brought to enforce or determine liability. After notice by an indemnifying
party of its election to assume the defense of a suit or administrative or
other proceeding, the indemnifying party shall not be liable for any legal or
other expenses subsequently incurred by the indemnified party in connection
with the defense, except to the extent that the indemnified party has
additional defenses not available to the indemnifying party, in which event the
costs and expenses of one attorney or law firm for the indemnified party will
be borne by the indemnifying party.

         (d)     The indemnifying party need not indemnify any person for any
payment made in settlement of any suit or claim unless the payment is consented
to by the indemnifying party, which consent shall not be unreasonably withheld.





                                       7
<PAGE>   8

                 3.       Definitions. As used herein, unless the context
otherwise requires, the following terms have the following respective meanings:

                 Commission: The Securities and Exchange Commission or any
                 other Federal agency at the time administering the Securities
                 Act.

                 Company: As defined in the introductory paragraph of this
                 Agreement. For purposes of this Agreement, all references to
                 the Company shall be deemed to include any successor entity or
                 transferee.

                 Demand Holders: Any of the GAP Parties, RIMCO, or the
                 Brighams.

                 Exchange Act: The Securities Exchange Act of 1934, or any
                 similar Federal statute, and the rules and regulations of the
                 Commission thereunder, all as the same shall be in effect at
                 the time. Reference to a particular section of the Securities
                 Exchange Act of 1934 shall include a reference to the
                 comparable section, if any, of any such similar Federal
                 statute.

                 Initial Registration Date: The first to occur of (i) March 31,
                 1998, and (ii) the 180th day after a registration statement
                 shall have been filed and declared effective under the
                 Securities Act with respect to the initial public offering of
                 the Company's securities.

                 Majority Holders: At any time, the holder or holders of more
                 than 50% (by number of shares) of all Registrable Securities
                 then outstanding.

                 Person: A corporation, an association, a partnership, a
                 business, an individual, a governmental or political
                 subdivision thereof or a governmental agency.

                 Registrable Securities: any Company Common Stock owned by an
                 Owner and any securities issued or issuable with respect to
                 any such Company Common Stock by way of distribution or in
                 connection with any reorganization, recapitalization, merger,
                 consolidation or otherwise. As to any particular Registrable
                 Securities, once issued such securities shall cease to be
                 Registrable Securities when (a) a registration statement with
                 respect to the sale of such securities shall have become
                 effective under the Securities Act and such securities shall
                 have been disposed of in accordance with such registration
                 statement, (b) they shall have been distributed to the public
                 pursuant to Rule 144 or Rule 144A (or any successor provision)
                 under the Securities Act, (c) they shall have been otherwise
                 transferred, new certificates for them not bearing a legend
                 restricting further transfer shall have been delivered by the
                 Company and subsequent disposition of them shall not require
                 registration or qualification of them under the Securities Act
                 or any similar state law then in force, or (d) they shall have
                 ceased to be outstanding.





                                       8
<PAGE>   9
                 Securities Act: The Securities Act of 1933, or any similar
                 Federal statute, and the rules and regulations of the
                 Commission thereunder, all as of the same shall be in effect
                 at the time. References to a particular section of the
                 Securities Act of 1933 shall include a reference to the
                 comparable section, if any, of any such similar Federal
                 Statute.

                 Transfer: Any disposition or offer to dispose of any
                 Registrable Securities, or any interest therein, which would
                 constitute a sale of or an offer to sell such Registrable
                 Securities or any such interest within the meaning of the
                 Securities Act.

                 4.       Rule 144 and Rule 144A: If the Company shall have
filed a registration statement pursuant to the requirements of Section 12 of
the Exchange Act or a registration statement pursuant to the requirements of
the Securities Act, the Company will file the reports required to be filed by
it under the Securities Act and the Exchange Act and the rules and regulations
adopted by the Commission thereunder (or, if the Company is not required to
file such reports, will, upon the request of any holder of Registrable
Securities, make publicly available other information) and will take such
further action as any holder of Registrable Securities may reasonably request,
all to the extent required from time to time to enable such holder to sell
Registrable Securities without registration under the Securities Act within the
limitation of the exemptions provided by (a) Rule 144 under the Securities Act,
as such Rule may be amended from time to time or (b) any similar rule or
regulation hereafter adopted by the Commission. Upon the request of any holder
of Registrable Securities, the Company will deliver to such holder a written
statement as to whether it has complied with such requirements. After any sale
of Registrable Securities pursuant to this Section 4, the Company will, to the
extent allowed by law, cause any restrictive legends to be removed and any
transfer restrictions to be rescinded with respect to such Registrable
Securities.  In order to permit the holders of Registrable Securities to sell
the same, if they so desire, pursuant to Rule 144A promulgated by the
Commission (or any successor to such rule), the Company will comply with all
rules and regulations of the Commission applicable in connection with use of
Rule 144A (or any successor thereto). Prospective transferees of Registrable
Securities that are Qualified Institutional Buyers (as defined in Rule 144A)
which would be purchasing such Registrable Securities in reliance upon Rule
144A may request from the Company information regarding the business,
operations and assets of the Company. Within five business days of any such
request, the Company shall deliver to any such prospective transferee copies of
annual audited and quarterly unaudited financial statements of the Company and
such other information as may be required to be supplied by the Company for it
to comply with Rule 144A.


                 5.       Amendments and Waivers. This Agreement may be amended
and the Company may take any action herein prohibited or omit to perform any
act herein required to be performed by it, only if the Company shall have
obtained the written consent to such amendment, action or omission to act, of
the Majority Holders; provided, however, that no amendment to this Agreement
that would adversely affect the rights of a party hereto may be





                                       9
<PAGE>   10
made without the prior written consent of such party, with the exception that
temporary waivers and suspensions of the rights of all of the Owners pursuant
to customary terms at the request of the managing underwriter in connection
with any underwritten offering of the Company's securities, may be authorized
by consent of the Majority Holders. Each holder of any Registrable Securities
at the time or thereafter outstanding shall be bound by any consent authorized
by this Section 5, whether or not such Registrable Securities shall have been
marked to indicate such consent.

                 6.       Nominees for Beneficial Owners. In the event that any
Registrable Securities are held by a nominee for the beneficial owner thereof,
the beneficial owner thereof may, at its election, be treated as the holder of
such Registrable Securities for purposes of any request or other action by any
holder or holders of Registrable Securities pursuant to this Agreement or any
determination of any number or percentage of shares of Registrable Securities
held by any holder or holders of Registrable Securities contemplated by this
Agreement. If the beneficial owner of any Registrable Securities so elects, the
Company may require assurances reasonably satisfactory to it of such owner's
beneficial ownership of such Registrable Securities.

                 7.       Notices. All communications provided for hereunder
shall be sent by first-class mail addressed to such party at the address set
forth opposite such parties name on the execution page hereof or at such other
address as such party shall furnish to the other parties hereto from time to
time.

                 8.       Assignment. This Agreement shall be binding upon and
inure to the benefit of and be enforceable by the parties hereto and their
respective successors and assigns. In addition, and whether or not any express
assignment shall have been made, the provisions of this Agreement which are for
the benefit of the parties hereto other than the Company shall also be for the
benefit of and enforceable by any subsequent holder of any Registrable
Securities, subject to the provisions respecting the minimum numbers or
percentages of shares of Registrable Securities required in order to be
entitled to certain rights, or take certain actions, contained herein.

                 9.       Termination. This Agreement shall terminate when no
Registrable Securities remain outstanding.

                 10.      Termination of Registration Rights Under Partnership
Agreement. The parties hereto who are parties to the Partnership Agreement
agree that on the Effective Date the registration rights under Article X of the
Partnership Agreement are hereby terminated and of no further force or effect.

                 11.      Descriptive Headings. The descriptive headings of the
several sections and paragraphs of this Agreement are inserted for reference
only and shall not limit or otherwise affect the meaning hereof.





                                       10
<PAGE>   11
                 12.      Specific Performance. The parties hereto recognize
and agree that money damages may be insufficient to compensate the holders of
any Registrable Securities for breaches by the Company of the terms hereof and,
consequently, that the equitable remedy of specific performance of the terms
hereof will be available in the event of any such breach.

                 13.      Governing Law. This Agreement shall be construed and
enforced in accordance with, and the rights of the parties shall be governed
by, the laws of the State of Texas.

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





                                       11
<PAGE>   12
         IN WITNESS WHEREOF, the parties have executed this Agreement or caused
the same to be executed by their duly authorized corporate officers, all as of
the day and year first above written.
                     
                     
                             BRIGHAM EXPLORATION COMPANY, a 
                             Delaware corporation
                     
                     
                                                                         
                             By: /s/ Ben M. Brigham                      
                                -----------------------------------------
                             Name: Ben M. Brigham                        
                                  ---------------------------------------
                             Title: President                            
                                   --------------------------------------
                                                                         
                                                                         
                     
                             GENERAL ATLANTIC PARTNERS III, L.P., a Delaware 
                             limited partnership
                     
                             By: GAP III Investors, Inc., its General Partner
                     
                     
                     
                             By: /s/ Stephen P. Reynolds                 
                                -----------------------------------------
                             Name: Stephen P. Reynolds                   
                                  ---------------------------------------
                             Title: President                            
                                   --------------------------------------
                     
                     
                     
                             GAP-BRIGHAM PARTNERS, L.P., a Delaware 
                             limited partnership
                     
                     
                     
                             By: /s/ Stephen P. Reynolds                 
                                -----------------------------------------
                             Name: Stephen P. Reynolds                   
                                  ---------------------------------------
                             Title: General Partner                      
                                   --------------------------------------
                     
                     
                     
                                     12
                     
                     
<PAGE>   13
                             RIMCO PARTNERS, L.P. II
                             RIMCO PARTNERS, L.P. III
                             RIMCO PARTNERS, L.P. IV
                     
                             By: Resource Investors Management Company Limited
                             Partnership, the General Partner of each
                     
                             By: RIMCO Associates, Inc., its General Partner
                     
                     
                     
                             By: /s/ Gary J. Milavec                     
                                -----------------------------------------
                               Gary J. Milavec, Vice President
                     
                     
                     
                             /s/ Ben M. Brigham                                 
                             --------------------------------------------
                             BEN M. BRIGHAM
                     
                     
                             /s/ Anne L. Brigham                                
                             --------------------------------------------
                             ANNE L. BRIGHAM      
                     
                     
                             /s/ Harold D. Carter                               
                             --------------------------------------------
                             HAROLD D. CARTER
                     
                     
                             /s/ Craig M. Fleming                               
                             --------------------------------------------
                             CRAIG M. FLEMING
                     
                     
                             /s/ David T. Brigham                      
                             ---------------------------------------------
                             DAVID T. BRIGHAM
                     
                     
                             /s/ Jon L. Glass                                   
                             ---------------------------------------------
                             JON L. GLASS
                     
                     
                     


                                       13

<PAGE>   1
   
                                                                  EXHIBIT 10.30
    

                          BRIGHAM EXPLORATION COMPANY

                        1997 DIRECTOR STOCK OPTION PLAN


                                  I.  PURPOSE

         It is the purpose of the Plan to promote the interests of the Company
and its stockholders by attracting and retaining qualified directors by giving
them the opportunity to acquire a proprietary interest in the Company and an
increased personal interest in its continued success and progress.  The Options
granted hereunder shall not be qualified as "incentive stock options" within
the meaning of Section 422(b) of the Code.


                                II.  DEFINITIONS

           As used herein the following terms have the following meanings:

         (a)     "Board" means the Board of Directors of the Company.

         (b)     "Chairman of the Board" means the director elected to the
position of Chairman of the Board by the Board.

         (c)     "Code" means the Internal Revenue Code of 1986, as amended.

         (d)     "Common Stock" means the $.01 par value Common Stock of the
Company.

         (e)     "Company" means Brigham Exploration Company, a Delaware
corporation.

         (f)     "Effective Date" means March 4, 1997, which shall be the date
on which the Plan shall be effective.

         (g)     "Eligible Director" means an individual who (i) is on the
Effective Date, or thereafter becomes, a member of the Board, (ii) is neither
an employee nor an officer of the Company or any direct or indirect
majority-owned subsidiary of the Company and (C) has not elected to decline to
participate in the Plan pursuant to the following sentence.  A director
otherwise eligible to participate in the Plan may make an irrevocable, one-time
election, by written notice to the Company within ten days after his or her
initial election to the Board, or, in the case of the directors in office on
the Effective Date, within ten days prior to the Effective Date, to decline to
participate in the Plan.  For purposes of the Plan, "employee" shall mean an
individual whose wages are subject to the withholding of federal income tax
under Section 3402 of the Code, and "officer" shall mean an individual elected
or appointed by the Board or the board of directors of the subsidiary, as the
case may be, or chosen in such other manner as may be prescribed in the bylaws
of the Company or the subsidiary, to serve as such.





                                      1
<PAGE>   2
         (h)     "Fair Market Value" of a share of Common Stock means, as of a
particular date, (i) if shares of Common Stock are listed on a national
securities exchange, the mean between the highest and lowest sales price per
share of Common Stock on the consolidated transaction reporting system for the
principal national securities exchange on which shares of Common Stock are
listed on that date, or, if there shall have been no such sale so reported on
that date, on the last preceding date on which such a sale was so reported,
(ii) if shares of Common Stock are not so listed but are quoted on the Nasdaq
National Market, the mean between the highest and lowest sales price per share
of Common Stock reported by the Nasdaq National Market on that date, or, if
there shall have been no such sale so reported on that date, on the last
preceding date on which such a sale was so reported, (iii) if the Common Stock
is not so listed or quoted, the mean between the closing bid and asked price on
that date, or, if there are no quotations available for such date, on the last
preceding date on which such quotations shall be available, as reported by the
Nasdaq National Market, or, if not reported by the Nasdaq National Market, by
the National Quotation Bureau Incorporated or (iv) if shares of Common Stock
are not publicly traded, the most recent value determined in good faith by the
Board for such purpose.

         (i)     "Holder" means an Eligible Director to whom an Option has been
granted under the Plan.

         (j)     "Initial Options" means those options granted to each Eligible
Director who becomes a member of the Board automatically on the date of his or
her initial election as a director of the Company.

         (k)     "Option" means any option to purchase shares of Common Stock
granted pursuant to the provisions of the Plan, including Initial Options and
Subsequent Options.

         (l)     "Plan" means this Brigham Exploration Company 1997 Director 
Stock Option Plan.

         (m)     "Subsequent Options" means those options granted automatically
as of December 31 of each year to each Eligible Director who is serving the
Company as a director on such date beginning December 31, 1997.


                              III.  ADMINISTRATION

         The Plan shall be administered by the Board.  The Board shall have no
authority, discretion or power to select the participants who will receive
Options, to set the number of shares to be covered by any Option, to set the
exercise price of any Option or to set the period within which Options may be
exercised, or to alter any other terms or conditions specified herein, except
in the sense of administering the Plan subject to the express provisions of the
Plan and except in accordance with Section 6.02 hereof.  Subject to the
foregoing limitations, the Board shall have authority and power to adopt such
rules and regulations and to take such action as it shall consider necessary or
advisable for the administration of the Plan, and to construe, interpret and
administer the Plan.  The decisions of the Board relating to the Plan shall be
final and binding upon the Company, the Holders and all other persons.  No
member of the Board shall incur any liability by reason of any action or
determination made in good faith with respect to the Plan or any stock option
agreement entered into pursuant to the Plan.





                                      2
<PAGE>   3
                                  IV.  OPTIONS

         4.01    Participation.  Each Eligible Director who does not elect to
decline to participate in the Plan pursuant to paragraph (g) of Article II
hereof shall be granted an Option to purchase Common Stock under the Plan on
the terms and conditions herein described.

         4.02    Terms and Conditions of Options; Stock Option Agreements.
Each Option granted under the Plan shall be evidenced by a written stock option
agreement entered into by the Company and the Holder to whom the Option is
granted, which agreement shall include, incorporate or conform to the following
terms and conditions, and such other terms and conditions not inconsistent
therewith or with the terms and conditions of the Plan as the Board considers
appropriate in each case:

         (a)     Option Grant Dates.  An Option shall be granted (i) to each
Eligible Director who becomes a member of the Board after the Effective Date
automatically on the date of his or her initial election as a director of the
Company (an "Initial Option"), provided that such person does not elect to
decline to participate in the Plan pursuant to paragraph (g) of Article II
hereof, and (ii) automatically as of December 31 of each year to each Eligible
Director who is serving the Company as a director on such date, beginning
December 31, 1997 (a "Subsequent Option").  The date of grant of an Option
pursuant to the Plan shall be referred to hereinafter as the "Grant Date" of
such Option.

         (b)     Number of Shares.  Each Initial Option shall entitle the
Holder to purchase, in accordance with the terms of such Option and the Plan,
1,000 shares of Common Stock, subject to adjustment in accordance with Section
5.02 hereof.  Each Subsequent Option shall entitle the Holder to purchase, in
accordance with the terms of such Option and the Plan, 500 shares of Common
Stock, subject to adjustment in accordance with Section 5.02 hereof.  If, on
the Grant Date of any Option, fewer shares of Common Stock remain available for
grant than are necessary to permit the grant of Options to each person entitled
to receive an Option on such date in accordance with the provisions of this
Section 4.02, then (i) first, an Option covering an equal number of whole
shares of Common Stock, up to 1,000 shares, shall be granted on such date to
each Eligible Director who is to receive an Initial Option and (ii) thereafter,
Options shall be granted to the remaining Eligible Directors then serving
covering an equal number of whole shares of Common Stock and all such Options
shall cover, in the aggregate, all remaining shares of Common Stock then
available for grant under the Plan (or such smaller number as may be necessary
to permit each such Option to cover an equal number of whole shares of Common
Stock).

         (c)     Price.  The price at which each share of Common Stock covered
by an Option may be purchased pursuant to the Plan shall be the Fair Market
Value of a share of Common Stock on the Grant Date of the Option.





                                      3
<PAGE>   4
         (d)     Option Period.  Each option shall become exercisable in five
equal annual installments on each of the first five anniversaries of such
option's "Grant Date."  The period within which each Option may be exercised
shall expire on the seventh anniversary of such Grant Date (the "Option
Period"), unless terminated sooner pursuant to Section 4.02(e) hereof.

         (e)     Termination of Service, Death, Etc.  The following provisions
shall apply with respect to the exercise of an Option granted hereunder in the
event that the Holder thereof ceases to be a director of the Company for the
reasons described in this Section 4.02(e):

                 (i)  If the directorship of the Holder is terminated within
the Option Period on account of any act of (a) fraud or intentional
misrepresentation or (b) embezzlement, misappropriation or conversion of assets
or opportunities of the Company or any direct or indirect majority-owned
subsidiary of the Company, the Option shall automatically terminate as of the
date of such termination;

                 (ii)  If the Holder dies during the Option Period while such
Holder is a director of the Company (or during the additional three-month
period provided by paragraph (iii) of this Section 4.02(e)), the Option may be
exercised, to the extent that the Holder was entitled to exercise it at the
date of the Holder's death, within one year after such death (if within the
Option Period), but not thereafter, by the executor or administrator of the
estate of the Holder, or by the person or persons who shall have acquired the
Option directly from the Holder by bequest or inheritance; or

                 (iii)  If the directorship of the Holder is terminated for any
reason (other than the circumstances specified in paragraphs (i) and (ii) of
this Section 4.02(e)) within the Option Period, including a failure by the
stockholders of the Company to reelect the Holder as a director, the Option may
be exercised, to the extent the Holder was entitled to do so at the date of
termination of the directorship, within three months after such termination (if
within the Option Period), but not thereafter.

   
         (f)     Transferability.  An Option granted under the Plan shall not
be transferable by the Holder, otherwise than by will or pursuant to the laws
of descent and distribution or with the consent of the Board, and during the
lifetime of the Holder the Option shall be exercisable only by the Holder or
his or her guardian or legal representative or by transferees of the Holders in
such circumstances as the Board may approve.
    

         (g)     Requirement of Directorship.  Except as provided in Section
4.02(e) hereof, an Option may not be exercised unless the Holder is at the time
of exercise serving as a director of the Company, and, except as provided in
Section 4.02(e) hereof, such Option shall terminate upon termination of the
Holder's service as a director of the Company.

         (h)     Exercise, Payments, Etc.  Each Option granted hereunder may be
exercised, in whole or in part, by the Holder thereof at any time or (with
respect to partial exercises) from time to time during the Option Period,
subject to the provisions of the Plan and the stock option agreement evidencing
such Option, and the method for exercising an Option shall be by the personal
delivery to the Secretary of the Company of, or by the sending by United States
registered or certified mail, postage prepaid, addressed to the Company (to the
attention of its





                                      4
<PAGE>   5
Secretary), of, written notice signed by the Holder specifying the number of
shares of Common Stock with respect to which such Option is being exercised.
Such notice shall be accompanied by the full amount of the purchase price of
such shares, in cash and/or by delivery of shares of Common Stock already owned
by the Holder having an aggregate Fair Market Value (determined as of the date
of exercise) equal to the purchase price, including an actual or deemed
multiple series of exchanges of such shares.  Any such notice shall be deemed
to have been given on the date of receipt thereof (in the case of personal
delivery as above-stated) or on the date on which the same was deposited in a
regularly maintained receptacle for the deposit of United States mail,
addressed and sent as above-stated.  In addition to the foregoing, promptly
after demand by the Company, the exercising Holder shall pay to the Company an
amount equal to applicable withholding taxes, if any, due in connection with
such exercise.  No shares of Common Stock shall be issued upon exercise of an
Option until full payment therefor and for all applicable withholding taxes has
been made, and a Holder shall have none of the rights of a shareholder until
shares of Common Stock are issued to such Holder.


                          V.  AUTHORIZED COMMON STOCK

         5.01    Common Stock.  The total number of shares as to which Options
may be granted pursuant to the Plan shall be 25,000 shares of Common Stock, in
the aggregate, except as such number of shares shall be adjusted from and after
the Effective Date in accordance with the provisions of Section 5.02 hereof.
If any outstanding Option under the Plan shall expire or be terminated for any
reason, the shares of Common Stock allocable to the unexercised portion of such
Option shall again be available for grant under the Plan.

         5.02    Adjustments Upon Changes in Common Stock.  In the event the
Company shall effect a split of the Common Stock or a dividend payable in
Common Stock, or in the event the outstanding Common Stock shall be combined
into a smaller number of shares, the maximum number of shares as to which
Options may be granted under the Plan shall be increased or decreased
proportionately.  In the event that before delivery by the Company of all the
shares of Common Stock in respect of which any Option has been granted under
the Plan, the Company shall have effected such a split, dividend or
combination, the shares still subject to the Option shall be increased or
decreased proportionately and the purchase price per share shall be increased
or decreased proportionately so that the aggregate purchase price for all the
then optioned shares shall remain the same as immediately prior to such split,
dividend or combination.

         In the event of a reclassification of the Common Stock not covered by
the foregoing, or in the event of a liquidation or reorganization, including a
merger, consolidation or sale of assets, the Board shall make such adjustments,
if any, as it may deem appropriate in the number, purchase price and kind of
shares covered by the unexercised portions of Options theretofore granted under
the Plan.  The provisions of this Section 5.02 shall only be applicable if, and
only to the extent that, the application thereof does not conflict with any
valid governmental statute, regulation or rule.





                                      5
<PAGE>   6
                            VI.  GENERAL PROVISIONS

         6.01    Termination of Plan.  The Plan shall terminate whenever
(whether before or after the Effective Date) the Board adopts a resolution to
that effect.  If not sooner terminated in accordance with the preceding
sentence, the Plan shall wholly cease and expire on the tenth anniversary of
the Effective Date.  After termination of the Plan, no Options shall be granted
under the Plan, but the Company shall continue to recognize, and perform its
obligations with respect to, any Options previously granted.

         6.02    Amendment of Plan.  The Board may from time to time (whether
before, on or after the Effective Date) amend, modify or suspend the Plan.
Nevertheless, (a) no such amendment, modification or suspension shall impair
any Options theretofore granted under the Plan or deprive any Holder of any
shares of Common Stock which such Holder might have acquired through or as a
result of the Plan, and (b) after the stockholders of the Company have approved
and adopted the Plan in accordance with Section 6.04 hereof, no such amendment
or modification shall be made without the approval of the holders of the
outstanding shares of capital stock of the Company entitled to vote in the
election of directors generally where such amendment or modification would (i)
increase the total number of shares of Common Stock as to which Options may be
granted under the Plan or decrease the exercise price at which Options may be
granted under the Plan (other than as provided in Section 5.02 hereof), (ii)
materially alter the class of persons eligible to be granted Options under the
Plan, (iii) materially increase the benefits accruing to Holders under the Plan
or (iv) extend the term of the Plan or the Option Period specified in Section
4.02(d) hereof.

         Notwithstanding the foregoing, the provisions of the Plan relating to
(a) the number of shares of Common Stock covered by, and the exercise price of,
Options granted under the Plan, (b) the timing of grants of Options under the
Plan and (c) the class of persons eligible to be granted Options under the Plan
shall not be amended more than once every six months, other than to comport
with changes in the Code, the Employee Retirement Income Security Act of 1974,
as amended, or the rules thereunder.

         6.03    Treatment of Proceeds.  Proceeds from the sale of Common Stock
pursuant to Options granted under the Plan shall constitute general funds of
the Company.

         6.04    Effectiveness.  The Plan shall become effective as of the
Effective Date, subject to and upon the receipt of shareholder approval by the
affirmative votes of the holders of a majority of the shares of Common Stock
present, or represented, and entitled to vote at a meeting of stockholders duly
held in accordance with the applicable laws of the State of Delaware.

         6.05    Section Headings.  The section headings included herein are
only for convenience, and they shall have no effect on the interpretation of
the Plan.





                                      6

<PAGE>   1


                                                                   EXHIBIT 10.31

                          BRIGHAM EXPLORATION COMPANY

                       EMPLOYEE STOCK OWNERSHIP AGREEMENT


         THIS AGREEMENT, made by and between BRIGHAM EXPLORATION COMPANY, a
Delaware corporation (the "Company") and [See Schedule I attached]
("Employee"),

                                  WITNESSETH:

         WHEREAS, Employee is an employee of Brigham Oil & Gas, L.P., a
Delaware limited partnership (the "Partnership") of which the Company is both a
general partner and a limited partner and Brigham, Inc., a Texas corporation,
is a general partner;

         WHEREAS, prior to the date hereof, Employee owned an interest as a
limited partner (the "Limited Partner Interest") in the Partnership;

         WHEREAS, the Limited Partner Interest was acquired by Employee
pursuant to an Employment Equity Interests Plan Participation Agreement dated
October 14, 1994 which contained confidentiality, noncompetition and vesting
provisions (the "1994 Agreements"), among other terms;

         WHEREAS, in connection with the formation of the Company, which was
consummated on the date hereof, Employee contributed the Limited Partner
Interest to the Company in exchange for 66,964 shares of common stock in the
Company, par value $.01 per share (the "Shares"); and

         WHEREAS, Employee and the Company have agreed in connection with the
issuance of the Shares that the Shares should be subject to agreements similar
to the 1994 Agreements;

         NOW, THEREFORE, in consideration of the premises and the mutual
covenants herein contained, the parties hereto do hereby agree as follows:

         1.  Vesting, Forfeiture and Repurchase.  The Shares shall be subject
to vesting and forfeiture as follows:

                 (a)      Except as otherwise provided in this Paragraph 1,
         16.67% of the Shares (or 11,160 Shares) shall be deemed fully vested
         on the date of this Agreement, 28.33% of the Shares (or 18,974 Shares)
         shall be deemed fully vested on July 1, 1997, an additional 28.33% of
         the Shares (or 18,973 Shares) shall be deemed fully vested on July 1,
         1998, and the remaining 26.67% of the Shares (or 17,857 Shares) shall
         be deemed fully vested on July 1, 1999.
<PAGE>   2
                 (b)      If Employee's employment with the Company or any of
         its subsidiaries (including the Partnership), or any of its or their
         successors or affiliates (collectively, the "Employer") terminates at
         any time prior to July 1, 1999, for any reason other than the death of
         Employee, in which case subparagraph (c) of this Paragraph 1 shall
         control, the then unvested portion of the Shares shall be deemed
         automatically forfeited by Employee to the Company, effective on the
         date of such termination.

                 (c)      If Employee dies prior to July 1, 1999, in lieu of
         the vesting schedule provided in subparagraph (a) of this Paragraph 1,
         one sixtieth (1/60) of the Shares shall be deemed fully vested for
         each month ended prior to the date of death, beginning with the month
         ended July 31, 1994 and ending with the month ended immediately prior
         to the date of death.  Any remaining unvested portion of the Shares
         shall be deemed automatically forfeited by Employee to the Company,
         effective on the date of death.

                 (d)      Upon Employee's termination of employment, by death
         or otherwise, if the Company's common stock is not then listed on an
         established securities exchange, the Company shall have the right,
         exercisable at any time on or before the first anniversary of such
         termination by written notice delivered to Employee or his personal
         representative, to purchase all or any portion of the Shares which is
         not forfeited in accordance with the provisions of subparagraphs (b)
         or (c) of this Paragraph 1.  The purchase price for such Shares shall
         be the fair market value thereof on the date of termination.  For this
         purpose, fair market value shall be an amount equal to the value of
         the Shares on the termination date as mutually agreed upon by the
         Company and Employee or his personal representative.  If they are
         unable to reach agreement on such value, such value shall be computed
         in the same manner as it would be if all Company assets were sold for
         cash, all Company liabilities were paid and all remaining cash were
         distributed to the shareholders of the Company in liquidation of the
         Company.  For purposes of this computation, the value of the Company
         assets shall equal the excess of (i) the aggregate of (X) the present
         value of the future net revenues attributable to the Company's proved
         oil and gas reserves, as determined in accordance with the immediately
         succeeding sentence, as reflected on the Company's most recent
         engineering report, and (Y) the book value, as reflected on the
         Company's most recent financial statements, of all cash, unevaluated
         oil and gas properties and other assets of the Company, over (ii) an
         amount equal to all debts, obligations and liabilities of the Company
         of every kind whatsoever.  The present value of the future net
         revenues shall be discounted at a rate of ten percent (10%) per annum,
         and the valuation shall assume that prices for future oil and gas
         production shall remain fixed at the prices in effect as of the date
         of termination of employment.   Payment for such Shares shall be in
         cash and shall be paid within ninety days after the purchase price has
         been determined.  If the Company elects not to purchase any portion of
         the Shares of the terminated Employee, such





                                      -2-
<PAGE>   3
         portion shall be retained by Employee or pass to his successors by
         operation of law, and this Agreement shall thereupon terminate.

                 (e)      Unless and until any portion of the Shares is
         forfeited or repurchased as provided in this Paragraph 1, Employee
         shall have full rights of ownership with respect to such Shares from
         and after the date of this Agreement.

                 (f)  Upon the occurrence of a Change-in-Control, as defined in
         this subparagraph (f), any unvested portion of Employee's Shares shall
         be vested immediately.  A Change-in-Control for this purpose will
         occur if (i) as a result of any merger or acquisition transaction
         involving the Company or any transaction involving the issuance or
         redemption of equity interests in the Company, more than fifty percent
         (50%) of such equity interests is owned by parties other than those
         listed on Exhibit A attached hereto, and (ii) within twelve (12)
         months after the occurrence described in clause (i) of this
         subparagraph (f), either (A) Employee's job responsibilities are
         substantially diminished or (B) Employee is required to relocate to a
         principal place of business that is more than sixty (60) miles from
         the principal place of business of Employee immediately prior to such
         occurrence.

         2.  Confidentiality.  Employee hereby acknowledges that the Employer's
trade secrets and other confidential or proprietary information, as they may
exist from time to time (the "Proprietary Information") are valuable, special
and unique assets of the Employer's business, access to and knowledge of which
are essential to the performance of Employee's duties as an employee of the
Employer.  Employee agrees that Employee will hold in strict confidence and
will not directly or indirectly disclose or reveal to any person, or use for
Employee's own personal benefit or for the benefit of anyone else, any
Proprietary Information of any kind (including but not limited to compensation
data, partner lists, financial information, pending projects and proposals
information, proprietary processes, research and development strategy
information, scientific data, technological data and technological prototypes,
regardless of whether acquired, learned, obtained or developed by Employee
alone or in conjunction with others) belonging to or concerning the Employer or
any of its affiliates, participants, partners, customers or clients, except (i)
with the prior written consent of the President of the Company, (ii) in the
course of the proper performance of Employee's duties as an employee of the
Employer, or (iii) as required by applicable law or legal process.  The
provisions of this Paragraph 2 shall continue in effect notwithstanding the
termination of Employee's employment with the Employer for any reason.

         3.  Noncompetition.  During the period of Employee's employment with
the Employer and for a period of one year thereafter, Employee agrees that
Employee will not directly or indirectly engage or participate in, on
Employee's own behalf or for anyone else, whether as a director, officer,
shareholder, member, partner, employee, consultant, agent, representative,
proprietor, associate, investor or otherwise, any business or activity which is





                                      -3-
<PAGE>   4
competitive with the business of the Employer or any of its affiliates in any
geographical area in the continental United States, or in the offshore area
within the portion of the Gulf of Mexico over which the United States or any
State thereof asserts jurisdiction, which is within one-half (1/2) mile of
lands (i) in which the Employer has a mineral property interest (including but
not limited to a mineral lease, overriding royalty interest, production
payment, net profits interest, or mineral fee interest) or right, license or
authority to conduct or direct exploratory activities (including but not
limited to seismic, geophysical and geochemical activities) as of the date of
Employee's termination of employment with the Employer, or (ii) which are part
of an area of mutual interest designated by the Employer as of the date of
Employee's termination of employment with the Employer.  The term "area of
mutual interest" for this purpose shall not include geological areas of
interest ("Geological Areas") which are designated for preliminary geological
mapping (such as, for example, those areas covered by that certain MXC
Exploration Company Consulting Agreement dated as of February 28, 1994, between
MXC Exploration Company and the Partnership), but such term shall include all
areas designated by the Employer (including areas designated within the
Geological Areas) for three dimensional seismic acquisition ("3D Areas") over
the majority of the lands within each such 3D Area.  The foregoing restrictions
shall not apply, however, to Employee's ownership of or dealings with respect
to any securities of any corporation or other entity whose equity securities
are actively traded on any recognized stock exchange or in the over-the-counter
market so long as Employee's holdings in such corporation or other entity do
not exceed five percent (5%) of the outstanding equity securities of any class
in such corporation or other entity.  The provisions of this Paragraph 3 shall
continue in effect notwithstanding the termination of Employee's employment
with the Employer for any reason.

         4.  Enforceability.  If, for any reason, any provision contained in
this Agreement should be held invalid by a court of competent jurisdiction,
then it is the intent of each of the parties hereto that the balance of this
Agreement be enforced to the fullest extent permitted by applicable law.
Accordingly, should a court of competent jurisdiction determine that the scope
of any covenant is too broad to be enforced as written, it is the intent of
each of the parties that the court should reform such covenant to such narrower
scope as it determines enforceable.

         5.  Binding Agreement.  This Agreement shall be binding upon and
inure to the benefit of Employee and his beneficiaries, devisees, heirs and
legal representatives, and the Company and its successors and assigns.  This
Agreement shall also bind and be applicable to any interest received by
Employee, by virtue of the interests granted hereunder, in any entity which is
a successor to the Company except to the extent otherwise expressly provided
herein.

         6.  Employee Representations.  Employee represents that he is
acquiring the Shares as an investment and not with a view to any sale or
distribution of all or any portion of the Shares.  Employee will hold the
Shares subject to all applicable provisions of the Securities





                                      -4-
<PAGE>   5
Act of 1933, as amended (the "Act"), and the rules and regulations promulgated
thereunder, and will not at any time make any sale, transfer or other
disposition of the Shares in contravention of the Act or such rules and
regulations.  Further, Employee represents that he will not make any
disposition or transfer of any of the Shares unless and until (a) he has given
the Company notice in writing of the proposed disposition or transfer and the
circumstances surrounding it, and (b) either (i) the Shares to be so disposed
of or transferred shall have been registered under the Act or (ii) counsel for
the Company or other counsel satisfactory to the Company shall have given a
written opinion that registration under the Act is not required.

         7.      Employment at Will.  The execution of this Agreement does not
enlarge or otherwise affect the terms of Employee's employment with the
Company, and the Company may terminate the employment of Employee at will and
as freely and with the same effect as if this Agreement had not been executed.

         IN WITNESS WHEREOF, this Agreement has been executed this _____ day of
February, 1997.



                                      BRIGHAM EXPLORATION COMPANY



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


                                      EMPLOYEE:



                                                                         
                                      --------------------------------------
                                      [See Schedule I attached]





                                      -5-
<PAGE>   6
                                   EXHIBIT A



BRIGHAM EXPLORATION COMPANY, A Delaware corporation

BRIGHAM OIL & GAS, L.P., A Delaware limited partnership

BRIGHAM, INC. (f/k/a Brigham Exploration Company), a Texas corporation

GENERAL ATLANTIC PARTNERS III, L.P., a Delaware limited partnership

GAP-BRIGHAM PARTNERS, L.P., a Delaware limited partnership

BEN M. BRIGHAM

ANNE L. BRIGHAM

HAROLD D. CARTER

RIMCO PARTNERS, L.P. II

RIMCO PARTNERS, L.P. III

RIMCO PARTNERS, L.P. IV





                                      -6-
<PAGE>   7
                                   Schedule I

Jon L. Glass

Craig M. Fleming

David T. Brigham





                                      -7-

<PAGE>   1
                                                                   EXHIBIT 10.32


                             UNCONDITIONAL GUARANTY


         THIS UNCONDITIONAL GUARANTY ("Guaranty") is made as of the 26th day of
March, 1997, by Guarantor (as hereinafter defined) for the benefit of Bank (as
hereinafter defined).

         A.      Definitions.  As used in this Guaranty, the following terms
shall have the meanings indicated below:

                 1.       The term "Bank" shall mean BANK ONE, TEXAS, NATIONAL
         ASSOCIATION, the address for notice purposes for the Bank is the
         following:

                          1717 Main Street, 4th Floor
                       Dallas, Dallas County, Texas 75201
                            Attn:  Mynan C. Feldman

                 2.       The term "Borrower" (whether one or more shall mean
                          the following:

                            Brigham Oil & Gas, L.P.
                          5949 Sherry Lane, Suite 1616
                              Dallas, Texas  75225

                 3.       The term "Guarantor" shall mean each of BRIGHAM
         EXPLORATION COMPANY and BRIGHAM, INC., whose address for notice
         purposes is the following:

                          5949 Sherry Lane, Suite 1616
                              Dallas, Texas  75225

                 4.       The term "Guaranteed Indebtedness" shall mean (i) all
         indebtedness, obligations and liabilities of Borrower to Bank of any
         kind or character now existing or hereafter arising, whether direct,
         indirect, related, unrelated, fixed, contingent, liquidated,
         unliquidated, joint, several or joint and several, and regardless of
         whether such indebtedness, obligations and liabilities may, prior to
         their acquisition by Bank, be or have been payable to or in favor of a
         third party and subsequently acquired by Bank (it being contemplated
         that Bank may make such acquisitions from third parties), including
         without limitation all indebtedness, obligations and liabilities of
         Borrower to Bank now existing or hereafter arising by note, draft,
         acceptance, guaranty, endorsement, letter of credit, assignment,
         purchase, overdraft, discount, indemnity agreement or otherwise, (ii)
         all accrued but unpaid interest on any of the indebtedness described
         in (i) above, (iii) all obligations of Borrower to Bank under any
         documents evidencing, securing, governing and/or pertaining to all or
         any part of the indebtedness described in (i) and (ii) above, (iv) all
         costs and expenses incurred by Bank in connection with the collection
         and administration of all or any part of the indebtedness and
         obligations described in (i), (ii) and (iii) above or the protection
         or preservation of, or realization upon, the collateral securing all
         or any part of such indebtedness and obligations,
<PAGE>   2
         including without limitation all reasonable attorneys' fees, and (v)
         all renewals, extensions, modifications and rearrangements of the
         indebtedness and obligations described in (i), (ii), (iii) and (iv)
         above.

         B.      Obligations.  As an inducement to Bank to extend or continue
to extend credit and other financial accommodations to Borrower, Guarantor, for
value received, does hereby unconditionally and absolutely guarantee the prompt
and full payment and performance of the Guaranteed Indebtedness when due
whether by its terms, by acceleration or otherwise, and at all times
thereafter.

         C.      Character of Obligations.  This is an absolute, continuing and
unconditional Guaranty of payment and not of collection and if at any time or
from time to time there is no outstanding Guaranteed Indebtedness, the
obligations of the Guarantor with respect to any and all Guaranteed
Indebtedness of Borrower to Bank incurred thereafter shall not be affected.
All Guaranteed Indebtedness heretofore, concurrently herewith or hereafter made
by Bank to Borrower shall be conclusively presumed to have been made or
acquired in acceptance hereof.  Guarantor shall be primarily liable, jointly
and severally, with Borrower and any other guarantor of all or any part of the
Guaranteed Indebtedness.

         D.      Representations and Warranties.  Guarantor hereby represents
and warrants the following to Bank:

                 1.       This Guaranty may reasonably be expected to benefit,
         directly or indirectly, Guarantor, and (i) if Guarantor is a
         corporation, the Board of Directors of Guarantor has determined that
         this Guaranty may reasonably be expected to benefit, directly or
         indirectly, Guarantor, or (ii) if Guarantor is a partnership, the
         requisite number of Guarantor's partners have determined that this
         Guaranty may reasonably be expected to benefit, directly or
         indirectly, Guarantor;

                 2.       Guarantor is familiar with, and has independently
         reviewed the books and records regarding, the financial condition of
         Borrower and is familiar with the value of any and all collateral
         intended to be security for the payment of all or any part of the
         Guaranteed Indebtedness; provided, however, Guarantor is not relying
         on such financial condition or collateral as an inducement to enter
         into this Guaranty;

                 3.       Guarantor has adequate means to obtain from Borrower
         on a continuing basis information concerning the financial condition
         of Borrower and Guarantor is not relying on Bank to provide such
         information to Guarantor either now or in the future;

                 4.       Guarantor has the power and authority to execute,
         deliver and perform this Guaranty and any other agreements executed by
         Guarantor contemporaneously herewith, and the execution, delivery and
         performance of this Guaranty and any other agreements executed by
         Guarantor contemporaneously herewith does not and will not violate (i)
         any agreement or instrument to which Guarantor is a party, (ii) any
         law, rule, regulation or 



                                      2
<PAGE>   3
         order of any governmental authority to which Guarantor is subject, or 
         (iii) Guarantor's Articles of Incorporation or Bylaws if Guarantor is 
         a corporation, or Guarantor's Partnership Agreement if Guarantor is a
         partnership;

                 5.       Neither Bank nor any other Bank or any other party
         has made any representation, warranty or statement to Guarantor in
         order to induce Guarantor to execute this Guaranty;

                 6.       The financial statements and other financial
         information regarding Guarantor heretofore and hereafter delivered to
         Bank are and shall be true and correct in all material respects and
         fairly present the financial position of Guarantor as of the dates
         thereof, and no material adverse change has occurred in the financial
         condition of Guarantor reflected in the financial statements and other
         financial information regarding Guarantor heretofore delivered to Bank
         since the date of the last statement thereof; and

                 7.       As of the date hereof, and after giving effect to
         this Guaranty and the obligations evidenced hereby, (i) Guarantor is
         and will be solvent, (ii) the fair saleable value of Guarantor's
         assets exceeds and will continue to exceed Guarantor's liabilities
         (both fixed and contingent), (iii) Guarantor is and will continue to
         be able to pay Guarantor's debts as they mature, and (iv) if Guarantor
         is not an individual, Guarantor has and will continue to have
         sufficient capital to carry on its business and all businesses in
         which it is about to engage.

         E.      Covenants.  Guarantor hereby covenants and agrees with Bank as
follows:

                 1.       As soon as available and in any event within ninety
         (90) days after the end of each fiscal year of Brigham Exploration
         Company ("BEC"), BEC shall deliver to Bank consolidated and
         consolidating annual financial statements of BEC consisting of at
         least a balance sheet, statement of cash flow and statement of
         contingent liabilities, prepared in a form acceptable to Bank and in a
         manner consistent with prior periods;

                 2.       Guarantor shall promptly notify Bank if it becomes
         aware of the occurrence of any Event of Default or of any fact,
         condition or event that only with the giving of notice or passage of
         time or both, could become an Event of Default, or of the failure of
         the Guarantor to observe any of its undertakings hereunder, or of any
         materially adverse change in the financial condition of the Borrower
         or the Guarantor;

                 3.       Guarantor shall promptly give written notice to Bank
         of (i) any action, proceeding or claim, of which Guarantor may have
         notice, which may be commenced or asserted against Guarantor or relate
         to this Guaranty, and (ii) any dispute which may exist between
         Guarantor and any governmental regulatory body, which in either case
         may substantially affect the properties and assets of Guarantor, and
         (iii) contingent liabilities, whether asserted or unasserted, of
         Guarantor which exceed $100,000 individually or in the aggregate;





                                       3
<PAGE>   4
                 4.       Guarantor shall duly pay and discharge (i) all taxes,
         assessments and governmental charges or levies imposed upon or against
         Guarantor or Guarantor's property or assets, or upon any property
         leased by Guarantor, prior to the date on which penalties attach
         thereto, unless and to the extent only that such taxes, assessments
         and governmental charges or levies are being contested in good faith
         and by appropriate proceedings, and (ii) all lawful claims, whether
         for labor, materials, supplies, services or anything else, which might
         or could, if unpaid, become a lien or charge upon the property or
         assets of Guarantor, unless and to the extent only that the validity
         thereof is being contested in good faith and by appropriate
         proceedings;

                 5.       Guarantor shall allow any representative of Bank to
         visit and inspect any of its property, to examine its books of record
         and account and to discuss its affairs, finances and accounts with any
         of its officers, employees and agents, all at such reasonable times
         during usual business hours and as often as Bank may reasonably
         request;

                 6.       Guarantor shall not incur, create, assume, have
         outstanding, guaranty or otherwise be or become, directly or
         indirectly, liable in respect of any Indebtedness except: (i)
         presently existing indebtedness reflected on the most recent financial
         statements delivered by Guarantor to Bank prior to the date hereof;
         and (ii) indebtedness as allowed under that certain Loan Agreement
         dated April 1, 1996 between Borrower and Bank, as from time to time
         amended (the "Loan Agreement");

                 7.       Guarantor shall comply with all terms and provisions
         of the instruments and agreements evidencing, governing and securing
         all or any part of the Guaranteed Indebtedness that apply to
         Guarantor; and

                 8.       Guarantor shall promptly furnish to Bank at any time
         and from time to time such other financial information of Guarantor as
         Bank may reasonably require, in form and substance satisfactory to
         Bank.

         F.      Consent and Waiver.

                 1.       Guarantor waives (i) promptness, diligence and notice
         of acceptance of this Guaranty and notice of the incurring of any
         obligation, indebtedness or liability to which this Guaranty applies
         or may apply and waives presentment for payment, notice of nonpayment,
         protest, demand, notice of protest, notice of intent to accelerate,
         notice of acceleration, notice of dishonor, diligence in enforcement
         and indulgences of every kind, and (ii) the taking of any other action
         of Bank, including without limitation giving any notice of default or
         any other notice to, or making any demand on, Borrower, any other
         guarantor of all or any part of the Guaranteed Indebtedness or any
         other party.





                                       4
<PAGE>   5
                 2.       Guarantor waives any rights Guarantor has under, or
         any requirements imposed by, Chapter 34 of the Texas Business and
         Commerce Code, as in effect on the date of this Guaranty or as it may
         be amended from time to time.

                 3.       Bank may at any time, without the consent of or
         notice to Guarantor, without incurring responsibility to Guarantor and
         without impairing, releasing, reducing or affecting the obligations of
         Guarantor hereunder:  (i) change the manner, place or terms of payment
         of all or any part of the Guaranteed Indebtedness, or renew, extend,
         modify, rearrange or alter all or any part of the Guaranteed
         Indebtedness; (ii) sell, exchange, release, surrender, subordinate,
         realize upon or otherwise deal with in any manner and in any order any
         collateral for all or any part of the Guaranteed Indebtedness or this
         Guaranty or setoff against all or any part of the Guaranteed
         Indebtedness; (iii) neglect, delay, omit, fail or refuse to take or
         prosecute any action for the collection of all or any part of the
         Guaranteed Indebtedness or this Guaranty or to take or prosecute any
         action in connection with any instrument or agreement evidencing,
         governing or securing all or any part of the Guaranteed Indebtedness
         or this Guaranty; (iv) exercise or refrain from exercising any rights
         against Borrower or others, or otherwise act or refrain from acting;
         (v) settle or compromise all or any part of the Guaranteed
         Indebtedness and subordinate the payment of all or any part of the
         Guaranteed Indebtedness to the payment of any obligations,
         indebtedness or liabilities which may be due or become due to Bank or
         others; (vi) apply any deposit balance, fund, payment, collections
         through process of law or otherwise or other collateral of Borrower to
         the satisfaction and liquidation of the indebtedness or obligations of
         Borrower to Bank not guaranteed under this Guaranty pursuant to
         paragraph 4 herein; and (vii) apply any sums paid to Bank by
         Guarantor, Borrower or others to the Guaranteed Indebtedness in such
         order and manner as Bank, in their sole discretion, may determine.

                 4.       Notwithstanding any provision in this Guaranty to the
         contrary, Guarantor hereby waives and releases (i) any and all rights
         of subrogation, reimbursement, indemnification or contribution which
         Guarantor may have, after payment in full or in part of the Guaranteed
         Indebtedness, against others liable on all or any part of the
         Guaranteed Indebtedness, (ii) any and all rights to be subrogated to
         the rights of Bank in any collateral or security for all or any part
         of the Guaranteed Indebtedness after payment in full or in part of the
         Guaranteed Indebtedness, and (iii) any and all other rights and claims
         of such Guarantor against Borrower or any third party as a result of
         such Guarantor's payment of all or any part of the Guaranteed
         Indebtedness.

                 5.       Should Bank seek to enforce the obligations of
         Guarantor hereunder by action in any court or otherwise, Guarantor
         waives any requirement, substantive or procedural, that (i) Bank first
         enforce any rights or remedies against Borrower or any other person or
         entity liable to Bank for all or any part of the Guaranteed
         Indebtedness, including without limitation that a judgment first be
         rendered against Borrower or any other person or entity, or that
         Borrower or any other person or entity should be joined in such cause,
         or (ii) Bank shall first enforce rights against any collateral which
         shall





                                       5
<PAGE>   6
         ever have been given to secure all or any part of the Guaranteed
         Indebtedness or this Guaranty.  Such waiver shall be without prejudice
         to Bank' right, at its option, to proceed against Borrower or any
         other person or entity, whether by separate action or by joinder.

                 6.       In addition to any other waivers, agreements and
         covenants of Guarantor set forth herein, Guarantor hereby further
         waives and releases all claims, causes of action, defenses and offsets
         for any act or omission of Bank, their directors, officers, employees,
         representatives or agents in connection with Bank's administration of
         the Guaranteed Indebtedness, except for Bank's willful misconduct and
         gross negligence.

         G.      Obligations Not Impaired.

                 1.       Guarantor agrees that Guarantor's obligations
         hereunder shall not be released, diminished, impaired, reduced or
         affected by the occurrence of any one or more of the following events:
         (i) the death, disability or lack of corporate power of Borrower,
         Guarantor or any other guarantor of all or any part of the Guaranteed
         Indebtedness, (ii) any receivership, insolvency, bankruptcy or other
         proceedings affecting Borrower, Guarantor or any other guarantor of
         all or any part of the Guaranteed Indebtedness, or any of their
         respective property; (iii) the partial or total release or discharge
         of Borrower or any other guarantor of all or any part of the
         Guaranteed Indebtedness, or any other person or entity from the
         performance of any obligation contained in any instrument or agreement
         evidencing, governing or securing all or any part of the Guaranteed
         Indebtedness, whether occurring by reason of law or otherwise; (iv)
         the taking or accepting of any collateral for all or any part of the
         Guaranteed Indebtedness or this Guaranty; (v) the taking or accepting
         of any other guaranty for all or any part of the Guaranteed
         Indebtedness; (vi) any failure by Bank to acquire, perfect or continue
         any lien or security interest on collateral securing all or any part
         of the Guaranteed Indebtedness or this Guaranty; (vii) the impairment
         of any collateral securing all or any part of the Guaranteed
         Indebtedness or this Guaranty; (viii) any failure by Bank to sell any
         collateral securing all or any part of the Guaranteed Indebtedness or
         this Guaranty in a commercially reasonable manner or as otherwise
         required by law; (ix) any invalidity or unenforceability of or defect
         or deficiency in any instrument or agreement evidencing, governing or
         securing all or any part of the Guaranteed Indebtedness or this
         Guaranty; or (x) any other circumstances which might otherwise
         constitute a defense available to, or discharge of, Borrower or any
         other guarantor of all or any part of the Guaranteed Indebtedness.

                 2.       This Guaranty shall continue to be effective or be
         reinstated, as the case may be, if at any time any payment of all or
         any part of the Guaranteed Indebtedness is rescinded or must otherwise
         be returned by Bank upon the insolvency, bankruptcy or reorganization
         of Borrower, Guarantor, any other guarantor of all or any part of the
         Guaranteed Indebtedness, or otherwise, all as though such payment had
         not been made.





                                       6
<PAGE>   7
                 3.       In the event Borrower is a corporation, joint stock
         association or partnership, or is hereafter incorporated, none of the
         following shall affect Guarantor's liability hereunder:  (i) the
         unenforceability of all or any part of the Guaranteed Indebtedness
         against Borrower by reason of the fact that the Guaranteed
         Indebtedness exceeds the amount permitted by law; (ii) the act of
         creating all or any part of the Guaranteed Indebtedness is ultra
         vires; or (iii) the officers or partners creating all or any part of
         the Guaranteed Indebtedness acted in excess of their authority.
         Guarantor hereby acknowledges that withdrawal from, or termination of,
         any ownership interest in Borrower now or hereafter owned or held by
         Guarantor shall not alter, affect or in any way limit the obligations
         of Guarantor hereunder.

         H.      Subordination.  If Borrower is now or hereafter becomes
indebted to Guarantor (such indebtedness and all interest thereon is referred
to as the "Affiliated Debt"), such Affiliated Debt shall be subordinate in all
respects to Borrower's full payment and performance of the Guaranteed
Indebtedness, and Guarantor shall not be entitled to enforce or receive payment
thereof while any Event of Default exists under the Loan Agreement, until all
of the Guaranteed Indebtedness of Borrower to Bank have been paid.  Guarantor
agrees that any liens, mortgages, deeds of trust, security interests, judgment
liens, charges or other encumbrances upon Borrower's assets securing the
payment of the Affiliated Debt shall be and remain subordinate and inferior to
any liens, security interests, judgment liens, charges or other encumbrances
upon Borrower's assets securing the payment of the Guaranteed Indebtedness, and
without the prior written consent of Bank, Guarantor shall not exercise or
enforce any creditor's rights of any nature against borrower to collect the
Affiliated Debt (other than demand payment therefor).  In the event of the
receivership, bankruptcy, reorganization, arrangement, debtor's relief or other
insolvency proceedings involving Borrower as a debtor, Bank has the right and
authority, either in its own name or as attorney-in-fact for Guarantor, to file
such proof of debt, claim, petition or other documents and to take such other
steps as are necessary to prove the rights of Bank hereunder and receive
directly from the receiver, trustee or other court custodian, payments,
distributions or other dividends which would otherwise be payable upon the
Affiliated Debt.  Guarantor hereby assigns such payments, distributions and
dividends to Bank, and irrevocably appoints Bank as its true and lawful
attorney-in-fact with authority to make and file in the name of Guarantor any
proof of debt, amendment of proof of debt, claim, petition or other document in
such proceedings and to receive payment of any sums becoming distributable on
account of the Affiliated Debt, and to execute such other documents and to give
acquittances therefor and to do and perform all such other facts and things for
and on behalf of Guarantor as may be necessary in the opinion of Bank in order
to have the Affiliated Debt allowed in any such proceeding and to receive
payments, distributions or dividends of or on account of the Affiliated Debt.

         I.      Actions against Guarantor.  In the event of a default in the
payment or performance of all or any part of the Guaranteed Indebtedness when
such Guaranteed Indebtedness becomes due, whether by its terms, by acceleration
or otherwise, Guarantor shall, without notice or demand, promptly pay the
amount due thereon to Bank, in lawful money of the United States, at Bank'
address set forth hereinabove.  One or more successive or concurrent





                                       7
<PAGE>   8
actions may be brought against Guarantor, either in the same action in which
Borrower is sued or in separate actions, as often as Bank deems advisable.  The
exercise by Bank of any right or remedy under this Guaranty or under any other
agreement or instrument, at law, in equity or otherwise, shall not preclude
concurrent or subsequent exercise of any other right or remedy.  The books and
records of Bank shall be admissible in evidence in any action or proceeding
involving this Guaranty and shall be prima facie evidence of the payments made
on, and the outstanding balance of, the Guaranteed Indebtedness.

         J.      Payment by Guarantor.  Whenever Guarantor pays any sum which
is or may become due under this Guaranty, written notice must be delivered to
Bank contemporaneously with such payment.  Such notice shall be effective for
purposes of this paragraph when contemporaneously with such payment Bank
receives such notice either by: (a) personal delivery to the address and
designated department of Bank identified in subparagraph A(1) above, or (b)
United States mail, certified or registered, return receipt requested, postage
prepaid, addressed to Bank at the address shown in subparagraph A(1) above.  In
the absence of such notice to Bank by Guarantor in compliance with the
provisions hereof, any sum received by Bank on account of the Guaranteed
Indebtedness shall be conclusively deemed paid by Borrower.

         K.      Notice of Sale.  In the event that Guarantor is entitled to
receive any notice under the Uniform Commercial Code, as it exists in the state
governing any such notice, of the sale or other disposition of any collateral
securing all or any part of the Guaranteed Indebtedness or this Guaranty,
reasonable notice shall be deemed given when such notice is deposited in the
United States mail, postage prepaid, at the address for Guarantor set forth in
subparagraph A(3) above, five (5) days prior to the date any public sale, or
after which any private sale, of any such collateral is to be held; provided,
however, that notice given in any other reasonable manner or at any other
reasonable time shall be sufficient.

         L.      Right of Offset.  Guarantor hereby grants to Bank a right of
offset at any time or from time to time, without notice to Guarantor or any
other person, any such notice being hereby waived, upon any and all monies,
securities or other property of Guarantor and the proceeds therefrom, now or
hereafter held or received by or in transit to Bank, for the account of
Guarantor, whether for safekeeping, custody, pledge, transmission, collection
or otherwise, and also upon any and all deposits (general or special, time or
demand, provisional or final) and any other indebtedness at any time held or
owing by Bank to or for the credit of the account of Guarantor, and any and all
claims of Guarantor against Bank at any time existing, regardless of whether
such Bank has made any demand hereunder.

         M.      Waiver of Bank.  No delay on the part of Bank in exercising
any right hereunder or failure to exercise the same shall operate as a waiver
of such right.  In no event shall any waiver of the provisions of this Guaranty
be effective unless the same be in writing and signed by an officer of each
Bank, and then only in the specific instance and for the purpose given.

         N.      Successors and Assigns.  This Guaranty is for the benefit of
Bank, their successors and assigns.  This Guaranty is binding upon Guarantor's
heirs, executors,





                                       8
<PAGE>   9
administrators, personal representatives and successors, including without
limitation any person or entity obligated by operation of law upon the
reorganization, merger, consolidation or other change in the organizational
structure of Guarantor.

         O.      Costs and Expenses.  Guarantor shall pay on demand by Bank all
costs and expenses (including without limitation all reasonable attorneys'
fees) incurred by Bank in connection with the preparation, administration,
enforcement and/or collection of this Guaranty.  This covenant shall survive
the payment of the Guaranteed Indebtedness.

         P.      Severability.  If any provision of this Guaranty is held by a
court of competent jurisdiction to be illegal, invalid or enforceable under
present or future laws, such provision shall be fully severable, shall not
impair or invalidate the remainder of this Guaranty and the effect thereof
shall be confined to the provision held to be illegal, invalid or
unenforceable.

         Q.      No Obligation.  Nothing contained herein shall be construed as
an obligation on the part of Bank to extend or continue to extend credit to
Borrower.

         R.      Amendment.  No modification or amendment of any provision of
this Guaranty, nor consent to any departure by Guarantor therefrom, shall be
effective unless the same shall be in writing and signed by an officer of Bank,
and then shall be effective only in the specific instance and for the purpose
for which given.

         S.      Cumulative Rights.  All rights and remedies of Bank hereunder
are cumulative of each other and of every other right or remedy which Bank may
otherwise have at law or in equity or under any instrument or agreement, and
the exercise of one or more of such rights or remedies shall not prejudice or
impair the concurrent or subsequent exercise of any other rights or remedies.

         T.      Governing Law.  THIS GUARANTY SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS AND APPLICABLE
FEDERAL LAWS.

         U.      Venue.  This Guaranty has been entered into in the county in
Texas where Bank's address for notice purposes is located, and it shall be
performable for all purposes in such county.  Courts within the State of Texas
shall have jurisdiction over any and all disputes arising under or pertaining
to this Guaranty and venue for any such disputes shall be in the county or
judicial district where the Bank's address for notice purposes is located.

         V.      Compliance with Applicable Usury Laws.  Notwithstanding any
other provision of this Guaranty or of any instrument or agreement evidencing,
governing or securing all or any part of the Guaranteed Indebtedness, Guarantor
and Bank by its acceptance hereof agree that Guarantor shall never be required
or obligated to pay interest in excess of the maximum nonusurious interest rate
as may be authorized by applicable law for the written contracts which
constitute the Guaranteed Indebtedness.  It is the intention of Guarantor and
Bank to conform





                                       9
<PAGE>   10
strictly to the applicable laws which limit interest rates, and any of the
aforesaid contracts for interest, if and to the extent payable by Guarantor,
shall be held to be subject to reduction to the maximum nonusurious interest
rate allowed under said law.

         W.      Descriptive Headings.  The captions in this Guaranty are for
convenience only and shall not define or limit the provisions hereof.

         X.      Gender.  Within this Guaranty, words of any gender shall be
held and construed to include the other gender.

         Y.      Entire Agreement.  THIS GUARANTY REPRESENTS THE FINAL
AGREEMENT BETWEEN GUARANTOR AND BANK REGARDING THE SUBJECT MATTER HEREOF AND
MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR SUBSEQUENT
ORAL AGREEMENTS OF THE PARTIES; PROVIDED, HOWEVER, THIS GUARANTY IS IN ADDITION
TO AND DOES NOT REPLACE, CANCEL, MODIFY OR AFFECT ANY OTHER GUARANTY OF
GUARANTOR NOW OR HEREAFTER HELD BY BANK THAT RELATES TO BORROWER OR ANY OTHER
PERSON OR ENTITY.  THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

         EXECUTED as of the date first above written.

                                 GUARANTOR:
                                 --------- 

                                 Brigham Exploration Company


                                 By: /s/ CRAIG M. FLEMING
                                    -------------------------------------------

                                 Name: Craig M. Fleming
                                      -----------------------------------------

                                 Title: Chief Financial Officer
                                       ----------------------------------------


                                 GUARANTOR:
                                 --------- 

                                 Brigham, Inc.


                                 By: /s/ CRAIG M. FLEMING
                                    -------------------------------------------

                                 Name: Craig M. Fleming
                                      -----------------------------------------

                                 Title: Chief Financial Officer
                                       ----------------------------------------





                                       10

<PAGE>   1
                                                                   EXHIBIT 10.33


                          AGREEMENT AND ASSIGNMENT OF
                 INTEREST IN GEOPHYSICAL EXPLORATION AGREEMENT
                             ESPERSON DOME PROJECT
                       LIBERTY AND HARRIS COUNTIES, TEXAS


         This Agreement and Assignment of Interest in the Geophysical
Exploration Agreement, Esperson Dome Project, Liberty and Harris Counties,
Texas (hereinafter referred to as the "Assignment") is made and entered into
effective as of the 1st day of November, 1994, by and between BRIGHAM OIL &
GAS, L.P. ("BOG") and VAQUERO GAS COMPANY, INC.  ("Vaquero") (BOG and Vaquero
are sometimes individually referred to herein as a "Party" and collectively
referred to herein as the "Parties").

                              W I T N E S S E T H:

         WHEREAS, BOG, Ameritex Minerals and Exploration, Ltd. ("AMX"), Bright
and Company ("Bright"), DDD Energy, Inc.  ("DDD"), RIMCO Production Company,
Inc. ("RPC"), RIMCO Exploration Partners, L.P.I ("REPI"), RIMCO Production
Partners, L.P.II ("REPII"), and Wilcox Oil & Gas, Inc. ("Wilcox") entered into
that certain Geophysical Exploration Agreement, Esperson Dome Project, Liberty
and Harris Counties, Texas, dated  November 1, 1994 (hereinafter referred to as
the "Exploration Agreement"), regarding the exploration and development of an
area of mutual interest (as more particularly described in the Exploration
Agreement and being hereinafter referred to as the "AMI") in Liberty and Harris
Counties, Texas (such lands as from time to time may be included within the AMI
are hereinafter referred to as the "Subject Lands"); and

         WHEREAS, BOG is interested in assigning its interest in the
Exploration Agreement and all rights and property interests related thereto to
Vaquero pursuant to the terms, provisions and reservations which are set forth
in this Assignment; and

         WHEREAS, Vaquero is interested in acquiring BOG's interest in the
Exploration Agreement and all rights and property interests related thereto
pursuant to the terms, provisions and reservations set forth herein;

         NOW, THEREFORE, for and in consideration of the mutual covenants
contained herein and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Parties hereto agree as
follows:

                                   ARTICLE I.
                              TERMS OF ASSIGNMENT

         Section 1.1.     Assignment of Interest in Exploration Agreement.  BOG
hereby grants, bargains, sells, assigns and conveys to Vaquero (a) all of BOG's
right, title and interest in, to and under the Exploration Agreement and (b)
all of BOG's right, title and interest in all Acquired Interests, Leases,
Options and Farm-Ins (as such terms are defined in the Exploration Agreement)
and all other property rights of every kind (whether legal or equitable, vested
or contingent) obtained under or in any way related to the Exploration
Agreement or otherwise covering or related to the Subject Lands, whether same
be now owned or hereafter acquired by Vaquero, reserving unto BOG, however, the
NPORRI, the PO#1 Interest and the PO#2 Interest, as such terms are hereinafter
defined (the properties, rights and interests described in (a) and (b) above,
subject to and less and except the properties, rights and interests reserved to
BOG hereunder, are herein collectively called the "Conveyed Interests").
Subject to such reservations, and further subject to the terms and provisions
of Section 1.5, 1.6 and 1.7 below, Vaquero hereby owns all of BOG's rights
under the Exploration Agreement to participate in Acquired Interests, Leases,
Options, Farm-Ins (as such terms are defined in the Exploration Agreement) and
other interests in or relating to oil, gas or other minerals in which BOG has
the right to participate and acquire an interest pursuant to the terms of the
Exploration Agreement.  Except as expressly provided herein to the contrary,
BOG also grants, bargains, sells and conveys to Vaquero all rights and benefits
under the Exploration Agreement which are appurtenant to or related to the
Exploration Agreement and the ownership of Acquired Interests, Leases, Options
and Farm-Ins relating to the Subject Lands.  Anything to the contrary contained
herein notwithstanding, BOG shall retain (i) the rights and responsibilities
set forth in Section 2.1 and elsewhere in the Exploration Agreement to conduct
and/or supervise the conduct of the Geophysical Program (as such term is
defined in the Exploration Agreement), and (ii) the right
<PAGE>   2
to receive the amounts that are to be paid to BOG for the use of its equipment
and personnel during the planning, processing and interpretation of the seismic
data as set forth in Section 2.3(a) of the Exploration Agreement.

         Section 1.2.     Vaquero Responsibility for Costs and Liabilities
Related to the Exploration Agreement and the Conveyed Interests.  Subject to
the terms and provisions of Sections 2.2 and 2.3 below, Vaquero hereby agrees
to assume and be responsible for, and indemnify and hold BOG harmless from, all
costs, expenses and liabilities that are incurred under the Exploration
Agreement or which are in any way associated with the Conveyed Interests.
Concurrent with the execution of this Assignment Vaquero agrees to pay all
costs and expenses which are allocated to the Conveyed Interests and which are
currently due under the terms of the Exploration Agreement, including without
limitation, all payments which are due pursuant to the terms of Section 1.3 of
the Exploration Agreement (being BOG's $171,754.44 share of the Historical
Costs) and the payment of the estimated Original Geophysical Program Costs
under Section 2.3(c) of the Exploration Agreement (being BOG's $941,670.00
share of such estimated costs).  Vaquero shall pay all other costs and expenses
that are related to the Exploration Agreement and allocated to the Conveyed
Interests in accordance with the terms set forth in the Exploration Agreement.

         Section 1.3.     Vaquero's Interests Subject to the Terms of the
Exploration Agreement.  Vaquero hereby recognizes and agrees that it is subject
to all of the terms and provisions of the Exploration Agreement and the
Conveyed Interests are subject to the terms, provisions and reservations set
forth in the Exploration Agreement.

         Section 1.4.     Vaquero Indemnification.  Vaquero hereby agrees to
assume, indemnify and hold BOG and its officers, employees, successors and
assigns, harmless from any and all liabilities, claims and responsibilities of
any kind whatsoever which are related in any way to its ownership of the
Conveyed Interests or otherwise under the Exploration Agreement and any
operations of any kind which are conducted in, on or relating to the Subject
Lands or otherwise which are conducted under the Exploration Agreement,
REGARDLESS OF WHETHER OR NOT SUCH LIABILITIES, CLAIMS OR RESPONSIBILITIES ARE
FOUND TO RESULT IN WHOLE OR IN PART FROM THE SOLE OR CONCURRENT NEGLIGENCE OR
OTHER FAULT OF BOG OR ITS OFFICERS, EMPLOYEES, SUCCESSORS OR ASSIGNS; provided,
however that Vaquero shall not be required to assume, indemnify or hold BOG or
its officers, employees, successors or assigns harmless from any liabilities,
claims or responsibilities which are related to operations which are conducted
after interests have been assigned to BOG pursuant to the terms of Sections 2.2
and 2.3 below, to the extent that such liabilities, claims or responsibilities
arise after such date and are allocated to the interests assigned to BOG or its
successors or assigns.

         Section 1.5.     Non-Consent Elections as to Acquired Interests.
Vaquero hereby agrees that in the event that an Acquired Interest (as such term
is defined in Section 3.5 of the Exploration Agreement) is obtained by another
party to the Exploration Agreement within the Subject Lands and Vaquero intends
to elect not to participate in the Acquired Interest or intends not to acquire
any other non-consent interests that may be available with respect to such
Acquired Interest, Vaquero shall notify BOG of such intent within a reasonable
amount of time, but in no event less than fifteen (15) days prior to the due
date for such election, and BOG shall have the option to receive an assignment
of Vaquero's right to participate in such Acquired Interest.  In such event,
Vaquero shall execute all conveyance instruments and perform any other acts
that may be necessary to vest BOG with such right to participate in the
Acquired Interest.  The Parties recognize and agree that this Section 1.5 shall
not prevent Vaquero from assigning or farming out its right to acquire its
interest in an Acquired Interest to a third-party (subject to the terms of
Article IV below); provided, however, that in the event that such third-party
assignee intends to elect not to participate in the Acquired Interest, BOG
shall be notified of such intent within a reasonable amount of time, but in no
event less than fifteen (15) days prior to the due date for such election, and
BOG shall have the option to receive an assignment of the right to participate
in the Acquired Interest as set forth in this Section 1.5.

         Section 1.6.     Non-Consent Elections as to Participation in Prospect
Areas.  Vaquero hereby agrees that in the event that it intends to elect not to
participate in a designated Prospect





Vaquero Gas Company, Inc.
Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project               2
<PAGE>   3
Area (as such term is defined in the Exploration Agreement) as provided in
Article IV of the Exploration Agreement, Vaquero shall notify BOG of such
intent within a reasonable amount of time, but in no event less than fifteen
(15) days prior to the due date for such election, and BOG shall have the
option to participate in such Prospect Area and receive an assignment of all of
Vaquero's interest in that part of all Leases, Options and Farm-Ins that would
have been relinquished by Vaquero in the event that it had elected not to
participate in the Prospect Area.  In such event, Vaquero shall execute all
conveyance instruments and perform any other acts that may be necessary to vest
BOG with such interests.  The Parties recognize and agree that this Section 1.6
shall not prevent Vaquero from assigning or farming out its right to
participate in a Prospect Area to a third-party (subject to the terms of
Article IV below); provided, however, that in the event that such third-party
assignee intends to elect not to participate in the Prospect Area, BOG shall be
notified of such intent within a reasonable amount of time, but in no event
less than fifteen (15) days prior to the due date for such election, and BOG
shall have the option to receive an assignment of the right to participate in
the Prospect Area and receive an assignment of all of the interests in the
Prospect Area as set forth in this Section 1.6.

         Section 1.7.     Non-Consent Elections as to Participation in Well
Operations.  Vaquero hereby agrees that in the event that it intends to elect
not to participate in the drilling or completion of a well that is drilled
within the Subject Lands, Vaquero shall notify BOG of such intent within a
reasonable amount of time, but in no event less than fifteen (15) days prior to
the due date for an election to participate in the drilling of a well or less
than twelve (12) hours prior to the expiration of the time for an election to
participate in a completion operation, and BOG shall have the option to
participate in such operation and acquire Vaquero's interest in the operation
and that part of all Leases, Options and Farm-Ins that would have been
relinquished by Vaquero in the event that it had elected not to participate in
the operation.  In such event, Vaquero shall execute all conveyance instruments
and perform any other acts that may be necessary to vest BOG with such
interests.  The Parties recognize and agree that this Section 1.7 shall not
prevent Vaquero from assigning or farming out its right to participate in the
drilling or completion of a well that is drilled within the Subject Lands to a
third-party (subject to the terms of Article IV below); provided, however, that
in the event that such third-party assignee intends to elect not to participate
in a drilling or completion operation within the Subject Lands, BOG shall be
notified of such intent within a reasonable amount of time, but in no event
less than fifteen (15) days prior to the due date for an election to
participate in the drilling of a well or less than twelve (12) hours prior to
the expiration of the time for an election to participate in a completion
operation, and BOG shall have the option to receive an assignment of the right
to participate in such drilling or completion operation and receive an
assignment of all of the interests that would have been relinquished in the
event that it had not participated in the operation as set forth in this
Section 1.7.

         Section 1.8.     Shorter Election Periods.  Anything to the contrary
contained in Sections 1.5, 1.6 and 1.7 above notwithstanding, in no event shall
Vaquero or its assignee be required to notify BOG of Vaquero's intent to elect
not to participate in an Acquired Interest, Prospect Area, drilling or
completion operation in less than one-half of the time that is allowed for the
election under the terms of the Exploration Agreement or the form Joint
Operating Agreement which is attached as Exhibit E to the Exploration Agreement
(such form Joint Operating Agreement being hereinafter referred to as the "Form
Joint Operating Agreement").

                                  ARTICLE II.
                        BOG NPORRI AND BACK-IN INTERESTS

         Section 2.1.     Net Revenues Obtained Prior to Payout #1.  Until the
occurrence of Payout #1 (as such term is defined below), BOG hereby reserves to
itself and its successors and assigns a net profits overriding royalty interest
(herein defined as the "NPORRI") in, to and carved out of the Subject
Hydrocarbons (as such term is defined below), equal to and measured by five
percent (5%) of the Net Revenues (as such term is defined below) that are
realized from or otherwise are attributable to production of Subject
Hydrocarbons, from and after the effective date hereof.  Payout #1 shall occur
on the last day of the calendar month during which the Net Revenues received by
or otherwise allocable to Vaquero (less and except the NPORRI), from and after
the effective date hereof, (a) equal or exceed one hundred percent (100%) of
all of the direct costs (excluding any costs for overhead, office
administration, insurance, amortization or





Vaquero Gas Company, Inc.
Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project               3
<PAGE>   4
depreciation) incurred and paid by Vaquero under the terms of the Exploration
Agreement, including without limitation, all Historical Costs, Geophysical
Program Costs, Spudding Bonus (as such terms are defined in the Exploration
Agreement), land acquisition and maintenance costs, and drilling and completion
costs (such costs being hereinafter collectively referred to as the "Direct
Costs"), such Direct Costs in no event include any lease operating expenses or
taxes deducted in calculating Net Revenues as described below, and (b) provide
Vaquero with a fifteen percent (15%) cash on cash annualized rate of return on
such Direct Costs.  As used herein, the term "Subject Hydrocarbons" shall mean
all of Vaquero's right, title and interest (whether legal or equitable, vested
or contingent, and whether now owned or hereafter acquired, by operation of law
or otherwise) in and to (i) any oil, gas or other minerals in, under or that
may be produced from the Subject Lands, and/or (ii) any oil, gas or other
minerals (or the proceeds thereof) that may otherwise be allocated to Vaquero
under or pursuant to the Exploration Agreement.  In addition, as used herein
the term "Net Revenues" shall mean all of the gross revenues received by or
otherwise allocable to Vaquero, from and after the effective date hereof, to
the extent same are from or attributable to the Subject Hydrocarbons, less all
lease operating expenses attributable to production of Subject Hydrocarbons and
all production, severance, ad valorem, excise and other taxes (other than
income taxes) attributable to or measured by production of Subject
Hydrocarbons.  Vaquero shall remit to BOG the Net Revenues attributable to its
NPORRI on or before the last day of the month immediately subsequent to the
month in which the revenues are actually received by Vaquero.

         Section 2.2.     Assignment to BOG Upon Payout #1.  BOG hereby
reserves to itself and its successors and assigns the PO#1 Interest (as such
term is defined below) which shall be triggered upon the occurrence of Payout
#1 and which shall remain in effect in perpetuity thereafter.  Upon the
occurrence of Payout #1, Vaquero shall assign and convey to BOG the PO#1
Interest, with the PO#1 Interest being defined as an undivided forty percent
(40%) of all of Vaquero's right, title and interest in and to the Exploration
Agreement and all property interests (real, personal, tangible or intangible)
obtained or owned by Vaquero under the terms of the Exploration Agreement
and/or this Assignment, including without limitation, an undivided forty
percent (40%) of Vaquero's interest in all Program Data, Leases, Options and
Farm-Ins (as such terms are defined in the Exploration Agreement) and any and
all wells that have been drilled or are drilling on the Subject Lands as of the
occurrence of Payout #1.  Upon the occurrence of Payout #1, BOG shall become
responsible for all future costs, expenses and liabilities which are incurred
and allocated to the PO#1 Interest from and after the occurrence of Payout #1.

         Section 2.3.     Additional Assignment to BOG Upon Payout #2.  BOG
hereby reserves to itself and its successors and assigns the PO#2 Interest (as
such term is defined below) which shall be triggered upon the occurrence of
Payout #2 (as such term is defined below) and which shall remain in effect in
perpetuity thereafter.  Upon the occurrence of Payout #2, Vaquero shall assign
and convey the PO#2 Interest to BOG, with the PO#2 Interest being defined as an
additional ten percent (10%) of all of Vaquero's right, title and interest
(being 10% of the amount of Vaquero's interest that existed prior to the
assignment described in Section 2.2 above, not 10% of Vaquero's remaining
interest after such assignment) in and to the Exploration Agreement and all
property interests (real, personal, tangible or intangible) obtained or owned
by Vaquero under the terms of the Exploration Agreement and this Assignment,
including without limitation, an undivided ten percent (10%) of Vaquero's
interest in all Program Data, Leases, Options and Farm-Ins and any and all
wells that have been drilled or are drilling within the Subject Lands as of the
occurrence of Payout #2.  Payout #2 shall occur on the last day of the calendar
month during which the Net Revenues received by or otherwise allocable to
Vaquero, from and after the effective date hereof, equal or exceed one hundred
percent (100%) of the Direct Costs incurred and paid by Vaquero under the
Exploration Agreement and provides Vaquero with a thirty-five percent (35%)
cash on cash annualized rate of return.  Upon the occurrence of Payout #2, BOG
shall become responsible for all future costs, expenses and liabilities which
are incurred and allocated to the PO#2 Interest from and after the occurrence
of Payout #2.

         Section 2.4.     BOG's Right to Contribute Cash Toward Payout.  At any
time during the term of this Assignment BOG shall, in its sole discretion, have
the right and option, from time to time, to pay Vaquero cash consideration in
an effort to cause Payout #1 or Payout #2 to





Vaquero Gas Company, Inc.
Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project               4
<PAGE>   5
occur.  In the event that BOG elects to pay Vaquero cash consideration as
aforesaid, such cash consideration shall be deemed to be Net Revenues received
by Vaquero and attributable to production of Subject Hydrocarbons for purposes
of calculating the occurrence of Payout #1 and Payout #2.

         Section 2.5.     Reporting on Payout.  Until such time as Payout #2
has occurred, following the end of each calendar quarter Vaquero shall provide
BOG with a written report (the "Payout Report") setting forth the total amount
of Direct Costs incurred under the Exploration Agreement and both the Net
Revenues and gross revenues (i.e. Net Revenues plus any lease operating
expenses and taxes deducted in the calculation thereof) received by Vaquero.
Once the Net Revenues received by Vaquero (less and except the NPORRI) exceed
the Direct Costs, such Payout Report shall also indicate the cash on cash
annualized rate of return experienced by Vaquero at each month end.

         Section 2.6.     Calculating Payout In the Event of Assignments.

         (a)  In the event that in accordance with the provisions of Section
4.3 or Section 4.4 below, Vaquero assigns or conveys, or in the case of Section
4.4, hypothecates or otherwise encumbers all or any part of its interest in the
Conveyed Interests to a third-party on a basis in which such third-party takes
and receives such interests subject to its proportionate share of BOG's NPORRI,
the PO#1 Interest and the PO#2 Interest, then any Net Revenues received by the
third-party on account of the interests assigned or encumbered shall be deemed
to be Net Revenues received by Vaquero for purposes of determining when Payout
#1 and Payout #2 occur, and all land acquisition and maintenance costs, and
drilling and completion costs incurred by the third-party with respect to the
interests conveyed or encumbered shall be deemed to be Direct Costs incurred by
Vaquero (but only to the extent that such costs are not reimbursements made to
Vaquero for costs already incurred by Vaquero and previously applied as Direct
Costs in the Payout calculations) for purposes of determining when Payout #1
and Payout #2 occur.  In the event that Vaquero assigns less than all of its
interests in the Conveyed Interests on a basis in which the assignment is made
subject to BOG's NPORRI, the PO#1 Interest and the PO#2 Interest, Vaquero shall
be responsible for including any Net Revenues received by the assignee and
Direct Costs paid by the assignee in the Payout Report required to be provided
to BOG pursuant to the terms of Section 2.5 above and the cash consideration
received by Vaquero for the assignment or conveyance will not be included as
Net Revenues in the calculation of Payout #1 or Payout #2.

         (b)  In the event that in accordance with the provisions of Section
4.5 below, Vaquero assigns or conveys up to an aggregate of 50% of its interest
in any part of the Conveyed Interests, and the assignee takes and receives such
interests on a basis in which the assignee is not subject to the PO#1 Interest
or the PO#2 Interest, then the entire cash consideration received by Vaquero
for such assignment or conveyance shall be deemed to be Net Revenues received
by Vaquero and attributable to production of Subject Hydrocarbons for purposes
of calculating the occurrence of Payout #1 and Payout #2; provided, however
that any future Net Revenues received by the assignee from the interests
conveyed shall not be deemed to be Net Revenues received by Vaquero for
purposes of determining when Payout #1 and Payout #2 occur, and any land
acquisition and maintenance costs, drilling and completion costs or any other
costs incurred by the assignee with respect to the interests conveyed shall not
be deemed to be Direct Costs incurred by Vaquero for purposes of determining
when Payout #1 and Payout #2 occur.

                                  ARTICLE III.
                        SEISMIC DATA AND INTERPRETATIONS

         Section 3.1.     Program Data and Interpretations.

         (a)  BOG shall interpret the Program Data (as such term is defined in
the Exploration Agreement) for Vaquero pursuant to the terms set forth in the
Exploration Agreement; however, Vaquero UNDERSTANDS AND AGREES THAT BOG MAKES
NO REPRESENTATIONS OR WARRANTIES OF ANY KIND AS TO THE PROGRAM DATA OR
INTERPRETATIONS THAT ARE PROVIDED TO VAQUERO, INCLUDING WITHOUT LIMITATION,
THEIR FITNESS FOR A PARTICULAR PURPOSE, MERCHANTABILITY





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Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project               5
<PAGE>   6
OR ACCURACY, AND BOG HEREBY DISCLAIMS ANY AND ALL SUCH REPRESENTATIONS OR
WARRANTIES, AND ANY USE OF THE SEISMIC DATA OR INTERPRETATIONS BY VAQUERO, OR
ANY ACTION TAKEN BY VAQUERO SHALL BE BASED SOLELY ON VAQUERO'S OWN JUDGMENT,
AND BOG AND ITS, OFFICERS, EMPLOYEES, SUCCESSORS AND ASSIGNS, SHALL NOT BE
LIABLE OR RESPONSIBLE TO VAQUERO FOR ANY LOSS, COST, DAMAGES, OR EXPENSE
WHATSOEVER, INCLUDING INCIDENTAL OR CONSEQUENTIAL DAMAGES, INCURRED OR
SUSTAINED AS A RESULT OF THE USE OF OR RELIANCE UPON THE PROGRAM DATA OR
INTERPRETATIONS, REGARDLESS OF WHETHER OR NOT SUCH LOSS, COST, DAMAGE OR
EXPENSE IS FOUND TO RESULT IN WHOLE OR IN PART FROM THE SOLE OR CONCURRENT
NEGLIGENCE OR OTHER FAULT OF BOG OR ITS OFFICERS, AGENTS OR EMPLOYEES.

         (b)  Vaquero shall receive copies of the final interpretational maps
generated by BOG as soon as same are generated.  In addition, upon request,
Vaquero shall be entitled to receive copies of all processed Program Data as
well as fan fold copies of final and migrated stacks, every other inline and
crossline; provided, however, that Vaquero shall pay for all of the costs and
expenses which are incurred to generate such requested copies.

         Section 3.2.     Geophysical Program Costs.  Until such time as Payout
#1 occurs, Vaquero agrees to pay thirty- seven point five percent (37.5%) of
all Geophysical Program Costs (as such term is defined in Section 2.3(a) of the
Exploration Agreement) pursuant to the terms of the Exploration Agreement,
including, without limitation, 37.5% of the amounts that are to be paid to BOG
for the use of its equipment and personnel during the planning, processing and
interpretation of the seismic data as set forth in Section 2.3(a) of the
Exploration Agreement.  Upon the occurrence of Payout #1, Vaquero shall pay for
twenty-two point five percent (22.5%) and BOG shall pay for fifteen percent
(15%) of all Geophysical Program Costs incurred after the occurrence of Payout
#1.  Upon the occurrence of Payout #2, Vaquero shall pay for eighteen point
seven five percent (18.75%) and BOG shall pay for eighteen point seven five
percent (18.75%) of all Geophysical Program Costs incurred after the occurrence
of Payout #2.  The Parties recognize that in the event that the total
Geophysical Program Costs exceed the amount set forth in Section 2.3(b) of the
Exploration Agreement, their responsibility for future Geophysical Program
Costs shall be proportionately increased to account for the additional
responsibility for such costs as set forth in the Exploration Agreement.

                                      IV.
                                  ASSIGNMENTS

         Section 4.1.     BOG Assignments.  In the event that BOG assigns,
conveys, hypothecates or otherwise encumbers any of its rights or interests
herein or that are the subject of this Assignment or otherwise that are
acquired in or relating to the Subject Lands pursuant hereto, the terms and
provisions of this Assignment shall be binding upon and run to the benefit of
BOG's assignee or other party that receives the benefit of such assignment or
encumbrance; provided, however, that the conveyance, assignment or encumbrance
instrument vesting such party with all or part of such interests must expressly
provide that the assignment or encumbrance is made subject to the terms and
conditions contained in this Assignment.  Any subsequent assignment by such
party shall likewise contain express language providing that it is subject to
the terms and conditions contained in this Assignment.

         Section 4.2.     Vaquero Assignments.  Except as specifically provided
in Sections 4.3, 4.4 or 4.5 below, until such time as Payout #2 has occurred,
Vaquero shall not have the right to assign, convey, exchange, mortgage,
hypothecate, pledge as security or otherwise encumber or dispose of any part of
the Conveyed Interests, whether legal or equitable, vested or contingent, and
further whether owned by BOG (prior to giving effect to this Assignment) or
hereafter acquired by Vaquero.

         Section 4.3.     Vaquero Rights of Assignment Prior to Expiration of
Restricted Time Period.  During such period of time (the "Restricted Time
Period") between the effective date hereof and the earlier to occur of (a) a
date two (2) years after the date of the spudding of the first well that is
drilled by Vaquero, AMX, Bright, DDD, RPC, REPI, REPII and/or Wilcox





Vaquero Gas Company, Inc.
Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project               6
<PAGE>   7
(such parties being sometimes referred to herein as the "Exploration Parties")
within the Subject Lands, or (b) the date of the spudding of the fifteenth
(15th) well that is drilled by any of the Exploration Parties within the
Subject Lands, Vaquero shall not have the right to assign, convey, exchange,
mortgage, hypothecate, pledge as security or otherwise encumber or dispose of
any of its rights or interests in the Conveyed Interests; provided, however,
that at any time during the term of this Assignment Vaquero may unconditionally
assign or convey all, but not less than all, of its interest in all, but not
less than all, of the Conveyed Interests to a single party, provided that such
transaction is made subject to the terms and provisions of this Assignment,
including without limitation, the NPORRI, the rights of BOG at Payout #1 to
automatically enjoy the PO#1 Interest and the rights of BOG at Payout #2 to
automatically enjoy the PO#2 Interest and provided further that the
documentation relating to such transaction must expressly provide that the
transaction is made subject to the terms and conditions contained in this
Assignment and shall further expressly recognize the rights and interests of
BOG in and to the NPORRI, the PO#1 Interest and the PO#2 Interest as continuing
burdens against the Subject Lands.  Anything to the contrary contained in this
Section 4.3 notwithstanding, Vaquero's authority under this Section 4.3 to
assign or convey all, but not part, of its undivided interest in all, but not
less than all, of the Conveyed Interests to a single party shall not include
authority to execute a deed of trust, a mortgage, a pledge as security or any
other form of conditional assignment or conveyance.

         Section 4.4.     Vaquero Right to Make Assignments Subject To BOG's
Interests After Expiration of Restricted Time Period.

         (a)  Following the expiration of the Restricted Time Period, subject
to the terms of Section 4.6 below, Vaquero shall have the right to assign,
convey, exchange, mortgage, hypothecate, pledge as security or otherwise
encumber or dispose of all or any part of its interests in the Conveyed
Interests or any properties making up part of the Conveyed Interests on a basis
in which such interests are subject to the terms and provisions of this
Assignment, including without limitation, the NPORRI, the rights of BOG at
Payout #1 to automatically enjoy the PO#1 Interest and the rights of BOG at
Payout #2 to automatically enjoy the PO#2 Interest; provided, however, that any
instrument vesting such party with such interest in the Conveyed Interests or
individual properties must expressly provide that such instrument is made
subject to the terms and conditions contained in this Assignment and shall
further expressly recognize the rights and interests of BOG in and to the
NPORRI, the rights of BOG at Payout #1 to automatically enjoy the PO#1 Interest
and the rights of BOG at Payout #2 to automatically enjoy the PO#2 Interest as
continuing burdens against the interest in the Conveyed Interest or individual
property.

         (b)  In the event that Vaquero assigns, conveys, exchanges, mortgages,
hypothecates, pledges as security or otherwise encumbers or disposes all or
part of its interest in the Conveyed Interests or any properties making up part
of the Conveyed Interests in compliance with the terms and provisions contained
in Section 4.4(a) above, the interest assigned, conveyed, exchanged, mortgaged,
hypothecated, pledged as security or otherwise encumbered or disposed of and
the interests, if any, retained by Vaquero shall each bear a proportionate
share (being in the proportion that such transferred and retained interests
bear to the total interest in the Conveyed Interest or portion thereof subject
to the third-party transaction) of the NPORRI, the rights of BOG at Payout #1
to automatically enjoy the PO#1 Interest and the rights of BOG at Payout #2 to
automatically enjoy the PO#2 Interest.  Vaquero shall be responsible for
calculating total Payout Revenues received by Vaquero and by such
third-parties, all as contemplated in Section 2.6(a).

         Section 4.5.     Vaquero Right to Make Assignments of Up to 50%
Interest Without Being Subject to BOG Payout Interests After Expiration of
Restricted Time Period.

         (a)  Following the expiration of the Restricted Time Period, subject
to the terms and provisions of Section 4.6 below, Vaquero may assign or convey
to a third-party, which is not affiliated with Vaquero, up to an undivided
fifty percent (50%) interest (in the aggregate) in all of the Conveyed
Interests or up to an undivided fifty percent (50%) interest (in the aggregate)
in any single property making up part of the Conveyed Interests free and clear
of the rights of BOG at Payout #1 to automatically enjoy the PO#1 Interest and
the rights of BOG at Payout #2





Vaquero Gas Company, Inc.
Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project               7
<PAGE>   8
to automatically enjoy the PO#2 Interest; provided, however, that (a) such
assignment must be executed for cash consideration only, (b) such assignment or
conveyance shall be subject to the NPORRI, the terms and conditions of the
Exploration Agreement and BOG's rights under Sections 1.5, 1.6 and 1.7 of this
Assignment, (c) the conveyance or assignment vesting such party with such
undivided interest in the Conveyed Interests or individual property must
expressly provide that the assignment or conveyance is made subject to the
NPORRI, the terms and conditions contained in the Exploration Agreement and
BOG's rights under Sections 1.5, 1.6 and 1.7 of this Assignment and such
instrument shall further expressly recognize the rights and interests of BOG in
and to the NPORRI and under Sections 1.5, 1.6 and 1.7 as continuing burdens
against the undivided interest in the Conveyed Interest or individual property,
and (d) the interests so conveyed or assigned by Vaquero must constitute
traditional working interests and shall not, for example, constitute production
payments, net profits interests or similar interests not commonly held by
operators or producers of oil and gas properties in Texas.  Vaquero may never
convey or assign more than an aggregate fifty percent (50%) undivided interest
in any property included in the Conveyed Interests except as provided in
Sections 4.3 and 4.4 above.  By way of illustration, assume that Vaquero
acquires the following interest in Blackacre, a tract of land hypothetically
included within the Subject Lands: (a) an undivided thirty-seven and one-half
percent (37.5%) interest in a seismic permit and option agreement
hypothetically covering Blackacre acquired on May 1, 1996 (a date which is
hypothetically after the expiration of the Restricted Time Period), (b) an
undivided thirty seven and one-half percent (37.5%) interest in Lease A, a
lease hypothetically covering an undivided one-half of the mineral fee in
Blackacre, acquired on May 10, 1996, (c) an additional twenty percent (20%)
interest in Lease A acquired on May 15, 1996, and (d) an undivided eighteen and
three-quarters percent (18.75%) interest in Lease B, a lease hypothetically
covering the remaining one-half mineral fee interest in Blackacre acquired on
May 30, 1996.  Under the foregoing example, Vaquero may not, in any one sale or
in the aggregate, convey or assign free and clear of the PO#1 or PO#2 Interests
more than (i) fifty percent (50%) of its original thirty-seven and one-half
percent (37.5%) interest in the seismic permit with lease option, (ii) fifty
percent (50%) of its original thirty seven and one-half percent (37.5%)
undivided interest in Lease A acquired on May 10, 1996, (iii) fifty percent
(50%) of its additional twenty percent (20%) undivided interest in Lease A
acquired on May 15, 1996, or (iv) fifty percent (50%) of its original eighteen
and three-quarters percent (18.75%) undivided interest in Lease B.

         (b)  In the event that Vaquero assigns or conveys up to an undivided
fifty percent (50%) interest in all of the Conveyed Interests or up to an
undivided fifty percent interest (50%) in any single property making up part of
the Conveyed Interests on a basis in which such assigned interests are not
subject to the rights of BOG at Payout #1 to automatically enjoy the PO#1
Interest and the rights of BOG at Payout #2 to automatically enjoy the PO#2
Interest as provided in Section 4.5 (b) above, then the interest retained by
Vaquero shall bear all of the rights of BOG at Payout #1 to automatically enjoy
the full amount of the PO#1 Interest and the rights of BOG at Payout #2 to
automatically enjoy the full amount of the PO#2 Interest, but shall bear only
its proportionate share (being in the proportion that such assigned and
retained interests bear to the total interest in the Conveyed Interest or
property being assigned) of the NPORRI.  By way of illustration, if Vaquero
assigns to X an undivided twenty percent (20%) of its original interest in
Lease A, one of the leases hypothetically included in the Conveyed Interests,
on May 1, 1996, a date which hypothetically is after the expiration of the
Restricted Time Period, then, as of such date, X shall bear no part of BOG's
PO#1 Interest or PO#2 Interest, and Vaquero shall bear the entire burden of
BOG's PO#1 and PO#2 Interests out of the 80% of its original interest in Lease
A it has retained.  If Vaquero then sells to Y on May 30, 1996, an undivided
30% of Vaquero's original interest (i.e. its interest prior to giving effect to
the conveyance in favor of X) in Lease A (being the entire remaining interest
Vaquero may assign or convey in Lease A free and clear of the PO#1 Interest and
the PO#2 Interest), neither Y or X shall bear any part of BOG's PO#1 or PO#2
Interest, but instead Vaquero shall bear the entire burden of BOG's PO#1 and
PO#2 Interests out of the 50% of its original interest in Lease A it has
retained, thus leaving Vaquero with 10% of its original interest in Lease A
after Payout #1 has occurred and with none of its original undivided interest
in Lease A after Payout #2 has occurred.

         (c)  In the event that Vaquero assigns or conveys up to an undivided
fifty percent (50%) interest in all of the Conveyed Interests or up to an
undivided fifty percent interest (50%) in any





Vaquero Gas Company, Inc.
Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project               8
<PAGE>   9
single property making up part of the Conveyed Interests free and clear of the
rights of BOG at Payout #1 to automatically enjoy the PO#1 Interest and/or the
rights of BOG at Payout #2 to automatically enjoy the PO#2 Interest as provided
in Section 4.5 (b) above, BOG shall have the right to propose the drilling
and/or completion of wells within that part of the Subject Lands which are the
subject of the assignment or conveyance by providing Vaquero with written
notice of such proposal, including within such notice the proposed location of
the well and the proposed total depth of such well in the case drilling is
proposed, or the description of the formation to be completed in the case
completion is proposed.  Vaquero shall notify BOG in writing as to whether
Vaquero will propose and participate in such operation (a "BOG Proposed
Operation") under the terms of the Form Joint Operating Agreement within thirty
(30) days of its receipt of notice of BOG's Proposed Operation; provided,
however, that in the event that Vaquero fails to notify BOG in writing within
such time period Vaquero shall be deemed to have elected not to participate in
the BOG Proposed Operation.  In the event that Vaquero elects to participate in
such BOG Proposed Operation, Vaquero shall, within thirty (30) days of its
receipt of BOG's proposal, propose such operation to the Exploration Parties as
its own under the terms of the Form Joint Operating Agreement; provided,
however, that in the event that Vaquero fails to properly propose such BOG
Proposed Operation to the Exploration Parties in accordance with the Form Joint
Operating Agreement within the time frame set forth herein, Vaquero shall be
deemed to have elected not to participate in such BOG Proposed Operation for
purposes of this Section 4.5(c).  In the event that Vaquero elects, or is
deemed to have elected, not to participate in a BOG Proposed Operation, then
one or the other of the following shall occur:

         (i)  In the event the subject BOG Proposed Operation gives rise to an
         election under the applicable Form Joint Operating Agreement (assuming
         such operation had been proposed by a party to such Form Joint
         Operating Agreement) to either participate or not participate in such
         BOG Proposed Operation and further in the event that an election not
         to participate results in permanent forfeiture or relinquishment of
         all of such Exploration Party's interest that are subject to the
         applicable Form Joint Operating Agreement, then, in such events
         (collectively called "an election and Permanent Relinquishment
         Event"), Vaquero shall promptly relinquish and assign to BOG (A) all
         of Vaquero's interest in the Prospect Area (which is also the
         "Contract Area" for the applicable Form Joint Operating Agreement)
         covered by the applicable Form Joint Operating Agreement, including
         without limitation any Leases, Options and Farm-Ins covering lands and
         depths included within such Prospect Area, and (B) all of Vaquero's
         rights, interests and remedies under the applicable Form Joint
         Operating Agreement, effective in the case of items (a) and (b) as of
         the date of BOG's original written proposal; or

         (ii)  In any other event (e.g., in any event or series of events not
         constituting an election and Permanent Relinquishment Event), Vaquero
         shall, within thirty (30) days of its receipt of BOG's notice of the
         Proposed BOG Operation, in writing offer BOG the option to participate
         in the subject BOG Proposed Operation.  BOG shall have thirty (30)
         days to elect whether to participate in such BOG Proposed Operation by
         delivering written notice of such election to Vaquero.  If BOG elects
         not to participate in such BOG Proposed Operation, either itself or
         through the participation of a third-party designee, Vaquero shall be
         free to take no further action with respect to such BOG Proposed
         Operation.  If BOG elects to participate in the subject BOG Proposed
         Operation, either itself or through the participation of a third-party
         designee, Vaquero shall promptly and permanently relinquish and assign
         to BOG, effective as of the date of BOG's original written proposal,
         (A) all of Vaquero's interests (whether they be in the form of
         interests in Leases, Options, Farm-Ins or otherwise) in the Prospect
         Area under the applicable Form Joint Operating Agreement that would
         have been relinquished, either temporarily or permanently, had Vaquero
         elected under the terms of the applicable Form Joint Operating
         Agreement not to participate in the BOG Proposed Operation (assuming
         such operation had been proposed by a party to such Form Joint
         Operating Agreement), and (B) all of Vaquero's rights, interests and
         remedies under the applicable Form Joint Operating Agreement, insofar
         only as such rights, interests and remedies apply to the subject BOG





Vaquero Gas Company, Inc.
Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project               9
<PAGE>   10
         Proposed Operation and further insofar as same relate to the interests
         relinquished and assigned to BOG pursuant to item (A) immediately
         above; provided that, in the event Vaquero is contractually precluded
         from making the assignments described in items (A) and (B) immediately
         above, Vaquero shall instead propose the subject BOG Proposed
         Operation as its own under the terms of the applicable Form Joint
         Operating Agreement and shall hold in perpetuity the interests, rights
         and remedies described in items (ii) (A) and (B) as nominee for, and
         under the direction of, BOG.

Anything to the contrary contained in the provisions of (i) and (ii) above
notwithstanding, BOG shall be required to assign back to Vaquero all interests,
rights and remedies relinquished and assigned to BOG, whether outright or by
use of a nominee arrangement, to the extent same relate to a BOG Proposed
Operation that, at no fault of Vaquero, is not proposed by BOG, BOG's
third-party designee, an Exploration Party or any other party to the applicable
Form Joint Operating Agreement, or otherwise to the extent the subject BOG
Proposed Operation, once proposed, is not actually commenced within the time
frame set forth in the applicable Form Joint Operating Agreement, other than by
reason of force majeure or some fault or omission on the part of Vaquero.

         Section 4.6.     BOG's Preferential Right to Purchase.

         (a)  In the event that at any time prior to the occurrence of Payout
#2 Vaquero should desire to sell, transfer, assign or otherwise dispose of any
part of its interest in the Conveyed Interests or any part of the properties
making up the Conveyed Interests (the interest Vaquero desires to sell,
transfer, assign or otherwise dispose of being hereinafter referred to as the
"Offered Interest") and such sell, transfer, assignment or other disposition is
allowed pursuant to the other terms of this Article IV, Vaquero shall promptly
give notice (hereinafter referred to as the "Disposition Notice") of such
proposed disposition to BOG.  The Disposition Notice shall set forth in writing
all relevant information relating to the proposed disposition of the Offered
Interest, including without limitation, a complete description of the Offered
Interest, the name and address of the prospective acquirer, the purchase price
(which must be payable in cash) and the payment terms.  In the event that in
conjunction with Vaquero's proposed disposition of the Offered Interest Vaquero
also desires to package the Offered Interest with other properties which are
not the subject of this Assignment for purposes of the disposition, in the
Disposition Notice Vaquero shall set forth a description of all of the
properties being sold, the total purchase price of all of the properties and a
good faith allocation of the amount of the purchase price that is attributable
to the Offered Interest, which shall for purposes of this Section 4.6 and
Section 2.6 above, be deemed to be the purchase price for the Offered Interest.

         (b)  BOG shall have an optional preferential right (to be exercised by
written notice delivered to Vaquero within sixty (60) days after receipt of the
Disposition Notice) to acquire the Offered Interest for the same purchase price
and on the same payment terms that are set forth in the Disposition Notice.  If
BOG exercises such preferential right, the closing shall take place on the date
designated by BOG to Vaquero, but in no event more than ninety (90) days after
BOG's receipt of the Disposition Notice.

         (c)  If BOG fails to exercise the preferential purchase right
described in this Section 4.6, Vaquero shall have the right to dispose of the
Offered Interest strictly in accordance with the terms of the Disposition
Notice for a period of ninety (90) days after the expiration of the applicable
preferential right, provided that such disposition is made in accordance with
the other terms and provisions of this Article IV.  If Vaquero fails to dispose
of such Offered Interest within such ninety (90) day period, the Offered
Interest shall again become subject to the preferential purchase rights set
forth in this Section 4.6.

         (d)  Anything to the contrary contained in this Section 4.6
notwithstanding, in the event that Vaquero desires to sell, transfer, assign or
otherwise dispose of all of its right, title and interest in the Conveyed
Interests to a single party, such proposed disposition shall not be subject to
the preferential purchase rights set forth in this Section 4.6.

         Section 4.7.     Attempted Assignments in Breach of Article IV.  In
the event that either Party (or their successor or assign) assigns, conveys,
hypothecates or otherwise encumbers all or any part of its rights and interests
hereunder as allowed in this Article IV, any subsequent assignment by the
recipient of such assignment or encumbrance shall likewise be subject to the
terms and provisions of this Article IV and any assignment made by such
recipient shall contain express language providing that it is subject to the
applicable terms and conditions contained in





Vaquero Gas Company, Inc.
Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project                10
<PAGE>   11
this Article IV.  Any attempted conveyance, assignment or encumbrance of any
interest hereunder or in the Conveyed Interests which is not made in full and
complete conformance with the terms and provisions set forth in this Article IV
shall be null and void and of no force and effect.

                                       V.
                                 MISCELLANEOUS

         Section 5.1.     Memorandum of Assignment.  The Parties agree to
execute the Memorandum of Assignment which is attached hereto as Exhibit "A"
concurrent with their execution of this Assignment and either Party hereto
shall have the right to have such Memorandum of Assignment placed of record in
the official public records of Harris or Liberty Counties, Texas.

         Section 5.2.     Entirety of Agreement.  This Assignment contains the
entire understanding and agreement of the Parties with respect to the subject
matter hereof and supersedes all prior agreements, understandings,
negotiations, and discussions among the Parties with respect to such subject
matter.

         Section 5.3.     Execution in Counterparts.  This Assignment may be
executed in multiple counterparts, each of which shall be binding upon the
signing party or parties thereto as fully as if all parties had executed one
instrument, and all of such counterparts shall constitute one and the same
instrument.

ACCEPTED AND AGREED to by each of the Parties hereto on the date set forth
beside the signature of each, but to be effective as of the date first written
above:



   
Address:                                  BRIGHAM OIL & GAS, L.P.,
         5949 Sherry Lane, Suite 1616     by Brigham Exploration Company,
         Dallas, Texas  75225             its Managing General Partner
         Phone:  (214) 360-9182
         Fax:  (214) 360-9825
Dated:       03/13/95
      --------------------------------    By:       /s/ ANNE L. BRIGHAM
                                                -------------------------------
                                             Anne L. Brigham, Executive Vice 
                                             President
    



   

Address:                                  VAQUERO GAS COMPANY, INC.
         600 Travis Street, Suite 6875
         Houston, Texas  77002
         Phone:  (713) 229-8800
         Fax:  (713) 247-0730             By: /s/ GARY J. MILAVEC
Dated:                                       ------------------------------
      ----------------------------------  Gary J. Milavec, Vice President
    





Vaquero Gas Company, Inc.
Agreement and Assignment
Geophysical Exploration Agreement
Esperson Dome Project                 11

<PAGE>   1
                                                                  EXHIBIT 10.34




                       GEOPHYSICAL EXPLORATION AGREEMENT
                           SOUTHWEST DANBURY PROJECT
                             BRAZORIA COUNTY, TEXAS

         This Geophysical Exploration Agreement (this "Agreement"), dated
effective as of the 1st day of July, 1996, is by and among UNEXCO, INC.
("UNEXCO") and BRIGHAM OIL & GAS, L.P. ("BOG") (UNEXCO and BOG are sometimes
referred to herein individually as a "Participant" and collectively as the
"Participants" or individually as a "Party" and collectively as the "Parties").

                                   RECITALS:
         1.      BOG and UNEXCO have identified an area (the "Program Area") in
Brazoria County, Texas, being more particularly identified and described in
Part One of Exhibit A, attached hereto and made a part hereof, which the
Parties believe to be prospective for oil and gas exploration and production.

         2.      UNEXCO and Apache Corporation ("Apache") have entered into
that certain S.W. Danbury Exploration Agreement (the "Apache Agreement") dated
as of July 28, 1996, and concerning the exploration and development of the
Program Area.

         3.      Under instrument dated as of March 8, 1996 (the "Cinnabar
Agreement"), UNEXCO reached agreement with Cinnabar Investments Corporation
("Cinnabar") concerning the exploration of the Program Area.

         4.      Under that certain Basic Agreement for Geophysical Services
dated March 19, 1996 (herein called the "Basic USA Agreement"), as supplemented
under that certain Supplemental Agreement No. 7 (the "USA Supplement") dated
October 2, 1996, each by and between UNEXCO and USA, USA undertakes to acquire,
on behalf of UNEXCO and BOG, 3-D seismic data covering all or part of the
Program Area (the Basic USA Agreement, as supplemented by the USA Supplement,
is herein called the "USA Agreement", and a copy of same as attached hereto as
Exhibit G), all at USA's actual cost.

         5.      Under the "UST Agreement," as hereinafter defined, UST
undertakes to process on behalf of UNEXCO and BOG 3-D seismic data covering all
or part of the Program Area, as directed by BOG and UNEXCO, all at UST's actual
cost.

         6.      Each of BOG and UNEXCO may own existing licenses or permits to
conduct seismic or other geophysical operations on, under or across the Program
Area (the "Existing Permits"), option agreements to acquire oil and gas leases
(the "Existing Options"), oil and gas leases (the "Existing Leases") and other
agreements to earn or obtain interests in oil and gas leases, mineral
interests, royalty interests or other interests in oil, gas or other
hydrocarbons (the "Existing Farm-Ins"), including, without limitation the
Apache Agreement, covering portions of the Program Area (the Existing Permits,
Existing Options, Existing Leases and Existing Farm-Ins being described in
Exhibit B hereto), and BOG and UNEXCO anticipate that additional licenses or
permits to conduct seismic or other geophysical operations on, under or across
the Program Area (such licenses and permits, together with the Existing
Permits, being herein referred to as "Permits"), options to acquire oil and gas
leases (such options and the Existing Options being herein referred to as
"Options"), oil and gas leases (such leases and the Existing Leases being
herein referred to as "Leases"), and other agreements to obtain interests in
oil and gas leases, mineral interests, royalty interests or other interests in
oil, gas or other hydrocarbons (such agreements and the Existing Farm-Ins being
referred to herein as "Farm-Ins") may in accordance herewith be obtained in the
future covering all or any portion of the Program Area.

         7.      The Participants have reached an agreement with respect to
certain matters concerning the ownership and operation of Permits, Options,
Leases and Farm-Ins, taking into due account the USA Agreement, the UST
Agreement, the Apache Agreement and the Cinnabar Agreement.

         8.      The Participants have also reached an agreement with respect
to the exploration, development and evaluation by them of the Program Area,
taking into due account the USA Agreement, the UST Agreement, the Apache
Agreement and the Cinnabar Agreement.
<PAGE>   2
                                  DEFINITIONS:

"Acquired Interests" means any Permits, Options, Leases or Farm-ins acquired by
one of the Parties hereto during the term hereof, insofar and only insofar as
any of same cover or relate to lands within the AMI; Acquired Interests shall
not include any Existing Permit, Existing Option, Existing Lease or Existing
Farm-In.

"Affiliate" means, as to any particular Party, all of the officers and
employees of such Party and any other person or entity which either: (a) owns
more than twenty percent (20%) of the total voting equity of the Party; (b) has
one or more employees or officers which are also employees or officers of the
Party; or (c) the Party owns more than twenty percent (20%) of the total voting
equity of such entity.

"Apache" has the meaning assigned to it in the Recitals set out above.

"Apache Agreement" has the meaning assigned to it in the Recitals set out
above.

"Apache Survey data" means all data supplied to UNEXCO and/or BOG under Article
4.A. of the Apache Agreement.

"Cinnabar" has the meaning assigned to it in the Recitals set out above.

"Cinnabar Agreement" has the meaning assigned to it in the Recitals set out
above.

"Completion Date" means the date of completion of processing of interpretable
and acceptable Program Data.

"Direct Charges" means actual, appropriate and reasonable out-of-pocket costs
and expenses paid to third parties who are not Affiliates; provided that such
Affiliate limitation does not apply to any USA Shoot Costs payable to USA under
the USA Agreement or to any Processing Costs payable to UST under the UST
Agreement.

"Existing Farm-ins" has the meaning assigned to it in the Recitals set out
above.

"Existing Leases" has the meaning assigned to it in the Recitals set out above.

"Existing Options" has the meaning assigned to it in the Recitals set out
above.

"Existing Permits" has the meaning assigned to it in the Recitals set out
above.

"Farm-ins" has the meaning assigned to it in the Recitals set out above.

"Geophysical Program" has the meaning assigned to it in Section 2.1.

"Geophysical Program Costs" means the sum of (a) the USA Shoot Costs, (b) any
Processing Costs, (c) any Permitting Costs, and (d) any Reproduction Costs.

"Leases" has the meaning assigned to it in the Recitals set out above.

"Options" has the meaning assigned to it in the Recitals set out above.

"Permits" has the meaning assigned to it in the Recitals set out above.

"Permitting Costs" means any Direct Charges (including without limitation any
bonus payments or, to the extent only approved by BOG, surface damage payments)
incurred in securing, extending or maintaining Permits, Options, Leases, or
Farm-ins necessary or appropriate to allow USA to conduct the Geophysical
Program.

"Processed Data" has the meaning assigned to it in subsection 2.1(c) hereof.


                                              Geophysical Exploration Agreement 
                                              Southwest Danbury Project
                                      2
<PAGE>   3
"Processing Costs" shall mean any Direct Charges payable to UST under the UST
Agreement for processing the Program Data, it being understood that such Direct
Charges are to be billed at the rates quoted for UNEXCO in the UST Agreement.
Notwithstanding any provision hereof to the contrary, under no circumstances
shall Processing Costs ever exceed the amount then (i.e., at the time of
processing) being assessed by Veritas Geophysical, Ltd. ("Veritas") for similar
work performed by Veritas for BOG.

"Program Area" has the meaning assigned to it in the Recitals set out above.

"Program Data" means any and all data or other related information secured or
acquired in the conduct of the Geophysical Program, including without
limitation any 3-D seismic data, logs, survey and shotpoint and receiver maps,
tapes, and reproducibles; the Program Data shall include the Processed Data,
once in existence, but the Program Data shall in no event include any
interpretations of the Program Data.

"Reproduction Costs" means any Direct Charges incurred in copying or otherwise
reproducing any Program Data, Processed Data and/or interpretations thereof; in
no event shall Reproduction Costs be charged to the extent they are already
considered in the Processing Costs or the USA Shoot Costs.

"3-D" means three dimensional.

"USA" means Universal Seismic Acquisition, Inc.

"USA Agreement" has the meaning assigned to it in the Recitals set out above.

"USA Shoot Costs" means the lesser of (a) the actual and reasonable costs
incurred in the field by USA in conducting the 3-D survey that makes up a part
of the Geophysical Program, to the extent such costs are attributable to the
allocable time spent by employees and/or leased or owned equipment of USA, and
(b) the sum of any Direct Charges payable to USA under Section IV, V and VI of
the USA Supplement; provided that under no circumstances shall USA Shoot Costs
include any costs otherwise included in Geophysical Program Costs, or otherwise
exceed an average of $36,500.00 per square mile.

"UST" means Universal Seismic Technologies, Inc.

"UST Agreement" means that certain letter agreement executed by UST on October
1,1996, and accepted by UNEXCO on October 2, 1996, relating to bid #61001DCA, a
copy of which is attached hereto as Exhibit H.

         NOW, THEREFORE, for and in consideration of the mutual covenants
contained herein and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Parties agree as follows:

                                   ARTICLE I.
                            RELATIONSHIP OF PARTIES

         Section 1.1.     No Partnership.  The liabilities of the Parties
hereunder shall be several, not joint or collective.  It is not the intention
of the Parties to create, nor shall this Agreement be deemed as creating, a
joint venture or a mining, tax or other partnership or association or to render
the Parties liable as partners.  However, if for federal income tax purposes,
this Agreement and the operations hereunder are regarded as a partnership, each
Party thereby affected elects to be excluded from the application of all of the
provisions of Subchapter "K," Chapter 1, Subtitle "A," of the Internal Revenue
Code of 1986, as amended (hereinafter referred to as the "Code"), as permitted
and authorized by Section 761 of the Code and the regulations promulgated
thereunder.  Should there be any requirement that each Party hereby affected
give further evidence of this election, each such Party shall execute such
documents and furnish such other evidence as may be required by the Federal
Internal Revenue Service or as may be necessary to evidence this election.  No
Party shall give any notice or take any other action





                                              Geophysical Exploration Agreement 
                                              Southwest Danbury Project
                                       3
<PAGE>   4
inconsistent with the election made hereby.  In making the foregoing election,
each Party states that the income derived by such Party from operations
hereunder can be adequately determined without the computation of partnership
taxable income.

         Section 1.2.     Third Party Claims and Liability.  In the event any
third party (to include any governmental authority) claim or suit arising,
directly or indirectly out of this Agreement or any interest acquired or
operation conducted pursuant hereto is made against any Party, such Party shall
immediately notify all other Parties.

                                  ARTICLE II.
                               EVALUATION PROGRAM

         Section 2.1.     Scope and Conduct of Program.

         (a)     Design.  The Participants have agreed that a 3-D geophysical
survey (the "Geophysical Program") will be conducted to cover all or part of
the Program Area.  BOG and UNEXCO have reached mutual agreement on the design
of the Geophysical Program, and subject to the rights afforded Apache under the
Apache Agreement, the scope and parameters of the Geophysical Program are set
out in Exhibit I hereto.

         (b)     Conduct.  UNEXCO will conduct or will cause USA to conduct, or
supervise third parties in conducting, the Geophysical Program.  In satisfying
its obligations hereunder to conduct (or cause to be conducted) the 3-D survey,
UNEXCO shall itself follow, or cause USA to follow, the parameters set forth in
Exhibit I hereto.

         (c)  Processing of Program Data.  UNEXCO shall process, or shall cause
UST to process, the Program Data into migrated seismic sections in a SEGY
format capable of being loaded on BOG's 3-D work stations.  At a minimum,
UNEXCO will comply, or will cause UST to comply, with the basic processing
parameters set out in Exhibit I.

         (d)  Processing and/or Reprocessing of the Apache Survey data.  UNEXCO
shall be responsible for processing and/or reprocessing, or for causing UST to
process or reprocess the seismic field data included in the Apache Survey data
in a SEGY format capable of being loaded on BOG's 3-D work stations.  At a
minimum, UNEXCO will comply, or will cause UST to comply, with the basic
processing parameters set out in Exhibit I.

         (e)  Completion Date.  The Parties agree that "completion of
processing of interpretable and acceptable Program Data" (and thus the
Completion Date) shall be deemed to occur when final processed, migrated
seismic sections of the Program Data and the Apache Survey data (herein
collectively called the "Processed Data") have been delivered to BOG in SEGY
format capable of being loaded on BOG's 3-D work stations.

         (f)  Interpretation of Program Data.  UNEXCO or UST shall supply to
BOG the Processed Data.  BOG shall then be responsible for interpreting, free
of charge other than Direct Charges, the Processed Data on its 3-D work
stations, and BOG will provide to UNEXCO and, to the extent necessary or
appropriate under the Cinnabar Agreement, to Cinnabar, copies of all resulting
final interpretations of the Processed Data.  It is hereby recognized by the
Parties that UNEXCO and Cinnabar each has expertise in interpreting seismic
data and specific knowledge of the geology of this prospect, and BOG shall meet
with UNEXCO and Cinnabar at reasonable times in BOG's offices to prepare and
discuss interpretation of the Processed Data.

         Section 2.2.     Ownership, Use and Disclosure of Program Data.

         (a)     Ownership.  The Program Data shall be owned jointly by the
Participants in the following percentages (hereinafter referred to as such
Participants' "Ownership Interests"):

                        Participant               Percentage
                        -----------               ----------
                        BOG                        50%
                        UNEXCO                     50%.





                                              Geophysical Exploration Agreement 
                                              Southwest Danbury Project
                                       4
<PAGE>   5
The Ownership Interest of each of BOG and UNEXCO in the Program Data shall be
subject to any license or joint ownership rights in such Program Data afforded
to Apache under the Apache Agreement.  Provided such Participant has paid its
share of the Geophysical Program Costs (if such Participant is responsible for
such costs as provided in Section 2.3), and subject to any restrictions that
may be contained in any applicable license or other agreements, upon request,
each Participant shall receive copies of the Program Data.

         (b)  Use, Disclosure and Transfer of Program Data.  Each of BOG and
UNEXCO has the right to use the Program Data and any interpretations thereof
for its own internal purposes in connection with its exploration and
development of the Program Area.  No Participant shall sell, license, trade,
exchange or otherwise disclose the Program Data or any interpretations thereof
to any third party within two (2) years of the Completion Date without prior
written consent from the other Participant, except that each Participant may
disclose, license, trade, exchange or otherwise transfer ownership rights to or
interests in the Program Data and any interpretations thereof at any time
without the consent of the other Participant to (i) Cinnabar, as contemplated
in the Cinnabar Agreement, or Apache, as contemplated in the Apache Agreement,
(ii) third parties engaged in bona fide negotiations with the disclosing
Participant concerning the acquisition from such third-party of an interest in
or the right to participate in the exploration and/or development of all or
parts of interests owned by such third-party and located within the Program
Area, (iii) third parties that have entered into bona fide negotiations for
participation with the disclosing Participant in the exploration and/or
development of all or parts of the Program Area with an interest in the
disclosing Participant's Ownership Interest in Permits, Leases, Options and/or
Farm-Ins, (iv) third parties that have entered into an agreement through which
they are participating with the disclosing Participant in the exploration
and/or development of all or parts of the Program Area with an interest in the
disclosing Participant's Ownership Interest in Permits, Leases, Options and/or
Farm-Ins, (v) third parties that have invested in, or that are engaged in bona
fide discussions concerning investing in, the disclosing Participant's
exploration and/or development operations within the Program Area, or (vi)
third parties that are hired by a Participant as a consultant to help or
facilitate such Participant's efforts in analyzing or interpreting the Program
Data; provided, however, that the disclosing Participant must cause all third
parties that are described in (ii), (iii), (iv), (v) or (vi) above, to which
the Program Data and/or interpretations are to be disclosed prior to the
expiration of such two year period, to execute a confidentiality agreement in
the form attached hereto as Exhibit D covering the acreage which is covered by
the Program Data that is to be disclosed and naming all of the Participants as
"Offeror" in such confidentiality agreement, prior to the third party's review
of the Program Data or interpretations.  Any cash proceeds resulting from any
sale, license, trade or exchange of the Program Data which occurs within five
(5) years from the effective date of this Agreement shall be divided among the
Participants in accordance with their percentage Ownership Interest (as set
forth in the table contained in Section 2.2(a) above).  In the event that any
Participant sells, trades or exchanges any part of the Program Data after the
expiration of such five (5) year period, such Participant shall have the right
to retain all of the proceeds resulting from such sale, trade or exchange.
The Participants recognize and agree that in the event that a Participant
assigns to a third-party all or part of its Ownership Interest under this
Agreement, including all or part of its Ownership Interest in any Permits,
Options, Leases, Farm-Ins, and such third party also receives part of such
Participants' Ownership Interest in all or part of the Program Data as part of
such transaction, the other Participants hereto shall not be entitled to any
part of the consideration received from the third-party pursuant to the
transaction and such assignment shall not be deemed to be a sale, trade or
exchange of the Program Data for purposes of this subsection 2.2(b).  If any
Party is aware that any Participant has not paid for its proportionate part of
the Geophysical Program Costs in accordance with the terms of Section 2.3
below, such Party shall not intentionally disclose the Program Data or any
interpretations thereof to the non-paying Participant without the consent of
all other Participants hereto.

         Section 2.3.     Payment of Costs of Geophysical Program.  Except as
expressly provided otherwise herein, each of the Participants shall pay their
Ownership Interest (as set forth in the table contained in Section 2.2(a)
above) share of all Geophysical Program Costs.  BOG shall invoice UNEXCO for
UNEXCO's fifty percent (50%) share of all Geophysical Program Costs properly
incurred by BOG in accordance with this Agreement as such costs are incurred;
UNEXCO shall have fifteen (15) days from receipt of the invoice to forward BOG
payment in





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       5
<PAGE>   6
full.  UNEXCO shall invoice BOG for BOG's fifty percent (50%) share of any
Geophysical Program Costs properly incurred by UNEXCO in accordance with this
Agreement as such costs are incurred; BOG shall have fifteen (15) business days
from receipt of the invoice to forward UNEXCO payment in full.  Notwithstanding
any provision hereof to the contrary, any costs associated with the actual
conduct of the 3-D Survey, other than USA Shoot Costs, shall be borne and paid
by UNEXCO.

         Section 2.4.     Disclaimer of Warranties.  The Parties understand
that BOG will use reasonable efforts to provide good quality interpretation of
such Program Data; however, BOG AND ITS OFFICERS, EMPLOYEES, AGENTS, AFFILIATES
AND SHAREHOLDERS (hereinafter collectively referred to as the "BOG GROUP") MAKE
NO REPRESENTATIONS OR WARRANTIES OF ANY KIND AS TO THE INTERPRETATIONS,
INCLUDING WITHOUT LIMITATION, THEIR FITNESS FOR A PARTICULAR PURPOSE,
MERCHANTABILITY OR ACCURACY, AND THE BOG GROUP HEREBY DISCLAIMS ANY AND ALL
SUCH REPRESENTATIONS OR WARRANTIES, AND ANY USE OF THE INTERPRETATIONS BY THE
PARTIES OR THEIR SUCCESSORS OR ASSIGNS, OR ANY ACTION TAKEN BY THE PARTIES OR
THEIR SUCCESSORS OR ASSIGNS SHALL BE BASED SOLELY ON THEIR OWN JUDGMENT, AND
NEITHER THE BOG GROUP OR THEIR SUCCESSORS OR ASSIGNS, SHALL BE LIABLE OR
RESPONSIBLE TO THE OTHER PARTIES OR THEIR SUCCESSORS OR ASSIGNS FOR ANY LOSS,
COST, DAMAGES, OR EXPENSE WHATSOEVER, INCLUDING INCIDENTAL OR CONSEQUENTIAL
DAMAGES, INCURRED OR SUSTAINED AS A RESULT OF THE USE OF OR RELIANCE UPON THE
INTERPRETATIONS, REGARDLESS OF WHETHER OR NOT SUCH LOSS, COST, DAMAGE OR
EXPENSE IS FOUND TO RESULT IN WHOLE OR IN PART FROM THE SOLE OR CONCURRENT
NEGLIGENCE OR OTHER FAULT OF ANY MEMBER OF THE BOG GROUP.  The Parties
understand that UNEXCO will use reasonable efforts to provide good quality
interpretation of such Program Data; however, UNEXCO AND ITS OFFICERS,
EMPLOYEES, AGENTS, AFFILIATES AND SHAREHOLDERS (hereinafter collectively
referred to as the "UNEXCO GROUP") MAKE NO REPRESENTATIONS OR WARRANTIES OF ANY
KIND AS TO THE INTERPRETATIONS, INCLUDING WITHOUT LIMITATION, THEIR FITNESS FOR
A PARTICULAR PURPOSE, MERCHANTABILITY OR ACCURACY, AND THE UNEXCO GROUP HEREBY
DISCLAIMS ANY AND ALL SUCH REPRESENTATIONS OR WARRANTIES, AND ANY USE OF THE
INTERPRETATIONS BY THE PARTIES OR THEIR SUCCESSORS OR ASSIGNS, OR ANY ACTION
TAKEN BY THE PARTIES OR THEIR SUCCESSORS OR ASSIGNS SHALL BE BASED SOLELY ON
THEIR OWN JUDGMENT, AND NEITHER THE UNEXCO GROUP OR THEIR SUCCESSORS OR
ASSIGNS, SHALL BE LIABLE OR RESPONSIBLE TO THE OTHER PARTIES OR THEIR
SUCCESSORS OR ASSIGNS FOR ANY LOSS, COST, DAMAGES, OR EXPENSE WHATSOEVER,
INCLUDING INCIDENTAL OR CONSEQUENTIAL DAMAGES, INCURRED OR SUSTAINED AS A
RESULT OF THE USE OF OR RELIANCE UPON THE INTERPRETATIONS, REGARDLESS OF
WHETHER OR NOT SUCH LOSS, COST, DAMAGE OR EXPENSE IS FOUND TO RESULT IN WHOLE
OR IN PART FROM THE SOLE OR CONCURRENT NEGLIGENCE OR OTHER FAULT OF ANY MEMBER
OF THE UNEXCO GROUP.

                                  ARTICLE III.
                            AREA OF MUTUAL INTEREST

         Section 3.1.     Establishing an Area of Mutual Interest.

         (a)     The Participants have agreed to establish an Area of Mutual
Interest ("AMI") which shall initially encompass all of the land located in the
Program Area.  However, as of the Completion Date, the AMI shall be deemed to
be modified to thereafter include only those parcels of land within the Program
Area which are covered by the 3-D seismic survey conducted as part of the
Geophysical Program.  The AMI shall remain in force for a period of five (5)
years from the date of this Agreement, unless sooner terminated by mutual
agreement of the Participants.





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       6
<PAGE>   7
         (b)     The Participants agree that for purposes of this Agreement the
acreage or lands that are "covered by the 3-D seismic survey conducted as part
of the Geophysical Program" shall include all lands within the Program Area
that are located within the outside perimeter of the area that is depicted on
the final bin/fold map resulting from the Geophysical Program which is provided
by the seismic processor.  Within sixty (60) days after the Completion Date,
BOG shall prepare a legal description of the acreage which is covered by the
3-D seismic survey and the Participants agree that such legal description shall
definitively and for all purposes hereof constitute the AMI, effective as of
the Completion Date.  BOG shall use reasonable efforts to cause the legal
description to depict the outside perimeter of the area that is depicted on the
final bin/fold map provided by the seismic processor; however, the Parties
recognize that in order to provide a legal description of the area covered by
the 3-D seismic survey, BOG shall not be required to have a survey conducted on
the ground and may approximate, in its sole and reasonable discretion, the
location of the outside perimeter depicted on the final bin/fold map for
purposes of aiding BOG in the preparation of the legal description.

         Section 3.2.     Payment for and Ownership of Options, Farm-Ins and
Leases.

         (a)  All costs incurred prior to the execution of this Agreement in
acquiring, extending and maintaining the Existing Permits, Existing Options,
Existing Leases and Existing Farm-Ins shall be paid for by the Participants in
accordance with their Ownership Interests (as set forth in the table contained
in Section 2.2(a) above).

         (b)  BOG shall, to the extent it deems necessary or advisable, secure
or extend any Permits, Options, Leases or Farm-ins as may be necessary or
appropriate to allow USA to conduct the Geophysical Program (herein called the
"Seismic Access Instruments"), and any Permitting Costs incurred by BOG in so
doing shall, notwithstanding the election procedures set forth in Section 3.3
and/or Section 3.4, below, be paid for by the Participants in accordance with
their Ownership Interests, as set forth in the table contained in Section
2.2(a), above).

         (c)  Subject to the election procedures contained in Sections 3.3 and
3.4 below and further subject to the rights of Apache under the Apache
Agreement, all other costs incurred in acquiring and maintaining Permits,
Leases, Options and Farm-Ins located within the AMI during the term of this
Agreement shall be paid for by the Participants in accordance with their
Ownership Interests therein.

         (d)  All Existing Permits, Existing Options, Existing Leases and
Existing Farm-Ins shall be owned by the Participants in accordance with their
Ownership Interests.  Subject to the election procedures contained in Sections
3.3 and 3.4 below and further subject to the rights of Apache under the Apache
Agreement, all other Options, Leases and Farm-Ins acquired by the Participants
within the AMI during the term of this Agreement shall also be owned by the
Participants in accordance with their undivided Ownership Interests.  However,
unless a Participant requests prior record assignment of its interest in the
Leases, Permits, Options or Farm-Ins, record title to all Permits, Options,
Leases and Farm-Ins shall remain in the Participant originally acquiring same
until such time as the acreage covered by such Options, Permits, Leases and
Farm-Ins is to be included within a drilling and/or proration unit of a well
that is to be drilled within the AMI as provided in Section 5.5 below.

         (e)  Within fifteen (15) days from receipt of an invoice from any
Party hereto or a third party, each Party shall pay in full the balance of any
amounts due for their share of the costs of acquiring or maintaining Options,
Leases or Farm-Ins.   Concurrent with their execution of this Agreement the
Parties shall reimburse the acquiring Party for their Ownership Interest share
of all of the third-party costs incurred prior to the execution of this
Agreement in acquiring and maintaining Existing Options, Existing Leases and
Existing Farm-Ins; an invoice setting out these costs shall have been provided
to UNEXCO prior to its execution thereof.

         Section 3.3.     Notification and Response Procedures.  Should any
Participant own on the date hereof, or hereafter acquire or propose to acquire
at any time prior to the date the AMI terminates hereunder, by purchase,
exchange, gift or otherwise, Acquired Interests, such Participant (the
"Acquiring Party") shall notify the other Parties, in writing, of such
acquisition





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       7
<PAGE>   8
or proposed acquisition and the initial consideration paid or to be paid for
the Acquired Interest.  Each non-acquiring Participant shall, within thirty
(30) days after receipt of such a notice from the Acquiring Party, notify the
Acquiring Party, in writing, whether it wishes to participate in such
acquisition; provided that failure to respond within the time and in the manner
set forth above shall be deemed to be an election to not participate in such
acquisition.  However, if a non-acquiring Participant reasonably desires
additional information with respect to an Acquired Interest before it makes its
election whether or not to participate in the acquisition of an Acquired
Interest, such Participant may notify the Acquiring Party in writing within
fifteen (15) days of its receipt of the Acquiring Party's notice, detailing in
such notice to the Acquiring Party the additional information reasonably
desired by such non-acquiring Participant, and such non-acquiring Participant
shall have fifteen (15) days from the date of its receipt of the additional
information it has reasonably requested from the Acquiring Party in which to
make its election whether to participate in the acquisition of the Acquired
Interest.  Anything to the contrary contained herein notwithstanding, a sale,
exchange, gift or other transfer of any part of a Participant's Ownership
Interest share in any Leases, Permits, Options or Farm-ins to any other
Participant hereto shall not be deemed to be an Acquired Interest for purposes
of this Section 3.3 and this Section 3.3 shall not apply to any such
assignment, exchange, gift, sale or other transfer.

         Section 3.4.     Effect of a Participant's Election Regarding
Participation.  Should all of the Participants elect to participate in an
acquisition of an Acquired Interest, upon payment of its share of the
acquisition costs, each Participant shall own, subject to the rights of Apache
under the Apache Agreement, its Ownership Interest share of the Acquired
Interest.  However, unless a Participant requests prior record assignment of
its interest in the Acquired Interest, record title to all Acquired Interests
shall remain in the Participant originally acquiring same until such time as
the acreage covered by such Acquired Interests have been included within the
drilling and/or proration unit for a proposed well as provided in Section 5.5
below.  If any Participant elects not to participate in such acquisition, the
Ownership Interests for the Participants electing to participate shall, unless
all of the Participants electing to participate agree otherwise and subject to
the rights of Apache under the Apache Agreement, be the percentage determined
by dividing, for each participating Participant, the Ownership Interest
otherwise applicable (if all Participants had participated) to such
participating Participant by the total Ownership Interests for all
participating Parties.  The Participants that acquire part of a
non-participating Party's Ownership Interest in an Acquired Interest shall be
responsible for a proportionate share (being in the proportion that the
percentage of such non-participating Participant's Ownership Interest that is
acquired by such Participant bears to such non-participating Participant's
original total Ownership Interest) of such non-participating Participant's
share of the costs of such Acquired Interest.

         Section 3.5.     Exercise of Options.  Should any Participant propose
to exercise an Option with respect to some or all of the lands covered thereby,
such Participant shall notify the other Participants owning an interest in such
Option in the same manner as provided for in Section 3.3 above with respect to
acquisitions of Acquired Interests, and each Participant owning an interest in
the Option shall elect to participate or to not participate in the exercise of
such Option in the same manner as provided in Sections 3.3 and 3.4 with respect
to elections to participate or to not participate in the acquisition of
Acquired Interests and the Participant proposing the exercise of the Option
shall be deemed to be the "Acquiring Party" under those Sections.   The effect
of a Participant's election to participate in such an exercise of an Option,
and the payment of costs and the ownership of interests in the Leases acquired
pursuant to such exercise, shall be handled in the same manner as provided in
Sections 3.3 and 3.4 with respect to elections to participate or not
participate in acquisitions of Acquired Interests.  Notwithstanding the
foregoing, should any Participant having the right to participate in such
exercise furnish notice (within the time provided for written notice with
respect to such an election) to the Acquiring Party that it wishes to defer
exercise of such Option, and should it be possible under the terms of the
Option to defer such exercise without any loss of costs or rights, the
Acquiring Party shall withdraw its proposal to exercise such Option.
Notwithstanding anything to the contrary contained herein, if a Participant has
not elected to participate in the acquisition of an acquired Option as provided
in Section 3.4, such Participant shall not have the right to participate in the
exercise of such Option and shall own no interest in the Leases resulting from
the exercise of such Option.





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       8
<PAGE>   9
         Section 3.6.     Election as to Participation in Maintenance or
Extension Costs.  In the event maintenance or extension costs are incurred with
respect to a Permit, Lease, Option or Farm-In, each Participant that owns an
Ownership Interest in such Lease, Option or Farm-In shall have the right to
elect whether to participate in such maintenance or extension cost for the
Lease, Option or Farm-In utilizing the same procedures set forth in Sections
3.3 and 3.4 above for Acquired Interests; provided, however, that in the event
that a Participant elects not to participate in a maintenance or extension
cost, such Participant shall, subject to the rights of Apache under the Apache
Agreement, promptly relinquish and assign to the Participants participating in
such maintenance or extension cost (in proportion to their relative Ownership
Interests) all of such non-participating Participant's Ownership Interest in
the interests in the Lease, Option or Farm-In that would have been relinquished
or lost if the maintenance or extension cost had not been paid.

         Section 3.7.     Apache Agreement.  As noted elsewhere in this Article
III, the right of BOG and UNEXCO in any Acquired Interest are subject to the
"AMI" created under Article XV.II. of any Operating Agreement executed under
the Apache Agreement, and to the rights afforded Apache thereunder.

         Section 3.8.     Joint Shoot Agreements.  The Participants recognize
that, in planning the Geophysical Program, one or more Participants may have
encountered, and may in the future encounter, third parties that own mineral or
leasehold interests (hereinafter sometimes referred to as "Third-Party Owners")
within the Program Area that are unwilling to farm-out, lease or option their
interests or grant seismic permits under terms and conditions that the
Participant finds acceptable.  In its efforts to obtain (or allow USA to
obtain) good quality Program Data across the Program Area, a Participant may in
the future enter into, but has not heretofore entered into, agreements
(hereinafter referred to as "Joint Shoot Agreements") with some of such
Third-Party Owners whereby one or more Participants agrees to cause the
Geophysical Program to be conducted across such Third Party Owner's acreage at
no cost to the Participants.  Under the terms of such Joint Shoot Agreements,
the Third-Party Owner may receive copies of the seismic data and/or
interpretations relating to such Third-Party Owner's acreage as well as some
additional tail acreage located adjacent to the Third-Party Owner's acreage and
located within the Program Area and the Participants hereto will be entitled to
receive and review copies of the seismic data that is obtained across the
Third-Party Owner's acreage.  Though the Participants will be entitled to
receive copies of and review the seismic data obtained over such Third-Party
Owner's acreage as provided above, the Joint Shoot Agreements may provide that
such Third-Party Owner shall own the seismic data covering its acreage and the
Participants may be subject to confidentiality requirements with respect to
such seismic data covering the Third-Party Owner's acreage.  In any future such
Joint Shoot Agreements, BOG shall require that for a minimum of one year from
the date thereof, the Third-Party Owner and its successors and assigns will not
compete with the Participants within the tail acreage over which such
Third-Party Owner receives seismic data and BOG may be required to agree that
the Participants and their successors and assigns shall not compete with such
Third-Party Owner within such Third-Party Owner's acreage even though such
acreage is located within the Program Area and AMI hereunder.

                                  ARTICLE IV.
                     PROSPECT DESIGNATION AND PARTICIPATION

         Section 4.1.     Prospect Designation.  Upon completion of the initial
interpretation of the Program Data, the Participants will meet to review the
interpretations and delineate prospects (hereinafter individually referred to
as a "Prospect Area") for exploration and development within the AMI.  The
Participants shall attempt to agree on 1) the number of Prospect Areas, and 2)
the acreage to be included in each Prospect Area.  As to all Prospect Areas
proposed and agreed upon by all of the Participants in the initial meeting,
such Prospect Areas shall be deemed to be designated and the Participants shall
document their agreement in writing in the form attached hereto as Exhibit C.
Any Prospect Area proposed at the initial meeting which is not agreed to by the
Participants may be re-submitted by any Party utilizing the procedures
contained in Section 4.2 below.





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       9
<PAGE>   10
         Section 4.2.     Additional Proposals by Participants for Prospect
Areas.  After the meeting described in Section 4.1 above, any Party hereto may
propose (hereinafter referred to as the "Proposing Party") that a portion of
the AMI be designated as a Prospect Area by giving written notice to the other
Participants, which notice shall contain 1) the proposed location for the
initial well on the Prospect Area, and 2) the acreage which such Party would
include in the Prospect Area.  The acreage proposed to be included in a
Prospect Area shall not include any acreage included within a previously
designated Prospect Area.

         Section 4.3.     Response to a Prospect Area Proposal.  Each Party
desiring to participate in a Prospect Area proposed by another Party under
Section 4.2 shall notify such Proposing Party, in writing, within thirty (30)
days after its receipt of such proposal, or sooner if an Option, Lease or
Farm-In is expiring (but in no event shall a Party be required to respond in
less than 48 hours), of its election to participate in the proposed Prospect
Area and stating whether or not such Party agrees with the acreage being
proposed for inclusion in the Prospect Area by the Proposing Party; an election
to participate in a Prospect Area which contains no statement as to whether the
Party agrees with the acreage proposed for inclusion in the Prospect Area shall
be deemed agreement to the acreage proposed for inclusion in the Prospect Area.
A Party who elects not to participate in the Prospect Area and who disagrees
with the acreage proposed to be included in the Prospect Area shall give notice
of such disagreement to the Proposing Party within the time and in the manner
provided above for elections to participate.  A Party failing to respond,
within the time and in the manner provided above, to a proposal for a Prospect
Area, or a Party responding and electing to not participate in a Prospect Area
but making no statement as to whether it agrees with the acreage proposed to be
included in the Prospect Area, will be deemed to have elected not to
participate in the Prospect Area and to have agreed to the acreage proposed to
be included in the Prospect Area.  If no Party disagrees with the acreage
proposed to be included in the proposed Prospect Area, such Prospect Area shall
be deemed to be designated and the Participants that have elected to
participate therein shall have the right to explore and/or develop such
Prospect Area to the exclusion of the Participants that have elected (or have
been deemed to have elected) not to participate in the Prospect Area.  If no
other Participants elect to participate with the Proposing Party in a
designated Prospect Area, the Proposing Party shall have the right to develop
the Prospect Area for its own account in accordance with the terms of Section
4.6 hereof.

         Section 4.4.     Determining Prospect Area Disagreements.  If, with
respect to a Prospect Area proposed under Section 4.1 or 4.2, there is
disagreement concerning the lands to be included in the Prospect Area, the
Participants shall, for a period of ten (10) days after the expiration of the
response period described in Section 4.3 above, attempt to agree upon the lands
to be included in the Prospect Area and, failing to reach such agreement within
such time, the Prospect Area shall be deemed to be designated and the lands
included in the Prospect Area shall consist of a 640 acre tract in the form of
a square with the proposed location for the initial well being located in the
center of the tract and the east and west boundary lines of such square running
due north and south.  Provided, further, any such Prospect Area determined
pursuant to this Section 4.4 shall not include any acreage included within a
previously designated Prospect Area unless all of the Participants agree to
amend the acreage included within the previously designated Prospect Area.  In
the event of such a Prospect Area disagreement, once the acreage to be included
within the Prospect Area has been resolved and the Prospect Area has been
designated in accordance with this Section 4.4, the Proposing Party must give
all of the Participants notice of the acreage included within the Prospect Area
and each of the Participants shall notify the Proposing Party, in writing,
within fifteen (15) days after its receipt of such notice, or sooner, if an
Option, Lease or Farm-In is expiring, of its election to participate in the
Prospect Area.

         Section 4.5.     Participation of the Participants.  With respect to
each Prospect Area proposed under Section 4.1 or 4.2, the participation of the
Participants therein shall be (unless all Participants agree otherwise) in
accordance with the terms set forth in Article II above, provided that if fewer
than all Participants participate in any Prospect Area, the participation of
each of the Participants participating therein shall be in the percentage
ownership interest in which such Participants agree to participate.  If fewer
than all of the Participants elect to participate and if the participating
Participants are unable to agree upon the percentages in which they will
participate





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       10
<PAGE>   11
(each Party electing to participate will be deemed to have agreed to
participate with the percentage Ownership Interest set forth for such Party in
the table contained in Section 2.2(a) above, but each Party will have no
obligation to participate for a larger interest) within 60 days after the date
of such Prospect Area proposal, the proposal for such Prospect Area will be
deemed withdrawn.  In the event that a Party elects not to participate in a
designated Prospect Area as aforesaid, for a period of five years from and
after the date hereof, such Party shall not compete within such Prospect Area
with the Participants which have elected to participate in the Prospect Area,
by owning or acquiring, directly or indirectly, through any agents,
representatives or Affiliates, any mineral, leasehold or royalty interests
within the Prospect Area.  Anything to the contrary contained in this Article
IV notwithstanding, in the event that a Party has elected not to participate in
an Acquired Interest that is included within a Prospect Area, such Party shall
not be entitled to receive an assignment in or otherwise participate in such
Acquired Interest even though it is included within a Prospect Area in which
such Party has elected to participate, except as to such Party's proportionate
share of any interest in the Acquired Interest that has been relinquished by a
Party that has elected not to participate in the applicable Prospect Area.

         Section 4.6.     Relinquishment of Interests by Non-Participating
Participants.  If a Party agrees or elects (or is deemed to have elected) not
to participate in a particular Prospect Area, then, such Party shall relinquish
and assign (without reimbursement for any costs) all interest, other than
rights to Program Data and/or the Apache Survey data, in such Prospect Area
(including, without limitation, rights under Options, Leases and Farm-Ins
insofar as they cover the Prospect Area) to the Participants electing to
participate in such designated Prospect Area in the proportions set forth in
Section 4.5 above.

         Section 4.7.     Operating Agreements.    The Participants agree that,
except as provided expressly otherwise herein, operations on each Prospect Area
shall be governed by the terms of the Operating Agreement which is in the form
attached hereto as Exhibit F (the "Operating Agreement") and the Participants
electing to participate in the Prospect Area shall be deemed subject to the
terms of such Operating Agreement, insofar as it covers the Prospect Area.

         Section 4.8.     Cinnabar Override and Fee.  The Participants
expressly recognize and agree that certain of their interests in the Program
Area and AMI are, or shall be, proportionately subject to an overriding royalty
in favor of Cinnabar pursuant to the terms of the Cinnabar Agreement.  In
addition, BOG agrees to reimburse UNEXCO for BOG's 50% share of the initial
$12,500 payment actually made to Cinnabar pursuant to the Cinnabar Agreement
within 15 days after receipt from UNEXCO of a written invoice for such amount,
and BOG agrees to reimburse UNEXCO for BOG's 50% share of the second and final
$12,500 payment actually made to Cinnabar pursuant to the Cinnabar Agreement
within 15 days after receipt from UNEXCO of written request for same.  UNEXCO
shall not amend or modify the Cinnabar Agreement without first securing the
consent of BOG, which consent may be granted or denied in the sole and absolute
discretion of BOG.

         Section 4.9.     Lease Burdens.  No Party hereto shall burden or
encumber any other Party's legal or equitable interest in a Permit, Lease,
Option or Farm-In with any overriding royalty, production payment, mortgage,
security interest or other burden except as provided in Sections 4.8 above,
without the consent of the other Participants; provided, however, that in its
efforts to obtain a Lease, Option or Farm-In from a third-party,  a Party
hereto may burden such Lease, Option or Farm-In with a royalty, overriding
royalty, production payment or other similar burden (other than a lien or
security interest), or acquire such interest subject to reservation of such a
burden, in favor of a third party owning such Lease, Option or Farm-In (farmor,
mineral owner, assignor, lessee or lessor) in such Party's reasonable efforts
to obtain the Lease, Option or Farm-In.  If any Party hereto burdens or
encumbers its own Ownership Interest, whether legal or beneficial, vested or
contingent, in any Option, Lease or Farm-In with any overriding royalty,
production payment, lien, security interest or other burden (hereinafter
referred to as "Subsequently Created Burdens") except as provided in this
Section 4.9 or in Section 4.8 above, and such Party is thereafter required
under the terms of this Agreement, or the applicable Operating Agreement, to
assign or relinquish to any other Party or Participants, all or a portion of
its Ownership Interest and/or the production attributable thereto, said other
Party or Participants shall receive such assignment and/or production free and
clear of such Subsequently Created





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       11
<PAGE>   12
Burdens and such Party shall indemnify and hold harmless the Party or
Participants entitled to the assignment or forfeiture from any and all claims
and demands for payment asserted by owners of such Subsequently Created
Burdens.

                                   ARTICLE V.
                              DRILLING OPERATIONS

         Section 5.1.     Drilling Operations.

         (a)     A Party's election to participate in a Prospect Area in
accordance with the terms of Article IV above does not constitute a commitment
to participate in the drilling of a well within the Prospect Area.  Any Party
that has participated in a Prospect Area may propose the drilling of the
initial well (being the first well drilled by any of the Participants within
the applicable Prospect Area and being hereinafter referred to as an "Initial
Well") or any subsequent well (being any well drilled within a Prospect Area
following the drilling of the Initial Well and being hereinafter referred to as
a "Subsequent Well") within the Prospect Area in accordance with the procedures
set forth in the Operating Agreement.

         (b)     In the event that a Party elects not to participate in the
drilling of the Initial Well proposed and drilled within the Prospect Area,
anything to the contrary contained in the applicable (or deemed applicable)
Operating Agreement to the contrary, such Party (i) must permanently relinquish
and assign (without reimbursement for costs) all of its right, title and
interest in the applicable Prospect Area to the Participants participating in
the drilling of such Initial Well (in the ratio that each participating Party's
leasehold working interest in the acreage included within the drilling and/or
proration unit for such Initial Well bears to the total of the leasehold
working interests of all of the Participants hereto participating in the
operation), (ii) shall no longer (as of the date it elects not to participate
in the drilling of the Initial Well) be deemed a party to the Operating
Agreement for such Prospect Area, and (iii) shall not own or acquire any
mineral, leasehold, royalty or other interest in oil, gas and/or other minerals
within such Prospect Area for a period of five (5) years from the date of this
Agreement.

         (c)     In the event that a Party has participated in the drilling of
the Initial Well drilled within a Prospect Area but such Party does not
participate in the drilling of any Subsequent Well within such Prospect Area,
such Party (i) must permanently relinquish (without reimbursement for costs)
and assign all of its right, title and interest in the drilling and/or
proration unit for such Subsequent Well to the Participants participating in
the drilling of such Subsequent Well (in the ratio that each participating
Party's leasehold working interest in the acreage included within the drilling
and/or proration unit for such Subsequent Well bears to the total of the
leasehold working interests of all of the Participants hereto participating in
the operation), (ii) shall permanently relinquish (as of the date it elects not
to participate in the drilling of such Subsequent Well) all of its rights and
interests under the applicable Operating Agreement insofar as it covers the
relinquished drilling and/or proration unit, and (iii) shall not own or acquire
any mineral, leasehold, royalty or other interest in oil, gas and/or other
minerals within the drilling and/or proration unit for such Subsequent Well for
a period of five (5) years from the date of this Agreement.

         (d)     In the event that a Party has participated in the drilling of
the Initial Well or any Subsequent Well within a Prospect Area and then elects
not to participate in a completion operation proposed for such well, such Party
(i) must permanently relinquish (without reimbursement for costs) and assign
all of its right, title and interest in the completed formation within the
drilling and/or proration unit for such well and all of the production which
may be obtained from such completed formation within that well  to the
Participants participating in such completion of such formation (in the ratio
that each participating Party's leasehold working interest in the acreage
included within the drilling and/or proration unit for such well bears to the
total of the leasehold working interests of all of the Participants hereto
participating in the operation), (ii) shall relinquish (as of the date it
elects not to participate in the completion operation) all of its rights and
interests under the applicable Operating Agreement insofar as it covers the
relinquished completed formation within the drilling and/or proration unit for
such well, and (iii) shall not own or acquire any mineral, leasehold, royalty
or other interest in oil, gas





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       12
<PAGE>   13
and/or other minerals located within the completed formation within the
drilling and/or proration unit for such well for a period of five (5) years
form the date of this Agreement.  If a Party has elected to participate in the
drilling of a well and then elects not to participate in a proposed completion
operation within the well, but then subsequently participates in the completion
of another formation within the same well, such Party will be obligated to pay
for its proportionate share of the completion operation costs which were
previously incurred in completing the other formation in accordance with the
drilling footage ratio method set forth in COPAS Bulletin No. 2 in paragraph
B.1(b) for intangible costs and in paragraphs B.1 and B.2 for tangible costs.

         (e)     If there is no drilling or proration unit for a well or if
there is no other allocation for spacing or allowable purposes, then to the
extent practicable, an area in the form of a square within the Prospect Area
with the well being located in the center thereof of six hundred and forty
(640) acres around a gas well and eighty (80) acres around an oil well, shall
be deemed to be the drilling or proration unit for such well, in either event
with the east and west boundary lines of such square running as nearly as
possible due north and south; provided, however, that it is the Participants'
intent that the relinquishment and assignment of interests provided for in this
Section 5.1 for failure to participate in the drilling of a Subsequent Well or
a completion operation apply to all and only all of the leasehold interests,
mineral interests and production that are allocated to the relevant well (or
completed formation) and the Participants hereto agree that in the event that
such allocation changes in the future, the Participants shall execute any
future or further relinquishment instruments or other documentation that is
necessary to effectuate that intent.

         (f)     Any well drilled to replace a well drilled within a Prospect
Area because of drilling or mechanical difficulties incurred in the drilling of
such well shall be deemed to be the same well for purposes of the
relinquishment and assignment provisions of this Section 5.1; provided,
however, that only the Participants that participated in the original drilling
of the well shall have the right to participate in the drilling of a
replacement well for such well.

         (g)     In the event of any required relinquishment and assignment of
interests as provided in this Section 5.1, the relinquishing Party shall
promptly execute all conveyance instruments necessary to effectuate such
relinquishment and assignment.

         Section 5.2.     Designation of Initial Operator.  It is agreed and
understood that Apache is designated as the initial operator in the Operating
Agreement.

         Section 5.3.     AMI for Prospect Area.  Commencing with the
establishment of a Prospect Area, such Prospect Area shall from that time
forward no longer be subject to the AMI provided for in Section 3.1 above and
shall thereafter be considered covered instead by a new Prospect Area AMI.  The
new Prospect Area AMI (i) is binding on the Participants participating in such
Prospect Area, (ii) consists of such Prospect Area, (iii) lasts until the later
to occur of three (3) years from the date hereof or the date that the Operating
Agreement for such Prospect Area terminates, and (iv) is governed by the same
terms set forth in Sections 3.2, 3.3, 3.4, 3.5, 3.6, 4.8 and 4.9 with the
participation percentages of the Participants being in accordance with their
ownership interest in the Leases, Options and Farm-Ins located within the
Prospect Area; provided, however, that in the event that a Party has elected
not to participate in the Prospect Area or the drilling of the Initial Well
within such Prospect Area, such Party shall not own or acquire any interest in
that part of any Acquired Interest that is located within such Prospect Area.
Any portion of the AMI not designated as a Prospect Area shall continue to be
subject to the AMI provided for in Article III above.

         Section 5.4.     Assignment of Ownership Interests in Leases, Options
and Farm-Ins.  Unless such assignment is not permitted under the terms of the
applicable Option, Lease or Farm-In, the Participants agree that each Party's
Ownership Interest (as such Ownership Interest is subject to change in
accordance with the provisions hereof and subject to the rights afforded Apache
under the Apache Agreement) in each Lease, Option or Farm-In shall be assigned
to the Participants utilizing the form of assignment which is attached hereto
as Exhibit E prior to the commencement of drilling operations for any well
which includes all or part of the acreage that is covered by the Option, Lease
or Farm- in in the drilling and/or proration unit for such well.  In





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       13
<PAGE>   14
addition to the above, following the expiration of the AMI hereunder and
subject to the forfeiture provisions herein contained and the rights afforded
Apache under the Apache Agreement, the Participants shall be assigned their
Ownership Interests in any Options, Leases or Farm-Ins which have not already
been assigned to the Participants.

         Section 5.5.     Drilling Costs.  Subject to the terms of the
Operating Agreement and Section 5.1 above, the Participants shall pay for all
drilling, completion and workover costs in proportion to their working interest
in each well, as determined by the Participants Ownership Interests in the
Leases, Options and Farm-Ins included within the drilling and proration unit
for such well.

                                  ARTICLE VI.
                                 MISCELLANEOUS

         Section 6.1.     Assignments.  Any Participant hereto may assign all
or any part of its interest under the terms of this Agreement.  This Agreement
shall be binding upon and inure to the benefit of the Participants hereto and
their respective successors and their respective assigns of rights hereunder;
provided, however, that the conveyance or assignment instrument vesting such
assignee with all or part of such interests must expressly provide that the
assignment or conveyance is made subject to the terms and conditions contained
in this Agreement.  In addition, in any such assignment or conveyance, the
assignee shall expressly agree to assume and be responsible for any
liabilities, damages, obligations, covenants and agreements arising from and
after the date of such assignment or conveyance, in relation to or otherwise
out of the properties, rights and interests that are the subject of this
Agreement and/or such assignment or conveyance, and the assignor shall remain
responsible for any of the foregoing arising prior to the date of such
assignment or conveyance.  Any subsequent assignment or conveyance shall
likewise contain express language so allocating responsibility as between
assignor and assignee.  Unless (and then only to the extent that) this
Agreement is itself assigned at the same time, the benefits of this Agreement
shall not run with an assignment of a Participant's interests in the Options,
Leases or Farm-Ins, or any other rights in lands within the Program Area, but
the assigned interest shall be subject to the terms of this Agreement.

         Section 6.2.     Affiliate's Actions.  The Parties hereto agree that
the provisions of Sections 2.2, 3.1, 3.2, 3.3, 3.4, 4.5, 4.8, 4.9, 5.1 and 5.4
above shall be binding upon their Affiliates.  As such, the Parties hereto
agree that if any of their Affiliates disclose information which is
confidential pursuant to the terms of Section 2.2(b) of this Agreement or
acquire interests of any kind within the AMI hereunder, such Party shall be
deemed to have disclosed such information or acquired the interest itself,
shall be responsible to the other Parties hereunder for such acts, and must
cause its Affiliate to offer any interests that have been acquired by its
Affiliate to the other Parties hereto in accordance with the provisions
referenced in this Section 6.2.

         Section 6.3.     Notices.  All notices and other communications
required or permitted under this Agreement shall be in writing, and unless
otherwise specifically provided, shall be delivered personally, or by mail,
telecopier or delivery service, to the addresses set forth opposite the
signatures of the Parties below, and shall be considered delivered upon the
date of receipt.  Each Party may specify its proper address or any other post
office address within the continental limits of the United States by giving
notice to other Parties, in the manner provided in this section, at least ten
(10) days prior to the effective date of such change of address.

         Section 6.4.     Merger.  This Agreement supersedes any and all prior
and existing agreements, whether oral or in writing, between the Parties hereto
with respect to the subject matter hereof and contains all of the covenants and
agreements between the Parties with respect to the subject matter hereof.  Each
Party acknowledges that no Party to this Agreement or anyone on their behalf
has made any representations, inducements, promises or agreements, orally or
otherwise, relating to the subject matter of this Agreement that are not
embodied herein.





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       14
<PAGE>   15
         Section 6.5.     Limitation of Actions.  No claim may be asserted by
any Party against any other Party hereto with respect to any event, act or
omission that occurred more than two (2) years prior to such claim being
asserted.

         Section 6.6.     Right to Specific Performance.  Each Party
acknowledges (i) that its obligations under this Agreement are unique and (ii)
that the other Parties would be irreparably damaged and would not have an
adequate remedy at law for damages if such Party defaults in its obligations
hereunder.  Each Party expressly waives the defense that a remedy in damages
will be adequate.  If any Party should default in its obligations hereunder,
each non-defaulting Party, in addition to any other available rights or
remedies, may sue in equity for specific performance or injunctive relief.

         Section 6.7.     Right to Recoup Legal Fees.  In the event that any
Party files a lawsuit against any other Party hereto related in any way to this
Agreement and one of such Parties receives a final judgment in its favor as to
all of the claims which are made in such lawsuit, such prevailing Party shall
be reimbursed by the losing Party for all reasonable legal costs (including
without limitation attorneys' fees and court costs) and expenses which have
been incurred by such prevailing Party in such lawsuit.  In such event, the
amount of reasonable legal costs to be awarded to the prevailing Party shall be
determined by the same court which renders the judgment on the Parties' claims.

         Section 6.8.     Counterparts.  This Agreement may be executed in
multiple counterparts, each of which shall be binding upon the signing Party or
Parties thereto as fully as if all Parties had executed one instrument, and all
of such counterparts shall constitute one and the same instrument.  If
counterparts of this Agreement are executed, the signatures of the Parties, as
affixed hereto, may be combined in and treated and given effect for all
purposes as a single instrument.  However, anything to the contrary contained
herein notwithstanding, this Agreement shall not be binding upon any Party
hereto unless and until all of the Parties sign a counterpart thereof.

         Section 6.9      Other Agreements.  Neither Party will modify, amend,
extend or terminate the USA Agreement, the UST Agreement, the Apache Agreement
or the Cinnabar Agreement without first securing the written consent of the
other Party hereto, which consent may be granted or withheld in the sole and
absolute discretion of such Party.

         This Agreement is executed by the Parties on the dates set forth
opposite their respective signatures below, but is effective for all purposes
as of the date first set forth above.

Address:                                           BRIGHAM OIL & GAS, L.P.,
         5949 Sherry Lane, Suite 1616          by Brigham Exploration Company,
         Dallas, Texas  75225                  its Managing General Partner
         (214) 360-9182               
         Fax:  (214) 360-9825         
                                      
Date:    January 3, 1997                       By:  /s/ ANNE L. BRIGHAM 
      ----------------------------                -----------------------------
                                                  Anne L. Brigham,
Executive Vice President              
                                      
   
                                      
Address:                                          UNEXCO, INC.
         16420 Park Ten Place         
         Suite 300                    
         Houston, Texas 77084-5051    
         (713) 578-8081               
         Fax: (713) 578-7091                   By:/s/ PATRICK A. DONAIS        
                                                  -----------------------------
                                                  Patrick A. Donais
Date:    1/6/97                                   Vice President
      ----------------------------                                    
    
                                      
                                      



                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       15
<PAGE>   16
                                LIST OF EXHIBITS




Exhibit A -- Program Area

Exhibit B -- Existing Permits, Existing Options, Existing Leases and Existing
             Farm-Ins

Exhibit C -- Agreement as to Prospect Areas

Exhibit D -- Form Confidentiality Agreement

Exhibit E -- Form of  Assignment

Exhibit F -- Joint Operating Agreement

Exhibit G -- USA Agreement

Exhibit H -- UST Agreement

Exhibit I -- Parameters of 3-D survey





                                              Geophysical Exploration Agreement
                                              Southwest Danbury Project
                                       16

<PAGE>   1
                                                                   EXHIBIT 10.35


                       GEOPHYSICAL EXPLORATION AGREEMENT
                                 WELDER PROJECT
                              DUVAL COUNTY, TEXAS



       This Geophysical Exploration Agreement (this "Agreement"), dated
effective as of the 1 st day of October, 1996, is by and among UNEXCO, INC.
("UNEXCO") and BRIGHAM OIL & GAS, L.P. ("BOG") (UNEXCO and BOG are sometimes
referred to herein individually as "Party" and collectively as "Parties");

       WHEREAS, the Parties identified an area of mutual interest (the "AMI")
in Duval County, Texas, identified on Exhibit A which is attached hereto, which
UNEXCO and BOG believe to be prospective for oil and gas exploration and
production; and

       WHEREAS, the Parties reached an agreement with respect to the evaluation
by them of the AMI; and

       WHEREAS, BOG entered into that certain Seismic and Lease Option
Agreement with Roger F. Welder, et. al. (the "Welder Heirs"), dated effective
as of October 30, 1996, covering lands in Duval County, Texas, and a Memorandum
of Seismic and Lease Option Agreement has been filed of record at Volume 215,
Page 325 of the Official Public Records of Duval County, Texas, giving public
notice of the existence of the Seismic and Lease Option Agreement (such Seismic
and Lease Option Agreement being sometimes referred to herein as the "Welder
Option"); and

       WHEREAS, BOG has acquired that certain Oil and Gas Lease by and between
the State of Texas, acting by and through its agent Roger F. Welder, et al. and
BOG, dated December 24, 1996 (such Oil and Gas Lease being sometimes referred
to herein as the "First State Lease"); and

       WHEREAS, BOG entered into that certain Seismic Data Licensing Agreement,
Webb and Duval Counties, Texas, with Western Geophysical Company ("WGC") dated
November 6, 1996 (a copy of which is attached hereto as Exhibit G and being
hereinafter referred to as the "WGC Agreement"), providing for the non-
exclusive licensing of seismic data to BOG and the Welder Heirs covering all or
parts of the AMI, together with other lands; and

       WHEREAS, in addition to the Welder Option, the Parties may have obtained
other option agreements to acquire oil and gas leases (the Welder Option and
any other option agreements already obtained by either of the Parties being
sometimes referred to herein as "Existing Options"), and in addition to the
First State Lease the Parties may have obtained other oil and gas leases (the
First State Lease and any other oil and gas leases already obtained by either
of the Parties being sometimes referred to herein as the "Existing Leases") and
other agreements to obtain oil and gas leases, mineral interests, royalty
interests or other interests in oil, gas or other hydrocarbons (such other
agreements that have already been obtained by either of the Parties being
sometimes referred to herein as the "Existing Farm-Ins") covering portions of
the AMI (the Existing Options, Existing Leases and Existing Farm-Ins being
described on Exhibit B hereto), and the Parties anticipate that additional
options to acquire oil and gas leases (such options and the Existing Options
being herein referred to as "Options"), oil and gas leases (such leases and the
Existing Leases being herein referred to as "Leases"), and other agreements to
obtain oil and gas leases, mineral interests, royalty interests or other
interests in oil, gas or other hydrocarbons (such agreements and the Existing
Farm-Ins being referred to herein as "Farm-Ins") may be obtained in the future
covering portions of the AMI; and

       WHEREAS, the Parties also reached an agreement with respect to certain
matters concerning the ownership of Options, Leases and Farm-Ins, and the
future exploration, development and operation of the AMI;

       NOW, THEREFORE, for and in consideration of the mutual covenants
contained herein and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Parties hereto agree as
follows:
<PAGE>   2
                                   ARTICLE I.
                      CONTINGENCY OF UNEXCO PARTICIPATION

       Section 1.1.  Welder Heirs' Consent.  The Parties recognize and
acknowledge that under the terms of the Welder Option, an interest in the
Welder Option or any Lease obtained by exercising the Welder Option may not be
assigned to UNEXCO or any other party without first obtaining the Welder Heirs'
consent to such assignment.  The Parties agree that they shall utilize
reasonable efforts to obtain all of the Welder Heirs' consent to assignment to
UNEXCO.  In the event that on or before April 30, 1997, the Parties have not
obtained all of the Welder Heirs' written consent to such assignment, (i) this
Agreement shall terminate in its entirety, (ii) UNEXCO shall immediately assign
and convey to BOG all of the interests (whether real, personal, intangible,
contingent or vested) acquired by UNEXCO or any of its successors or assigns
which are related in any way to the AMI hereunder, and (iii) BOG shall promptly
reimburse UNEXCO for all of the costs which UNEXCO has paid or reimbursed BOG
for under the terms of this Agreement.

                                  ARTICLE II.
                            RELATIONSHIP OF PARTIES

       Section 2.1.  No Partnership.  The liabilities of the Parties hereunder
shall be several, not joint or collective.  It is not the intention of the
Parties to create, nor shall this Agreement be deemed as creating, a mining,
tax or other partnership or association or to render the Parties liable as
partners.  However, if for federal income tax purposes, this Agreement and the
operations hereunder are regarded as a partnership, each Party thereby affected
elects to be excluded from the application of all of the provisions of
Subchapter "K," Chapter 1, Subtitle "A," of the Internal Revenue Code of 1986,
as amended (hereinafter referred to as the "Code"), as permitted and authorized
by Section 761 of the Code and the regulations promulgated thereunder.  Should
there be any requirement that each Party hereby affected give further evidence
of this election, each such Party shall execute such documents and furnish such
other evidence as may be required by the Federal Internal Revenue Service or as
may be necessary to evidence this election.  No Party shall give any notice or
take any other action inconsistent with the election made hereby.  In making
the foregoing election, each Party states that the income derived by such Party
from operations hereunder can be adequately determined without the computation
of partnership taxable income.

       Section 2.2.  Representations and Third Party Claims and Liabilities.

       (a)    BOG represents and warrants that it has full power to enter into
and perform its obligations under this Agreement and has taken all appropriate
action to authorize entering into this Agreement and performance of its
obligations hereunder.  BOG represents and warrants that other than
requirements (if any) that there be obtained consents or waivers of
preferential rights regarding the transfer of Options, Leases or Farm-Ins,
neither the execution and delivery of this Agreement, nor the consummation of
the transactions contemplated hereby, nor the compliance with the terms hereof,
will result in any material default under any material agreement or instrument
to which BOG is a party or by which BOG is bound, or violate any order, writ,
injunction, decree, statute, rule or regulation applicable to BOG.  BOG
represents and warrants that this Agreement constitutes the legal, valid and
binding obligation of BOG, enforceable in accordance with its terms, except as
limited by bankruptcy or other laws applicable generally to creditor's rights
and as limited by general equitable principles.  BOG represents that there are
no suits, actions, claims, investigations, inquiries, proceedings or demands
pending (or, to the best of BOG's knowledge, threatened) which affect the
execution and delivery of this Agreement, or the consummation of the
transactions contemplated hereby.

       (b)    UNEXCO represents and warrants that it has full power to enter
into and perform its obligations under this Agreement and has taken all
appropriate action to authorize entering into this Agreement and performance of
its obligations hereunder.  UNEXCO represents and warrants that other than
requirements (if any) that there be obtained consents or waivers of
preferential rights regarding the transfer of Options, Leases or Farm-Ins,
neither the execution





Geophysical Exploration Agreement
Welder Project
                                       2
<PAGE>   3
and delivery of this Agreement, nor the consummation of the transactions
contemplated hereby, nor the compliance with the terms hereof, will result in
any material default under any material agreement or instrument to which UNEXCO
is a party or by which UNEXCO is bound, or violate any order, writ, injunction,
decree, statute, rule or regulation applicable to UNEXCO.  UNEXCO represents
and warrants that this Agreement constitutes the legal, valid and binding
obligation of UNEXCO, enforceable in accordance with its terms, except as
limited by bankruptcy or other laws applicable generally to creditor's rights
and as limited by general equitable principles.  UNEXCO represents and warrants
that there are no suits, actions, claims, investigations, inquiries,
proceedings or demands pending (or, to the best of UNEXCO's knowledge,
threatened) which affect the execution and delivery of this Agreement, or the
consummation of the transactions contemplated hereby.

       (c)    ANY THIRD PARTY (TO INCLUDE ANY GOVERNMENTAL AUTHORITY) DAMAGE OR
REMEDIATION CLAIM OR SUIT OF ANY KIND ARISING FROM ANY OPERATIONS CONDUCTED
PURSUANT TO THE TERMS OF THIS AGREEMENT, AND ALL COSTS AND EXPENSES OF
HANDLING, SETTLING, OR OTHERWISE DISCHARGING SUCH CLAIM OR SUIT SHALL BE AT THE
EXPENSE OF ALL OF THE PARTIES PARTICIPATING IN THE OPERATION GIVING RISE TO THE
CLAIM OR SUIT, EACH PARTY'S RESPONSIBILITY BEING IN THE PROPORTION THAT THEIR
OWNERSHIP INTEREST (AS SET FORTH IN THE TABLE IN SECTION 4.2(a) BELOW) BEARS TO
THE TOTAL OF THE OWNERSHIP INTERESTS OF ALL OF THE PARTIES PARTICIPATING IN THE
OPERATION GIVING RISE TO THE CLAIM OR SUIT, REGARDLESS OF WHETHER OR NOT SUCH
THIRD PARTY DAMAGE OR REMEDIATION CLAIM OR SUIT IS FOUND TO ARISE IN WHOLE OR
IN PART FROM ANY THE SOLE OR CONCURRENT NEGLIGENCE OR OTHER FAULT OF ANY KIND
OF ANY PARTY HERETO.  In the event any such claim or suit is made against any
Party hereto, such Party shall immediately notify all other Parties, and the
claim or suit shall be jointly handled by all of the Parties hereto
participating in the ownership and/or operation giving rise to the claim or
suit.  Anything to the contrary contained in this Section 2.2(c)
notwithstanding, this Section 2.2(c) shall not apply to any claims, actions or
suits which are related in any way to a Party's breach of any of the
representations or warranties which are set forth above in this Section 2.2.

                                  ARTICLE III.
                               EVALUATION PROGRAM

       Section 3.1.  Scope of the Geophysical Program.  The Parties recognize
and acknowledge that pursuant to the terms of the WGC Agreement, WGC shall
conduct a three-dimensional geophysical program across all or part of the AMI
(that part of the WGC three-dimensional geophysical program which covers the
AMI being herein referred to as the "Geophysical Program"), together with other
lands located in the general area of the AMI, and that pursuant to the terms of
the WGC Agreement, BOG and the Welder Heirs shall receive a license to the
three-dimensional seismic data which covers the AMI (that part of the three-
dimensional seismic data resulting from the WGC geophysical program and which
covers the AMI being herein referred to as the "Program Data").  BOG will
interpret the Program Data for the benefit of the Parties.  During the term of
the AMI (as defined in Section 4.1 below) hereunder, UNEXCO shall have the
right to come into BOG's offices at mutually agreeable times to review the
Program Data and BOG's interpretations with BOG and give BOG input with respect
to the interpretations prepared by BOG.  However, due to the restrictions
contained in the WGC Agreement, UNEXCO shall not have the right to actively
work the Program Data.  BOG shall also provide UNEXCO with copies of
interpretations generated by BOG.

           Section 3.2.  Use of the Program Data and Interpretations.

       (a)    BOG shall receive everything that it needs to adequately
interpret the Program Data at the cost of the Parties as set forth in Section
3.3 below.  Provided that BOG has paid its share of the Geophysical Program
Costs (as defined and set forth in Section 3.3 below) BOG





Geophysical Exploration Agreement
Welder Project
                                       3
<PAGE>   4
shall have the right to utilize and interpret the Program Data in its
exploration and development efforts within the AMI.

       (b)    Provided that UNEXCO has paid its share of the Geophysical
Program Costs (as defined and set forth in Section 3.3 below), UNEXCO shall
have the right to receive copies of the interpretations that are generated by
BOG from the Program Data.  UNEXCO shall have the right to utilize the
interpretations in its exploration and development efforts within the AMI.  In
addition, provided that UNEXCO has paid its share of the Geophysical Program
Costs, during the term of the AMI hereunder, UNEXCO shall have the right to
come into BOG's offices at mutually agreeable times to review the Program Data
and BOG's interpretations with BOG on a 3-D workstation.  However, due to the
restrictions contained in the WGC Agreement, UNEXCO shall not have the right to
actively work the Program Data.  UNEXCO recognizes and agrees that its right to
utilize the Program Data and interpretations are subject to the terms,
provisions, restrictions and conditions of the WGC Agreement and UNEXCO hereby
agrees to abide by all of the terms, provisions, conditions and restrictions
contained in the WGC Agreement.

       (c)    No Party shall trade, exchange or otherwise disclose any
interpretations of the Program Data to any third party within two (2) years of
the completion of processing of the Program Data without written consent from
the other Party hereto, except to the Welder Heirs as provided in the Welder
Option and except that each Party may trade, exchange or otherwise disclose the
interpretations, at any time, without the consent of the other Party hereto, to
(i) parties in connection with agreements or bona fide negotiations with such
parties for the farming-out or assignment to the disclosing Party of leasehold
or mineral interests covering acreage that is located within the AMI, (ii)
parties in connection with agreements or bona fide negotiations with such
parties for the farming-in or receiving an assignment from the disclosing Party
of part of the disclosing Party's Ownership Interests in Options, Leases or
Farm-Ins, (iii) parties who have entered into agreements or are interested in
entering into agreements to purchase an interest or otherwise participate in
the exploration and/or development of all or parts of the AMI with the
disclosing Party, (iv) parties that have invested in the disclosing Party's
exploration and/or development operations, (v) parties that are hired by a
Party as a consultant to help or facilitate such Party's exploration and/or
development operations within the AMI, or (vi) parties that are hired by a
Party to analyze or examine such Party's existing or potential oil and/or gas
reserves within the AMI for such Party's financial or regulatory reporting
purposes; provided, however, that the disclosing Party must cause all third
parties that are listed in (ii), (iii), (iv) and (v) above, to which the
interpretations are to be disclosed prior to the expiration of such two (2)
year period, to execute a confidentiality agreement in the form attached hereto
as Exhibit D covering the acreage which is covered by the interpretations that
are to be disclosed and naming all of the Parties hereto as "Offeror" in such
confidentiality agreement, prior to the third party's review of the
interpretations.

       (d)    The Parties recognize and acknowledge that under the terms of the
WGC Agreement there are limited rights of disclosure to the Program Data.  The
Parties agree to abide by the terms of the WGC Agreement.  In addition, no
Party shall disclose the Program Data to any Party within two (2) years of the
completion of processing of the Program Data without written consent from the
other Party hereto, except that, subject to the terms of the WGC Agreement,
each Party may disclose the Program Data, at any time, without the consent of
the other Party hereto, to (i) parties in connection with agreements or bona
fide negotiations with such parties for the farming-out or assignment to the
disclosing Party of leasehold or mineral interests covering acreage that is
located within the AMI, (ii) parties in connection with agreements or bona fide
negotiations with such parties for the farming-in or receiving an assignment
from the disclosing Party of part of the disclosing Party's Ownership Interests
in Leases or Farm-Ins, (iii) parties who have entered into agreements or are
interested in entering into agreements to purchase an interest or otherwise
participate in the exploration and/or development of all or parts of the AMI
with the disclosing Party, (iv) parties that have invested in the disclosing
Party's exploration and/or development operations, (v) parties that are hired
by a Party as a consultant to help or facilitate such Party's exploration
and/or development operations within the AMI, or (vi) parties that are hired by
a Party to analyze or examine such Party's existing or potential oil and/or gas
reserves within the AMI for such Party's financial or





Geophysical Exploration Agreement
Welder Project
                                       4
<PAGE>   5
regulatory reporting purposes; provided, however, that the disclosing Party
must cause all third parties that are listed in (ii), (iii), (iv) and (v)
above, to which the Program Data is to be disclosed prior to the expiration of
such two (2) year period, to execute a confidentiality agreement in the form
attached hereto as Exhibit D covering the acreage which is covered by the
Program Data that is to be disclosed and naming all of the Parties hereto as
"Offeror" in such confidentiality agreement, prior to the third party's review
of the Program Data.  The Parties recognize that under the terms of the WGC
Agreement UNEXCO cannot have a separate copy of the Program Data.  However, in
the event that UNEXCO has a third party described in (i), (ii), (iii), (iv),
(v) or (vi) above, to whom UNEXCO desires to disclose all or part of the
Program Data, UNEXCO shall have the right to bring such third-party into BOG's
offices at mutually agreeable times to review the Program Data with BOG and
UNEXCO.

       (e)    In the event that UNEXCO has not paid for its share of the
Geophysical Program Costs in accordance with the terms of Section 3.3 below,
BOG shall have no obligation to disclose or release any information of any kind
to UNEXCO which is in any way related to the Program Data or interpretations
until such time as UNEXCO has paid all of the Geophysical Program Costs which
are currently due.

       Section 3.3.  Payment of Costs of Seismic Program.

       (a)    Each of the Parties shall pay their percentage share listed
opposite such Party's name in the table set forth below in this Section 3.3(a),
of all of the costs and liabilities that are associated with the conduct of the
Geophysical Program, including, without limitation (i) the costs and charges
that are to be paid to WGC pursuant to the terms of the WGC Agreement which are
related to or allocable to the Geophysical Program (see additional provisions
contained in Section 4.8 and 6.5 below related to payments due to WGC under
Sections B and C of the WGC Agreement), insofar as they are related to the
Geophysical Program, (ii) the costs and charges that are to be paid to WGC
pursuant to the terms of the WGC Agreement in order to license the Program Data
to the Welder Heirs, (iii) all costs incurred to other third-parties which are
in any way associated with the conduct of the Geophysical Program or the
processing or interpretation of the Program Data resulting from the Geophysical
Program, (iv) geological consultant fees incurred by BOG to help the Parties in
their exploration and development efforts within the AMI , (v) a charge of
$60.00 for each half hour, or fraction thereof, of use of BOG's work stations
while modeling and/or interpreting the Program Data and $35.00 for each scaled
plot generated on BOG's plotter, (vi) the BOG Employee Time Charges (as defined
below in this Section 3.3(a), and (vii) any other costs associated with the
Geophysical Program (all of the costs described above in this Section 3.3(a)
being hereinafter sometimes collectively referred to as "Geophysical Program
Costs").

<TABLE>
<CAPTION>
                            Party                 Percentage
                            -----                 ----------
                            <S>            <C>   <C>
                            UNEXCO         30.00%
                            BOG                   70.00%.
</TABLE>

For purposes of this Agreement "BOG Employee Time Charges" shall mean the
amount BOG shall have the right to charge UNEXCO (in the percentage indicated
in the table above) for the time spent by of certain of its employees in
performing land, geological or geophysical work related to the Parties'
exploration and/or development efforts within the AMI.  The rates per hour that
BOG may charge UNEXCO for time spent by its landmen, geologists, geophysicists,
technicians and division order analysts performing work related to the Parties'
exploration and/or development efforts within the AMI is set forth in the table
below:
<TABLE>
<CAPTION>
                                                  Rate Per Hour for
                     Type of Employee             Work Performed 
                     ----------------             ---------------
                     <S>                          <C>
                     Geophysicist                 $60.00
                     Geologist                    $50.00
                     Technician                   $25.00
                     Landman                      $40.00
                     Division Order Analyst       $25.00.
</TABLE>





Geophysical Exploration Agreement
Welder Project
                                       5
<PAGE>   6
Anything to the contrary contained above notwithstanding, the Parties agree
that in the event that a contractor or consultant (as opposed to a BOG
employee) is utilized by BOG to provide any services or work related to the
Parties exploration and/or development operations within the AMI, the Parties
shall be charged for the actual cost of such consulting or contractor services
as part of the Geophysical Program Costs.

       (b)    Concurrent with its execution of this Agreement UNEXCO shall
forward to BOG UNEXCO's share of the estimated total Geophysical Program Costs
expected to be incurred by the Parties.  In the event that following WGC's
completion of the field acquisition of the Program Data it reasonably appears
to BOG that the total estimated Geophysical Program Costs will exceed the
original estimate of such amount which was used for pre-payment purposes, BOG
shall have the right to invoice UNEXCO for its  share of the amount by which
BOG reasonably expects the total Geophysical Program Costs to exceed the
original estimate.  In such event, UNEXCO shall remit to BOG the invoiced
amount within thirty (30) days of its receipt of such invoice.  In the event
that the total Geophysical Program Costs incurred is less than the total
estimate (as same may have been supplemented as provided above) utilized for
purposes of calculating UNEXCO's pre-payments, BOG shall reimburse to UNEXCO
its share of the difference between the estimated amount of the total
Geophysical Program Costs utilized for purposes of calculating the pre-payment
and the actual total amount of Geophysical Program Costs incurred.  In the
event that the Geophysical Program Costs exceed the amount of the estimated
pre-payment (as same may have been supplemented as provided above) or
Geophysical Program Costs, UNEXCO shall pay BOG its share of costs incurred
over and above the estimate within thirty (30) days of its receipt of an
invoice from BOG indicating the amount of any such costs.  BOG shall not be
obligated to deliver any information relative to the Program Data or
interpretations to UNEXCO until such time as all costs currently owed by UNEXCO
have been received by BOG.

       Section 3.4.  Disclaimer of Warranties and DTPA.  The Parties understand
that BOG will use reasonable efforts to obtain high quality Program Data and to
provide good quality interpretation of such Program Data; however, BOG AND ITS
OFFICERS, EMPLOYEES, AGENTS AND SHAREHOLDERS (HEREINAFTER COLLECTIVELY REFERRED
TO AS THE "BOG GROUP") MAKE NO REPRESENTATIONS OR WARRANTIES OF ANY KIND AS TO
THE PROGRAM DATA OR INTERPRETATIONS, INCLUDING WITHOUT LIMITATION, THEIR
FITNESS FOR A PARTICULAR PURPOSE, MERCHANTABILITY OR ACCURACY, AND THE BOG
GROUP HEREBY DISCLAIMS ANY AND ALL SUCH REPRESENTATIONS OR WARRANTIES, AND ANY
USE OF THE PROGRAM DATA OR INTERPRETATIONS BY THE PARTIES OR THEIR SUCCESSORS
OR ASSIGNS, OR ANY ACTION TAKEN BY THE PARTIES OR THEIR SUCCESSORS OR ASSIGNS
SHALL BE BASED SOLELY ON THEIR OWN JUDGMENT, AND NEITHER THE BOG GROUP OR THEIR
SUCCESSORS OR ASSIGNS, SHALL BE LIABLE OR RESPONSIBLE TO THE OTHER PARTIES OR
THEIR SUCCESSORS OR ASSIGNS FOR ANY LOSS, COST, DAMAGES, OR EXPENSE WHATSOEVER,
INCLUDING INCIDENTAL OR CONSEQUENTIAL DAMAGES, INCURRED OR SUSTAINED AS A
RESULT OF THE USE OF OR RELIANCE UPON THE PROGRAM DATA OR INTERPRETATIONS,
REGARDLESS OF WHETHER OR NOT SUCH LOSS, COST, DAMAGE OR EXPENSE IS FOUND TO
RESULT IN WHOLE OR IN PART FROM THE SOLE OR CONCURRENT NEGLIGENCE OR OTHER
FAULT OF ANY MEMBER OF THE BOG GROUP.  Each Party hereto waives all of the
provisions of any applicable Deceptive Trade Practices or Consumer Protection
Act ("DTPA"), other than Section 17.555 of the Texas DTPA, and expressly agrees
and acknowledges that it (i) has assets of five million dollars or more, (ii)
has knowledge and experience in financial and business matters that enable it
to evaluate the merits and risks of the transaction and operations contemplated
by this Agreement, and (iii) is not in a significantly disparate bargaining
position relative to each other Party to this Agreement, but has agreed to this
provision in negotiations involving real choice on the part of each Party.  In
the event that UNEXCO trades, exchanges or otherwise discloses any
interpretations of the Program Data, to the extent that same is allowed under
the terms of this Agreement, all such interpretations shall contain the
disclaimer set forth above in all capital letters in this Section 3.4 in
conspicuous print on the face of such interpretation.





Geophysical Exploration Agreement
Welder Project
                                       6
<PAGE>   7
                                  ARTICLE IV.
                            AREA OF MUTUAL INTEREST

       Section 4.1.  Establishing an Area of Mutual Interest.  The Parties
hereto have agreed to establish an AMI which shall encompass all of the lands
described in Exhibit A which is attached hereto and incorporated herein for all
purposes.  The AMI shall remain in force and effect for a period of five (5)
years from the date of this Agreement, unless sooner terminated by mutual
agreement of the Parties.

       Section 4.2.  Ownership and Payment for Options, Leases and Farm-Ins.

       (a)    Subject to any consent requirements contained in an Existing
Option, Existing Lease or Existing Farm-In, the Existing Options, Existing
Leases, and Existing Farm-Ins shall be owned by the Parties in accordance with
the percentages which are set forth in the table below (the percentages set
forth below being referred to in this Agreement as the Parties' "Ownership
Interests"):

<TABLE>
<CAPTION>
                            Party                 Ownership Interest
                            -----                 ------------------
                            <S>                          <C>
                            UNEXCO                       30.00%
                            BOG                          70.00%.
</TABLE>

       (b)    Subject to the notification and response procedures contained in
Section 4.4 below, all other Options, Leases and Farm-Ins acquired by the
Parties within the AMI during the term of this Agreement shall also be owned by
the Parties in accordance with their undivided Ownership Interests (as set
forth in the table contained in Section 4.2(a) above).  However, record title
to all Options, Leases and Farm-Ins shall remain in the Party originally
acquiring same until immediately prior to the commencement of drilling
operations for any well which includes all or part of the acreage that is
covered by the Option, Lease or Farm-In is included within the
Drilling/Proration Unit for such well as set forth in Section 6.7 below.

       (c)    All costs and expenses incurred prior to the Parties' execution
of this Agreement in acquiring and maintaining Options, Leases and Farm-Ins
will be paid for by the Parties in accordance with their Ownership Interests
(as set forth in the table contained in Section 4.2(a) above).  Subject to the
notification and response procedures contained in Section 4.4 below, all costs
and expenses incurred after the Parties' execution of this Agreement in
acquiring and maintaining Options, Leases and Farm-Ins during the term of this
Agreement shall also be paid for by the Parties in accordance with their
Ownership Interests.

       (d)    Concurrent with its execution of this Agreement, UNEXCO shall
reimburse BOG for UNEXCO's Ownership Interest share of all costs and expenses
incurred prior to UNEXCO's execution of this Agreement in acquiring and
maintaining the Existing Options, Existing Leases and Existing Farm-Ins.
Within fifteen (15) days from receipt of an invoice from any Party hereto or a
third party, each Party shall pay in full the balance of any amounts due for
their share of the costs and expenses incurred in acquiring or maintaining
Options, Leases or Farm-Ins.

       Section 4.3.  Completion of Processing of the Program Data.  For
purposes of this Agreement the "completion of processing of the Program Data"
shall be deemed to have occurred when the final processed, migrated seismic
sections have been delivered to BOG in a form and format that is capable of
being loaded and interpreted on BOG's 3-D workstations.

       Section 4.4.  Participation in Acquired Interests.

       (a)    Should any Party own on the date hereof, or hereafter acquire or
propose to acquire at any time prior to the date the AMI terminates hereunder,
by purchase, exchange, gift or otherwise, a Lease, Option or a Farm-In covering
lands any part of which are located within the AMI (such Leases, Options and
Farm-Ins, insofar and only insofar as they cover lands within the AMI (as it
then exists), being herein called "Acquired Interests" with the Existing
Leases, Existing Options and Existing Farm-Ins being excluded from the
definition of Acquired





Geophysical Exploration Agreement
Welder Project
                                       7
<PAGE>   8
Interests) such Party (the "Acquiring Party") shall notify the other Parties,
in writing, of such acquisition or proposed acquisition and the initial
consideration paid or to be paid for the Acquired Interest.  Each non-acquiring
Party shall, within thirty (30) days after receipt of such a notice from the
Acquiring Party, notify the Acquiring Party, in writing, whether it shall (i)
participate in such acquisition by acquiring its Ownership Interest share of
the Acquired Interest together with its proportionate share of any non-
participating Party's Ownership Interest share of the Acquired Interest, (ii)
participate in such acquisition by acquiring its Ownership Interest share, but
only its Ownership Interest share, of the Acquired Interest, or (iii) not
participate with any interest in the Acquired Interest; provided that failure
to respond within the time and in the manner set forth above shall be deemed to
be an irrevocable election not to participate with any interest in the Acquired
Interest.  Anything to the contrary contained in this Section 4.4
notwithstanding, in the event that there is a drilling rig on location within
one mile of any part of the Acquired Interest, the Acquiring Party may provide
in its written notice that the non-acquiring Parties must make their election
to participate within a shorter time period, provided, however, that in no
event shall the non-acquiring Parties have less than forty-eight (48) hours
(exclusive of week-ends and holidays) from the time of their receipt of such
notice in which to make their election to participate in the Acquired Interest.
If there is not a drilling rig on location within one mile of any part of an
Acquired Interest and a non-acquiring Party reasonably desires additional
information with respect to an Acquired Interest before it makes its election
whether or not to participate in the acquisition of an Acquired Interest, such
Party may notify the Acquiring Party in writing within fifteen (15) days of its
receipt of the Acquiring Party's notice, detailing in such notice to the
Acquiring Party the additional information reasonably desired by such non-
acquiring Party, and such non-acquiring Party shall have fifteen (15) days from
the date of its receipt of the additional information it has reasonably
requested from the Acquiring Party in which to make its election whether to
participate in the acquisition of the Acquired Interest.  Anything to the
contrary contained herein notwithstanding, a sale, exchange or assignment of
any part of a Party's Ownership Interest share in any Leases, Options or Farm-
Ins to any other Party hereto shall not be deemed to be an Acquired Interest
for purposes of this Section 4.4 and this Section 4.4 shall not apply to any
such sale, exchange or assignment.

       (b)    In the event that a Party desires to elect to participate in the
acquisition of an Acquired Interest, such Party must deliver its Ownership
Interest share of the costs which have been (or are to be) incurred to obtain
the Acquired Interest with its election to participate in the Acquired Interest
and within the time period set forth above in Section 4.4(a) for the election
to participate.  In the event that payment of a Party's Ownership Interest
share of the costs of an Acquired Interest is not included with the Party's
written election as to participation in the Acquired Interest as provided in
this Section 4.4(b), anything to the contrary contained above notwithstanding,
such Party shall be deemed to have irrevocably elected not to participate in
the Acquired Interest.  In the event that a Party elects to acquire its
Ownership Interest share of an Acquired Interest as well as its proportionate
share of any non-participation interests as provided in Section 4.4(a) above,
such Party shall pay the Acquiring Party the Party's share of the costs
incurred (or to be incurred) to acquire the Acquired Interest and which is
allocable to the non-participation interest to be acquired by the Party within
fifteen (15) days of such Party's receipt of notification of the amount of non-
participation interest acquired by the Party.

       (c)    Should all of the Parties elect to participate in an acquisition
of an Acquired Interest, upon payment of its share of the acquisition costs,
each Party shall own its Ownership Interest share of the Acquired Interest.
However, record title to all Acquired Interests shall remain in the Party
originally acquiring same until immediately prior to the commencement of
drilling operations for any well which includes all or part of the acreage that
is covered by the Acquired Interest is included within the Drilling/Proration
Unit for such well as set forth in Section 6.7 below.  If any Party elects not
to participate in such acquisition, such non-participating Party shall own no
interest of any kind in the Acquired Interest or any extension or renewal of
such Acquired Interest.  The Parties that elect to acquire their share of any
non-participating Party's Ownership Interest shall own and pay for a
proportionate part of the non-participating Party's original Ownership Interest
(being in the proportion that such participating Party's original Ownership
Interest bears to the total Ownership Interests of all of the Parties that have
elected to acquire their share of the non-participating Party's Ownership
Interest).





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Welder Project
                                       8
<PAGE>   9
       Section 4.5.  Exercise of Options.  Should any Party propose to exercise
an Option with respect to some or all of the lands covered thereby, such Party
shall notify the other Parties owning an interest in such Option in the same
manner as provided for in Section 4.4 above with respect to acquisitions of
Acquired Interests, and each Party owning an interest in the Option shall elect
to participate or to not participate in the exercise of such Option in the same
manner as provided in Section 4.4 with respect to elections to participate or
to not participate in the acquisition of Acquired Interests and the Party
proposing the exercise of the Option shall be deemed to be the "Acquiring
Party" under Section 4.4.  The effect of a Party's election to participate in
such an exercise of an Option, and the payment of costs and the ownership of
interests in the Leases acquired pursuant to such exercise, shall be handled in
the same manner as provided in Section 4.4 with respect to elections to
participate or not participate in acquisitions of Acquired Interests.  Anything
to the contrary contained above notwithstanding, should any Party having the
right to participate in such exercise furnish notice (within the time provided
for written notice with respect to such an election) to the Acquiring Party
that it wishes to defer exercise of such Option, and should it be possible
under the terms of the Option to defer such exercise without any loss of costs
or rights, the Acquiring Party shall withdraw its proposal to exercise such
Option.  However, if any Party does not wish to participate in the exercise of
any Option when the time to exercise arrives, then said non-participating Party
shall not have any interest in the leasehold appurtenant to such Option but
will still be subject to this Agreement in all other respects.  Anything to the
contrary contained herein notwithstanding, if a Party has not elected to
participate in the acquisition of an acquired Option as provided in Section
4.4, such Party shall not have the right to participate in the exercise of such
Option and shall own no interest in the Leases resulting from the exercise of
such Option.

       Section 4.6.  Mandatory Participation in Exercise of Welder Option.

       (a)    Anything to the contrary contained in Sections 4.4 and 4.5 above
notwithstanding, each of the Parties shall be required to participate in the
exercise of the Welder Option as to the minimum exercise requirement contained
in Article II thereof and shall be required to pay its Ownership Interest share
of the costs incurred to exercise the Welder Option to obtain Leases covering
3,200 net mineral acres.

       (b)    Anything to the contrary contained in Sections 4.4 and 4.5 above
notwithstanding, in the event that a Party does not pay its Ownership Interest
share of the costs incurred to exercise the Welder Option as to the 3,200 net
mineral acre minimum set forth in the Welder Option within thirty (30) days of
its receipt of an invoice for the Party's Ownership Interest share of such
costs, in addition to and without limitation of all other remedies which may be
available to the paying Party at law or in equity, at such Paying Party's
option, such non-paying Party shall be deemed to have irrevocably elected not
to participate in any Leases which are obtained as the result of the exercise
of the Welder Option and such non-paying Party shall own no interest and have
no rights of any kind in the Welder Option.  To exercise the option described
in this Section 4.6(b), the paying Party shall notify the non-paying Party in
writing of its election to exercise the option within sixty (60) days of the
invoice due date.  In the event that the paying Party exercises the option
described above in this Section 4.6(b), the non-paying Party shall promptly
(but in any event within fifteen days of its receipt of the instrument) execute
all assignments and other conveyance or relinquishment instruments that may be
requested by the paying Party to help evidence the relinquishment described in
this Section 4.6(b).

       Section 4.7.  Election as to Participation in Maintenance or Extension
Costs.  In the event maintenance or extension costs are incurred with respect
to an Option, Lease or Farm-In, each Party that owns an Ownership Interest in
such Option, Lease or Farm-In shall have the right to elect whether to
participate in such maintenance or extension cost for the Option, Lease or
Farm-In utilizing the same procedures set forth in Section 4.4 above for
Acquired Interests; provided, however, that in the event that a Party elects
not to participate in a maintenance or extension cost, such Party shall
promptly relinquish and assign to the Parties participating in such maintenance
or extension cost all of such non-participating Party's Ownership Interest in
the interests in the Option, Lease or Farm-In that would have been relinquished
or lost if the maintenance or extension cost had not been paid.





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Welder Project
                                       9
<PAGE>   10
       Section 4.8.  Lease Bonus Payments to WGC.  The Parties recognize and
acknowledge that under the terms of Section B of the WGC Agreement, certain
payments are to be made to WGC in the event that any Party hereto pays lease
bonus costs to mineral interest owners in order to lease mineral interests
within the AMI after November 6, 1996.  Each Party hereby agrees to pay its
Ownership Interest share of such costs that are to be made to WGC under the
terms of the WGC Agreement; provided, however, that in the event that any Party
hereto elects not to participate in the acquisition of a Lease that creates the
payment responsibility to WGC under the WGC Agreement, the Party(ies)
participating in the acquisition of the Lease shall be responsible for the full
payment that is to be made to WGC as the result of such Lease acquisition in
accordance with their Ownership Interests in the Lease and the non-
participating Party shall not be required to bear any part of such cost.
Anything to the contrary contained above notwithstanding, the Parties recognize
that BOG has already made payment to WGC for lease bonuses that have already
been paid to obtain Leases (including the First State Lease) within the AMI and
concurrent with its execution of this Agreement, UNEXCO shall reimburse BOG for
UNEXCO's 30% Ownership Interest share of the payments previously made to WGC.
Each Party shall timely pay WGC directly for its share of all lease bonus
charges that are to be made to WGC pursuant to the terms of Section B of the
WGC Agreement.

                                   ARTICLE V.
                     PROSPECT DESIGNATION AND PARTICIPATION

       Section 5.1.  Prospect Designation.  Upon completion of BOG's initial
interpretation of the Program Data, the Parties will meet to review the
interpretations and delineate prospects (hereinafter individually referred to
as "Prospect Area") for exploration and development within the AMI.  The
Parties shall attempt to agree on 1) the number of Prospect Areas, and 2) the
acreage to be included in each Prospect Area.  As to all Prospect Areas
proposed and agreed upon by all of the Parties in the initial meeting, such
Prospect Areas shall be deemed to be designated and the Parties shall document
their agreement in writing in the form attached hereto as Exhibit C.  Each such
Prospect Area will be governed by a separate operating agreement in the form
attached hereto as Exhibit F (the "Operating Agreement").  Any Prospect Area
proposed at the initial meeting which is not agreed to by the Parties may be
re-submitted by any Party utilizing the procedures contained in Section 5.2
below.

       Section 5.2.  Additional Proposals by Parties for Prospect Areas.  After
the meeting described in Section 5.1 above, any Party hereto may propose
(hereinafter referred to as the "Proposing Party") that a portion of the AMI be
designated as a Prospect Area by giving written notice to the other Parties,
which notice shall contain 1) a description of the acreage which such Party
would include in the Prospect Area, and 2) the Proposing Party's tentative
initial well location within the Prospect Area.  The acreage proposed to be
included in a Prospect Area shall not include any acreage included within a
previously designated Prospect Area.  The Parties recognize that the Proposing
Party's tentative initial well location described in a Prospect Area proposal
does not commit the Parties to the well location described or to participate in
the initial well that is drilled within the Prospect Area.  The "tentative
initial well location" is just provided in the proposal in order to facilitate
the designation of the acreage to be included within the Prospect Area.

       Section 5.3.  Response to a Prospect Area Proposal.  In the event that a
Party proposes the designation of a Prospect Area utilizing the terms of
Section 5.2 above, each Party shall notify such Proposing Party, in writing,
within thirty (30) days after its receipt of such proposal, or sooner (but in
no event shall a Party be required to respond in less than 48 hours) if an
Option, Lease or Farm-In is expiring, as to whether such Party agrees with the
acreage proposed to be included in the Prospect Area by the Proposing Party.
In the event that a Party does not respond to a Prospect Area proposal within
such time period, such Party shall be deemed to be in irrevocable agreement
with the acreage proposed for inclusion in the Prospect Area.  A Party who
disagrees with the acreage proposed to be included in the Prospect Area must
give notice of such disagreement to the Proposing Party within the time and in
the manner provided above.  If no Party disagrees with the acreage proposed to
be included in the proposed Prospect Area, such Prospect Area shall be deemed
to be designated.





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Welder Project
                                       10
<PAGE>   11
       Section 5.4.  Determining Prospect Area Disagreements.  If, with respect
to a Prospect Area proposed under Section 5.2, there is disagreement concerning
the lands to be included in the Prospect Area, the Parties shall, for a period
of ten (10) days after the expiration of the response period described in
Section 5.3 above, attempt to agree upon the lands to be included in the
Prospect Area and, failing to reach such agreement within such time, the
Prospect Area shall be deemed to be designated and the lands included in the
Prospect Area shall consist of the Governmental Section on which the initial
well is proposed to be located.  In the event that the acreage located in the
area of the proposed Prospect Area is not divided into 640 acre Governmental
Sections, to the extent practicable, the Prospect Area shall consist of a 640
acre tract in the form of a square (with the boundary lines running due North,
South, East and West) with the tentative initial well location being the center
of the tract.  Provided, further, any such Prospect Area determined pursuant to
this Section 5.4 may not include any acreage included within a previously
designated Prospect Area unless all of the Parties hereto agree to amend the
acreage included within the previously designated Prospect Area.  In the event
of such a Prospect Area disagreement, once the acreage to be included within
the Prospect Area has been resolved in accordance with the provisions of this
Section 5.4, the Prospect Area shall be deemed to be designated.

       Section 5.5.  Project Generator Burdens.  The Parties expressly
recognize and agree that their interests in the AMI are, or shall be,
proportionately subject to the overriding royalties created in that certain
Project Area Generation Agreement, Las Cabeza Ranch Project, by and between BOG
and R.J. Welder Company and Sable Energy Corp. dated October 1, 1996 (the
"Sable Agreement").  The Parties also agree to bear their Ownership Interest
share of all costs, expenses and payments which are due under the Sable
Agreement.  Concurrent with its execution of this Agreement UNEXCO shall
reimburse BOG for UNEXCO's 30% Ownership Interest share of all payments which
have been made by BOG pursuant to the terms of the Sable Agreement prior to the
Parties' execution of this Agreement.

       Section 5.6.  Lease Burdens.  No Party hereto shall burden or encumber
any other Party's legal or equitable interest in a Lease, Option or Farm-In
with any overriding royalty, production payment, mortgage, security interest or
other burden except as provided in Section 5.5 above, without the consent of
the other Parties; provided, however, that in its efforts to obtain a Lease,
Option or Farm-In, a Party hereto may grant or otherwise burden such Lease,
Option or Farm-In with a royalty, overriding royalty, production payment or
other similar burden (other than a lien or security interest), or acquire such
interest subject to reservation of such a burden, in favor of a third party
owning such Acquired Interest (farmor, mineral owner, assignor, lessee or
lessor) in such Party's reasonable efforts to obtain the Lease, Option or Farm-
In.  If any Party hereto burdens or encumbers its own Ownership Interest,
whether legal or beneficial, vested or contingent, in any Option, Lease, Farm-
In or Program Data with any overriding royalty, production payment, lien,
security interest or other burden (hereinafter referred to as "Subsequently
Created Burdens") except as provided in this Section 5.6 or in Section 5.5
above, and such Party is thereafter required under the terms of this Agreement,
or the applicable Operating Agreement, to assign or relinquish to any other
Party or Parties, all or a portion of its Ownership Interest and/or the
production attributable thereto, said other Party or Parties shall receive such
assignment and/or production free and clear of such Subsequently Created
Burdens and such Party shall indemnify and hold harmless the Party or Parties
entitled to the assignment or forfeiture, from any and all claims and demands
for payment asserted by owners of such Subsequently Created Burdens.

       Section 5.7.  Operating Agreements.  The Parties agree that once a
Prospect Area has been designated pursuant to the terms of this Article V, such
Prospect Area shall thereupon immediately be deemed covered by a separate
Operating Agreement which is in the form attached hereto as Exhibit F.





Geophysical Exploration Agreement
Welder Project
                                       11
<PAGE>   12
                                  ARTICLE VI.
                              DRILLING OPERATIONS

       Section 6.1.  Drilling Operations.

       (a)    The designation of a Prospect Area in accordance with the terms
of Article V above does not constitute a commitment to participate in the
drilling of a well within the Prospect Area.  After a Prospect Area has been
designated in accordance with terms of Article V above, subject to the
limitations set forth in Section 6.8 below, any Party owning an interest in
Options, Leases or Farm-Ins within such Prospect Area may propose the drilling
of the initial well (being the first well drilled by any of the Parties within
the applicable Prospect Area and being hereinafter referred to as an "Initial
Well") or any subsequent well (being any well drilled within a Prospect Area
following the drilling of the Initial Well within such Prospect Area and being
hereinafter referred to as a "Subsequent Well") within the Prospect Area in
accordance with the procedures set forth in the form Operating Agreement which
is attached hereto as Exhibit F.  In the event that a Party proposes a
completion operation within an Initial Well or Subsequent Well hereunder, in
addition to the information which must be included with the completion proposal
as set forth in the Operating Agreement, such proposing Party shall specify the
exact interval (by log depths) within the well bore which such Party reasonably
believes may produce from the completion operations which are proposed (the
formation(s) or partial formation(s) which are located between the high and low
log depth which are reasonably described in such completion proposal being
herein referred to as the "Completion Interval," regardless of the exact
location of the perforations within said Completion Interval).

       (b)    In the event that a Party does not participate in the drilling of
the Initial Well proposed and drilled within the Prospect Area, anything to the
contrary contained in the applicable (or deemed applicable) Operating Agreement
to the contrary, such Party (i) must permanently relinquish and assign (without
reimbursement for costs) to the Parties participating (in proportion to the
interest in the Initial Well acquired by such Party from the non-participating
Party in accordance with the terms of the Operating Agreement) in the drilling
of such Initial Well all of its right, title and interest in the applicable
Prospect Area as to all depths from the surface to two hundred feet (200')
below the deepest depth drilled in such Initial Well, and (ii) shall not own or
acquire any mineral, leasehold, royalty or other interest in oil, gas and/or
other minerals within such Prospect Area as to all depths located from the
surface to two hundred feet (200') below the deepest depth drilled in such
Initial Well for a period of fifteen (15) years from the effective date of this
Agreement.

       (c)    In the event that a Party has participated in the drilling of the
Initial Well drilled within a Prospect Area but such Party does not participate
in the drilling of any Subsequent Well which is proposed and drilled within
such Prospect Area, such Party (i) must permanently relinquish and assign
(without reimbursement for costs) to the Parties participating (in proportion
to the interest in the Subsequent Well acquired by such Party from the non-
participating Party in accordance with the terms of the Operating Agreement) in
the drilling of such Subsequent Well all of its right, title and interest in
the Drilling/Proration Unit (as such term is defined below in Section 6.1(e))
for such Subsequent Well as to all depths from the surface to two hundred feet
(200') below the deepest depth drilled in such Subsequent Well, and (ii) shall
not own or acquire any mineral, leasehold, royalty or other interest in oil,
gas and/or other minerals within the Drilling/Proration Unit for such well as
to all depths from the surface to two hundred feet (200') below the deepest
depth drilled in such well  for a period of fifteen (15) years from the
effective date of this Agreement.

       (d)    In the event that a Party has participated in the drilling of the
Initial Well or any Subsequent Well within a Prospect Area and then elects not
to participate in a completion operation proposed for such well, such Party (i)
must permanently relinquish and assign (without reimbursement for costs) all of
its right, title and interest in the Completion Interval within the
Drilling/Proration Unit for such well to the Parties participating (in
proportion to the interest in the completed formation acquired by such Party
from the non-participating Party in accordance with the terms of the Operating
Agreement) in the completion of such Completion Interval, and





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Welder Project
                                       12
<PAGE>   13
(ii) shall not own or acquire any mineral, leasehold, royalty or other interest
in oil, gas and/or other minerals located within the Completion Interval within
the Drilling/Proration Unit for such well for a period of fifteen (15) years
from the effective date of this Agreement.  The Parties recognize that the
depth of the Completion Interval may vary within the Drilling/Proration Unit
and it is the Parties' intent that the relinquishment and assignment provisions
contained in this Section 6.1(d) shall apply to the stratigraphic equivalent of
the Completion Interval within the Drilling/Proration Unit despite the fact
that the Completion Interval's depth may vary within the Drilling/Proration
Unit.

       (e)    For purposes of this Section 6.1, "Drilling/Proration Unit" shall
be defined as follows:  (1) in the event that a voluntary pooled unit is formed
prior to or after the drilling or completion of the well by the Parties that
are participating in the well operations that are being conducted at the time
that such unit is formed, the "Drilling/Proration Unit shall be made up of the
lands included within such voluntary pooled unit, provided that such voluntary
pooled unit does not violate the terms and provisions of any Lease or Farm-In
which covers any part of the lands that are included in the voluntary pooled
unit; (2) in the event that a voluntary pooled unit is not formed prior to or
after the drilling or completion of the well, (i) if the well is drilled or
completed as an oil well, the Drilling/Proration Unit shall be an 80 acre tract
with the well being located within the tract and the exact configuration of the
boundary lines of the 80 acre tract to be determined by the Parties
participating in the well operations that are being performed after any non-
consent or non-participation elections have been made with respect to such
operations, and (ii) if the well is drilled or completed as a gas well, the
Drilling/Proration Unit shall be a 640 acre tract with the well being located
within the tract and the exact configuration of the boundary lines of the 640
acre tract to be determined by the Parties participating in the well operations
that are being performed after any non-consent or non-participation elections
have been made with respect to such operations; provided, however, that in the
event that the Drilling/Proration Unit as described in this Section 6.1(e)
would violate the terms of any Lease or Farm-In which covers lands which are
included in the Drilling/Proration Unit, the Drilling/Proration Unit shall be
re-configured by the Parties participating in the well to conform to the terms
of the applicable Lease or Farm-In.  It is the intent of the Parties that the
relinquishment and assignment of interests provided for in this Section 6.1 for
failure to participate in the drilling of a Subsequent Well or a completion
operation apply to all and only all of the leasehold interests, mineral
interests and production that are allocated to the relevant well (or completed
formation) for production purposes and the Parties hereto agree that in the
event that such allocation changes in the future, the Parties shall execute any
future or further relinquishment instruments or other documentation that is
necessary to effectuate that intent.

       (f)    In the event that mechanical difficulties are experienced,
impenetrable substances are encountered or other conditions are encountered
which render further drilling or completion of any well impracticable before
such well reaches its proposed depth or formation or before such well can be
completed, the participating Parties may discontinue drilling or completing
said well and shall have the option for thirty (30) days to commence the
drilling of a "substitute well."  The substitute well must have a bottom hole
location that is within 1,000' of the bottom hole location that was originally
planned for the well that it is drilled to replace.  If a substitute well is
commenced and drilled and/or completed as herein provided, for purposes of the
non-participation provisions of this Section 6.1, the drilling Parties shall be
deemed to have complied with this Agreement to the same extent as if the well
it replaced had been commenced, drilled and/or completed in accordance with the
terms of this Section 6.1.  In such event, each reference herein to the well a
substitute well replaced shall include the substitute well.

       (g)    Nothing contained in this Section 6.1 shall be construed so as to
require an assignment of any Party's interest in a completed formation within a
previously existing well that was then producing or capable of producing even
though such completed formation is located within a Prospect Area or proration
unit that is to be relinquished because of such Party's failure to participate
in the drilling or completion of an additional well as provided herein.

       (h)    In the event of any required relinquishment and assignment of
interests as provided in this Section 6.1, the relinquishing Party shall,
promptly following the





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Welder Project
                                       13
<PAGE>   14
commencement of the operation as proposed and which results in such
relinquishment and assignment, execute all conveyance instruments necessary to
effectuate the relinquishment and assignment.  However, the Parties recognize
and agree that in the event that the proposed operation is not commenced within
the time frame set forth in Article VI.B.2. of the Operating Agreement, the
relinquishment and assignment provisions set forth in this Section 6.1 shall
not apply unless and until such operation is re-proposed to the non-
participating Party and the non-participating Party is again given the election
to participate in the operation.

       (i)    Except as provided herein to the contrary, or as otherwise
provided in any Lease, Farm-In or Option agreement to the contrary, all
drilling, completing, workover and other well and production operations on each
Prospect Area shall be governed by the terms of a separate Operating Agreement
for each such Prospect Area in the form attached hereto as Exhibit F (with
appropriate insertions and exhibits reflecting the agreements hereunder with
respect to the Prospect Area and participation percentages) as provided in
Section 5.7 above and Section 6.2 below.  In the event that there are any
irreconcilable inconsistencies or ambiguities between the terms of this
Agreement and the terms of the Operating Agreement, the terms and conditions
contained in this Agreement shall control.

       (j)    In the event that any Party proposes the drilling of the Initial
Test Well or a subsequent well within a Prospect Area and any other Party
hereto disagrees with the location of the proposed well, such Party shall
promptly (but in no event less than five (5) days following such Party's
receipt of the drilling proposal) notify all of the other Parties hereto in
writing of such disagreement.  In the event of such a disagreement, the Parties
that have the right to participate in the proposed well shall make a reasonable
attempt to reach agreement upon the location for the proposed well.  In the
event that within ten (10) days of the Parties' receipt of the notice of
disagreement, Parties which have the right to participate in the drilling of
the proposed well and which would together own a majority (at least 51%) of the
working interest in the well agree upon a location, the location selected by
such Parties shall be the location for the proposed well and all of the
Parties, including the Party which originally proposed the well, shall make
their election to participate or not participate in the proposed well in
accordance with the terms set forth in the Operating Agreement, the time for
election running from the Parties' receipt of the original drilling proposal.
In the event that within ten (10) days of the Parties' receipt of the notice of
disagreement, Parties which have the right to participate in the drilling of
the proposed well and which together would own a majority of the working
interest in the well have not agreed upon a location for the well, then the
location shall remain as originally proposed and each Party must make their
election to participate or not participate in the drilling of the proposed well
in accordance with the terms set forth in the Operating Agreement, the time for
election running from the Parties' receipt of the original drilling proposal.

       (k)    The Parties recognize and acknowledge that under the terms of the
Sable Agreement the R.J. Welder Company and Sable Energy Corp. have certain
rights to review well logs and results as set forth in the Sable Agreement.

       Section 6.2.  Execution of Prospect Area Operating Agreements.  Once a
Party (hereinafter referred to as the "Initiating Party") has proposed the
drilling of the Initial Well within a Prospect Area and the Parties have made
their elections (or they are deemed to have made their elections) to
participate, or not participate, in the drilling of such Initial Well under the
terms set forth in Section 6.1 above, if the other Party hereto has elected to
participate in the drilling of such Initial Well, the Initiating Party shall
prepare and deliver to the other Party electing to participate in the Initial
Well the following documentation and pages for the Operating Agreement that
governs all drilling, completion, workover and all other well operations for
such Prospect Area: (i) a cover page describing the Prospect Area as the
Contract Area for the Operating Agreement; (ii) multiple original execution and
acknowledgment pages for the Operating Agreement; (iii) the Exhibit A to the
Operating Agreement with appropriate insertions reflecting the agreements set
forth in this Agreement with respect to the Prospect Area and participation
percentages; and (iv) the Memorandum of Operating Agreement for such Operating
Agreement in the form attached to the form Operating Agreement which is
attached hereto as Exhibit F, completed to describe the Contract Area and the
participating Parties.  Prior





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Welder Project
                                       14
<PAGE>   15
to the date that preparations for the drilling of the Initial Well are expected
to commence, each Party that has elected to participate in the drilling of such
Initial Well shall execute and return to the Initiating Party fully executed
and completed duplicate originals of the execution pages and acknowledgment
pages to both the Operating Agreement and the Memorandum of Operating Agreement
and shall incorporate all of the pages and documentation described in (i), (ii)
and (iii) above into a copy of the form Operating Agreement which is attached
hereto as Exhibit F which it shall retain for its records.  Each participating
Party's completed copy of the Operating Agreement shall constitute a duplicate
counterpart original of the Operating Agreement which governs the participating
Party's well operations within the applicable Prospect Area.  Once the
Initiating Party receives the duplicate original execution and acknowledgment
pages from the participating Parties, the Initiating Party shall provide each
participating Party with a copy of execution pages for the Initiating Party and
for all of the other participating Parties.  In the event that a participating
Party fails to execute and return its duplicate original execution pages to the
Initiating Party (but without a diminution of such Party's obligation to so
execute and return duplicate original signature pages to the Initiating Party),
such Party shall nonetheless continue to be bound by the terms of the Operating
Agreement for such Prospect Area, which terms shall continue to be deemed to
apply to such Party as provided in Sections 5.7 and 6.2 above.

       Section 6.3.  Operator.  It is agreed and understood that, except as may
be provided in any Farm-In or Option agreement to the contrary, BOG shall be
designated as operator in the applicable Operating Agreement for each well in
which BOG participates.  In the event that BOG does not participate in the
drilling of a well, except as provided in any Farm-In or Option agreement to
the contrary, the Parties holding a majority working interest in the well shall
designate the operator.  The operator shall consult with all of the other
Parties participating in the well as to all drilling and completion operations.


       Section 6.4.  Drilling Costs.  Subject to the terms of the Operating
Agreement, the Parties shall pay for all drilling costs in proportion to their
working interest in each well, as determined by the Parties' respective
Ownership Interests in the Options, Leases and Farm-Ins included within the
drilling and proration unit for such well.

       Section 6.5.  Drilling Cost Payment to WGC.  The Parties recognize and
acknowledge that under the terms of Section B of the WGC Agreement, certain
payments are to be made to WGC in the event that either Party hereto
participates in the drilling and/or completion of a well within the AMI after
WGC has delivered a copy of the Program Data to BOG.  Each Party hereby agrees
to pay its Ownership Interest share of such costs that are to be made to WGC
under the terms of the WGC Agreement; provided, however, that in the event that
either Party elects not to participate in the drilling or completion of a well
that creates the payment responsibility to WGC under the WGC Agreement, the
participating Parties shall be responsible for the full payment that is to be
made to WGC as the result of the drilling and/or completion of such well in the
proportion that their respective Ownership Interests bear to the total of the
Ownership Interests of all of the participating Parties, and the non-
participating Parties shall not be required to bear any part of such cost.
Each Party shall timely pay WGC directly for its share of all drilling and
completion cost charges that are to be made to WGC pursuant to the terms of
Section B of the WGC Agreement.

       Section 6.6.  AMI for Prospect Area.  Commencing with the establishment
of a Prospect Area, such Prospect Area shall from that time forward no longer
be subject to the AMI provided for in Section 4.1 above and shall thereafter be
considered covered instead by a new Prospect Area AMI.  The new Prospect Area
AMI (i) is binding on all Parties, (ii) consists of such Prospect Area, (iii)
lasts until the later to occur of three (3) years from the date hereof or the
date that the Operating Agreement for such Prospect Area terminates, and (iv)
is governed by the same terms set forth in Sections 4.2, 4.4, 4.5, 4.6, 4.7,
4.8, 5.5, and 5.6, with the participation percentages of the Parties being in
accordance with their ownership interest in the Leases, Options and Farm-Ins
located within the Prospect Area; provided, however, that in the event that a
Party has elected not to participate in the drilling of the Initial Well within
such Prospect Area, such Party shall not have the right to own or acquire any
interest in that part of any Acquired





Geophysical Exploration Agreement
Welder Project
                                       15
<PAGE>   16
Interest that is located within such Prospect Area.  Any portion of the AMI not
designated as a Prospect Area shall continue to be subject to the AMI provided
for in Section 4.1.

       Section 6.7.  Assignment of Ownership Interests in Leases, Options and
Farm-Ins.  Unless such assignment is not permitted under the terms of the
applicable Option, Lease or Farm-In, the Parties agree that each Party's
Ownership Interest (as such Ownership Interest is subject to change in
accordance with the provisions of Sections 4.4, 4.5, 4.7 and 6.1) in each
Lease, Option or Farm-In shall be assigned to the Parties (utilizing the
general form of assignment which is attached hereto as Exhibit E) prior to the
commencement of drilling operations for any well which includes all or part of
the acreage that is covered by the Option, Lease or Farm-In in the drilling
and/or proration unit for such well.  In addition to the above, following the
expiration of the AMI hereunder, the Parties shall be assigned their Ownership
Interests in any Options, Leases or Farm-Ins which have not been included
within a designated Prospect Area.

       Section 6.8.  Limitation on Well Proposals.  Anything to the contrary
contained herein notwithstanding, the Parties agree that, without mutual
agreement of the Parties otherwise, during any forty-five day period hereunder
no more than one deep well may be proposed to be drilled to a subsurface depth
in excess of 10,000 feet ("Deep Wells") within lands that are within the AMI
and which are the subject of jointly owned Leases and/or Farm-Ins unless the
drilling of additional Deep Wells within lands that are the subject of such
jointly owned Leases and/or Farm-Ins is necessary in order to avoid losing
rights or interests under a Lease or Farm-In without incurring additional costs
to extend or renew such Lease or Farm-In.  Therefore, without the mutual
agreement of the Parties or a situation in which more drilling is necessary to
avoid losing rights or interests in a Lease or Farm-In as aforesaid, during any
three hundred sixty day period hereunder no more than eight Deep Wells can be
proposed to be drilled by the Parties on jointly owned Leases and/or Farm-Ins
within the AMI.  In addition, anything to the contrary contained herein
notwithstanding, the Parties agree that, without mutual agreement of the
Parties otherwise, during any forty-five day period hereunder no more than
three wells may be proposed to be drilled to total depths of less than 10,000
feet ("Shallow Wells") within lands that are within the AMI and which are the
subject of jointly owned Leases and/or Farm-Ins unless the drilling of
additional Shallow Wells within lands that are the subject of such jointly
owned Leases and/or Farm-Ins is necessary in order to avoid losing rights or
interests under a Lease or Farm-In without incurring additional costs to extend
or renew such Lease or Farm-In.  Anything to the contrary contained above
notwithstanding, in the event that a drilling proposal is subsequently
withdrawn by the proposing Party or a proposed well cannot be drilled within
the required time period set forth in the Operating Agreement, the Parties
agree that for purposes of this Section 6.8, such proposal shall not be counted
for purposes of calculating the drilling proposal limitations that are
contained in this Section 6.8.  In addition, anything to the contrary contained
above notwithstanding, in the event that only one Party hereto owns interests
in the Leases and/or Farm-Ins which are to be included within the
Drilling/Proration Unit for a well (whether as the result of non-participation
elections in Acquired Interests, well proposals or otherwise), and no jointly
owned Leases or Farm-Ins are to be included within the Drilling/Proration Unit
for such well, the well proposal for such well shall not be counted for
purposes of the well proposal limitations contained in this Section 6.8.
Finally, anything to the contrary contained herein notwithstanding, the Parties
agree that in the event that the Parties hereto and their successors and
assigns own less than fifty-one percent of the working interest in a well that
has been proposed to be drilled within the AMI, the well proposal for such well
shall not be counted for purposes of the well proposal limitations contained in
this Section 6.8.


                                  ARTICLE VII.
                                 MISCELLANEOUS

       Section 7.1.  Assignments.  Subject to any restrictions that may be
contained in any Option, Lease or Farm-In, any Party hereto may assign all or
any part of its interest under the terms of this Agreement.  This Agreement
shall be binding upon and inure to the benefit of the Parties hereto and their
respective successors and their respective assigns of rights hereunder;





Geophysical Exploration Agreement
Welder Project
                                       16
<PAGE>   17
provided, however, that the conveyance or assignment instrument vesting such
assignee with all or part of such interests must expressly provide that the
assignment or conveyance is made subject to the terms and conditions contained
in this Agreement.  In addition, in any such assignment or conveyance, the
assignee shall expressly agree to assume and be responsible for any
liabilities, damages, obligations, covenants and agreements arising from and
after the date of such assignment or conveyance, in relation to or otherwise
out of the properties, rights and interests that are the subject of this
Agreement and/or such assignment or conveyance, and the assignor shall remain
responsible for any of the foregoing arising prior to the date of such
assignment or conveyance.  Any subsequent assignment or conveyance shall
likewise contain express language so allocating responsibility as between
assignor and assignee.  Unless (and then only to the extent that) this
Agreement is itself assigned at the same time, the benefits of this Agreement
shall not run with an assignment of a Party's interests in the Options, Leases
or Farm-Ins, or any other rights in lands within the AMI, but the assigned
interest shall be subject to the terms of this Agreement.  Anything to the
contrary contained above notwithstanding, in the event that any Party hereto
assigns interests in this Agreement to more than two parties, in no event shall
the other Parties hereto be required to make more than three billings for the
entire Ownership Interest credited to such Party in the table contained in
Section 4.2(a) above.  It is further agreed that anything to the contrary
contained above notwithstanding, if any Party (herein referred to as the
"Selling Party") disposes of part of the Ownership Interest credited to it in
the table contained in Section 4.2(a) above to more than two parties, unless
the other Parties hereto agree in writing otherwise, the Selling Party shall be
solely responsible for billing its assignee or assignees, and shall remain
primarily liable to the other Parties hereto for the interest or interests
assigned and shall make prompt payment to the invoicing Party for the entire
amount of the statements or billings rendered to it.  It is further understood
and agreed that if a Selling Party disposes of all of its Ownership Interest,
whether to one or more assignees, the Parties hereto shall continue to issue
statements and billings to the Selling Party for the Ownership Interest
conveyed and the Selling Party shall remain liable for all payments due
hereunder until such time as the Selling Party has designated in writing one
financially sound assignee to receive and be liable for the billings and
statements for the entire Ownership Interest and such assignee has assumed such
responsibility in writing, a copy of which is delivered to all of the Parties
hereto.

       Section 7.2.  Memorandum Giving Notice.  Concurrent with their execution
of this Agreement each Party shall sign and deliver to the other Party hereto a
duplicate original of the Memorandum Giving Notice of Geophysical Exploration
Agreement and Area of Mutual Interest Provisions which is attached hereto as
Exhibit H and each Party shall have the right to place such Memorandum Giving
Notice of record in the Official Public Records of Duval County, Texas.

       Section 7.3.  Notices.  All notices and other communications required or
permitted under this Agreement shall be in writing, and unless otherwise
specifically provided, shall be delivered personally, or by mail, telecopier or
delivery service, to the addresses set forth opposite the signatures of the
Parties below, and shall be considered delivered upon the date of receipt.
Each Party may specify its proper address or any other post office address
within the continental limits of the United States by giving notice to other
Parties, in the manner provided in this Section, at least ten (10) days prior
to the effective date of such change of address.

       Section 7.4.  Merger.  This Agreement supersedes any and all prior and
existing agreements, whether oral or in writing, between the Parties hereto
with respect to the subject matter hereof and contains all of the covenants and
agreements between the Parties with respect to the subject matter hereof.  Each
Party acknowledges that no Party to this Agreement or anyone on their behalf
has made any representations, inducements, promises or agreements, orally or
otherwise, relating to the subject matter of this Agreement that are not
embodied herein.

       Section 7.5.  Governing Law.  THIS AGREEMENT AND ALL MATTERS PERTAINING
THERETO, INCLUDING, BUT NOT LIMITED TO, MATTERS OF PERFORMANCE, NON-
PERFORMANCE, BREACH, REMEDIES, PROCEDURES, RIGHTS, DUTIES, AND INTERPRETATIONS
OR CONSTRUCTION, SHALL, WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF LAW, BE
GOVERNED BY THE LAWS OF THE STATE OF TEXAS.





Geophysical Exploration Agreement
Welder Project
                                       17
<PAGE>   18
       Section 7.6.  Counterparts.  This Agreement may be executed in multiple
counterparts, each of which shall be binding upon the signing Party or Parties
thereto as fully as if all Parties had executed one instrument, and all of such
counterparts shall constitute one and the same instrument.  If counterparts of
this Agreement are executed, the signatures of the Parties, as affixed hereto,
may be combined in and treated and given effect for all purposes as a single
instrument.

       IN WITNESS WHEREOF this Agreement is executed by the Parties on the
dates set forth opposite their respective signatures below but is effective for
all purposes as of the date first set forth above.

Address:                                   BRIGHAM OIL & GAS, L.P.,
       5949 Sherry Lane, Suite 1616        by Brigham Exploration Company,
       Dallas, Texas  75225                its Managing General Partner
       (214) 360-9182
       Fax:  (214) 360-9825
Dated:   02/25/97                          By:    /s/ ANNE L. BRIGHAM          
       -----------------------                ---------------------------------
                                           Anne L. Brigham, Vice President


Address:                                   UNEXCO, INC.
       16420 Park Ten Place
       Suite 300
       Houston, Texas 77084-5051
       (713) 578-8081
       Fax: (713) 578-7091                 By: /s/ MICHAEL J. PAWELEL          
                                              ---------------------------------
Dated:   02/27/97                          (name printed) Michael J. Pawelel   
       -----------------------                           ----------------------
                                           Its:   President
                                               -------------------------------





Geophysical Exploration Agreement
Welder Project
                                       18
<PAGE>   19
                                LIST OF EXHIBITS




Exhibit A -- AMI

Exhibit B -- Existing Options, Existing Leases and Existing Farm-Ins

Exhibit C -- Agreement as to Prospect Areas

Exhibit D -- Form Confidentiality Agreement

Exhibit E -- Form of Assignment of Options, Leases and/or Farm-Ins

Exhibit F -- Form Joint Operating Agreement

Exhibit G -- Copy of the WGC Agreement

Exhibit H -- Memorandum Giving Notice





Geophysical Exploration Agreement
Welder Project
                                       19

<PAGE>   1
                                                                   EXHIBIT 10.36

                            PROPOSED TRADE STRUCTURE
                              RIMCO/TIGRE PROJECT
                          VERMILLION PARISH, LOUISIANA


         Following are the terms, provisions and concepts which Brigham Oil &
Gas, L.P. ("BOG"), Tigre Energy Corporation ("Tigre") and Resource Investors
Management Company ("RIMCO") are in general agreement to with respect to their
exploration efforts in the RIMCO/Tigre Project:

1)       The parties' initial ownership interests in the RIMCO/Tigre Project
(being ownership interests in all leasehold and other property of every kind
located within the lands described on Attachment 1 hereto) shall be as follows:

<TABLE>
<CAPTION>
                          Party                             Ownership Interest
                          -------                           ------------------
                          <S>                                       <C>
                          Tigre                                     37.5%
                          RIMCO                                     37.5%
                          BOG                                       25.0%.
</TABLE>

In order to cause BOG to have a 25% ownership interest in all of the existing
properties located within the RIMCO/Tigre Project, RIMCO and Tigre shall each
assign BOG an equal part (12.5% each) of the 25% ownership interest in all of
the existing properties.  BOG's 25% ownership interest shall be subject to the
3% overriding royalty interest (ORRI) created in favor of Huerfano Corporation
("Huerfano"), proportionately reduced to BOG's 25% ownership interest.  In
addition, BOG's 25% ownership interest shall be assigned subject to the 20%
back-in after payout ("APO") created pursuant to the terms of that certain
agreement dated September 13, 1994, by and between RIMCO and Tigre (the
"Original RIMCO/Tigre Agreement"), proportionately reduced to the 25% ownership
interest being assigned to BOG under this Section 1.  However, RIMCO and Tigre
shall also assign BOG its 25% share of the same 20% back-in APO.  This means
that the net effect is that BOG shall own the same amount of back-in APO that
its 25% ownership interest is subject to.  It is BOG's intent that its 25%
ownership interest be merged with its 25% share of the back-in APO such that
BOG ends up with a 25% ownership interest not subject to the back-in after
payout.  Similarly, BOG's 25% ownership interest in all existing and
subsequently acquired third-party interests within the RIMCO/Tigre Project
shall be subject to the 2% ORRI reserved by RIMCO and Tigre in the Original
RIMCO/Tigre Agreement, proportionately reduced to the 25% ownership interest
assigned to BOG in accordance with this Section 1.  However, RIMCO and Tigre
shall also assign BOG its proportionate 25% share of the same 2% ORRI reserved
by RIMCO and Tigre.  This means that the net effect is that BOG shall own the
same amount of the 2% ORRI that its 25% ownership interest is subject to.  It
is BOG's intent that its 25% ownership interest be merged with its 25% share of
the 2% ORRI such that BOG ends up with a 25% ownership interest not subject to
any part of the 2% ORRI.


2)       BOG, Tigre and RIMCO agree to acquire a license to a cumulative total
of 55 square miles of Fairfield Industries Incorporated ("Fairfield") 3-D
seismic data (the "Fairfield Data") and Geco-Prakla ("Geco") 3-D seismic data
(the "Geco Data") covering the lands located within the RIMCO/Tigre Project
(the 55 square miles of Geco Data and Fairfield Data to be licensed being
sometimes collectively referred to herein as the "Project Data").  BOG shall
pay all of the costs incurred to license the first 30 square miles of the
Project Data and, in the event that BOG causes any Project Data to be further
processed
<PAGE>   2
RIMCO/Tigre Project
Proposed Trade Structure
Page 2




or re-processed, BOG shall also incur all of the costs incurred to process or
re-process the first 30 square miles of such Project Data that is processed or
re-processed.  BOG, Tigre and RIMCO shall each pay their ownership interest
share (as set forth in the table contained in Section 1 above) of all of the
costs that are incurred to license the remaining 25 square miles (for a total
of 55 square miles) of the Project Data.  Likewise, in the event that more than
30 square miles of Project Data is further processed or re-processed, the
parties shall pay their ownership interest share of the costs incurred to
further process or re-process such additional Project Data up to an additional
25 square miles at a maximum charge of $1,500 per square mile as a
processing/re-processing charge.  BOG shall also provide Tigre and RIMCO with
interpretations of the Project Data without charge to Tigre or RIMCO, except as
provided below with respect to the right to recoup interpretational charges as
part of payout in the event that BOG exercises the option in Section 3 or 4
below, and except as provided in Section 5 below in the event that BOG does not
exercise the Section 3 or 4 option but Tigre or RIMCO assign part of their
interests to a third party for consideration.


3)       Within 90 days of BOG's receipt of the Fairfield Data that is licensed
in accordance with the terms of Section 2 above, but in no event later than
July 1, 1997 (the end of such period being referred to as the "A Lands Election
Date"), BOG has the exclusive option to acquire all of Tigre's remaining 37.5%
ownership interest and 12.5% out of RIMCO's remaining 37.5% ownership interest
in that part of the RIMCO/Tigre Project which is outlined on the plat which is
attached hereto as Attachment 2 (the lands described on Attachment 2 being
referred to herein as the "A Lands" and the additional ownership interests in
the A Lands to be acquired by BOG from Tigre and RIMCO being referred to herein
as the "Additional A Lands Ownership Interest"), by committing to the
following:

                 *        On or before the A Lands Election Date, BOG shall
                          notify Tigre and RIMCO, in writing, whether BOG is
                          electing to acquire the Additional A Lands Ownership
                          Interest.  The Additional A Lands Ownership Interest
                          shall only be subject to (i) a proportionately
                          reduced share of the 3% ORRI due to Huerfano (being
                          reduced in proportion to the Additional A Lands
                          Ownership Interest being acquired  -- i.e. 37.5% +
                          12.5% = 50%), (ii) a proportionately reduced share of
                          the 2% ORRI due to RIMCO and Tigre, and (iii) a
                          proportionately reduced share of the 20% back-in APO
                          ownership interest due to RIMCO and Tigre.  By way of
                          example, if BOG elects to acquire the full Additional
                          A Lands Ownership Interest (i.e. 37.5% from Tigre and
                          12.5% from RIMCO), the Additional A Lands Ownership
                          Interest acquired by BOG would be subject to its
                          proportionate share of the 3% Huerfano ORRI and the
                          2% ORRI reserved to RIMCO and Tigre and the parties'
                          total respective ownership interests in the A Lands
                          within the RIMCO/Tigre Project would be as follows:

<TABLE>
<CAPTION>
                                  Ownership Interest BPO
                                  ----------------------
                                       <S>     <C>     
                                       BOG      75%
                                       RIMCO    25%
</TABLE>

<TABLE>
<CAPTION>
                                  Ownership Interest APO
                                  ----------------------
                                       <S>      <C>    
                                       BOG      65%
                                       RIMCO    27.5%
                                       Tigre     7.5%.
</TABLE>

                 *        In the event that BOG elects to acquire the
                          Additional A Lands Ownership Interest from Tigre and
                          RIMCO as set forth in this Section 3, a proportionate
                          part (being in proportion to the 37.5% additional
                          interest acquired from Tigre





    
<PAGE>   3
RIMCO/Tigre Project
Proposed Trade Structure
Page 3




                          and the 12.5% additional interest acquired from
                          RIMCO) of BOG's interest in all subsequently acquired
                          leases and mineral interests covering the A Lands
                          shall be subject to the same proportionately reduced
                          (i) 3% ORRI due to Huerfano, (ii) 2% ORRI due to
                          RIMCO and Tigre, and (iii) 20% back-in ownership
                          interest APO due to RIMCO and Tigre.

                 *        In the event that BOG elects to acquire the
                          Additional A Lands Ownership Interest from Tigre and
                          RIMCO, BOG shall reimburse each of Tigre and RIMCO
                          for a proportionate (being a percentage equal to the
                          amount of the additional ownership interest that is
                          to be acquired by BOG from such party) part of the
                          previously incurred land and geological costs ("sunk
                          costs") allocated to the A Lands (the sunk costs
                          allocated to the A Lands being set forth on
                          Attachment 4).  In addition, in the event that BOG
                          elects to acquire the Additional A Lands Ownership
                          Interest as aforesaid, with respect to all prospect
                          costs, including but not limited to leasing, delay
                          rentals, drilling and completion operations
                          (including the initial test well operations) in which
                          BOG elects to participate (recognizing that BOG has
                          the obligation to participate in at least one initial
                          test well within the RIMCO/Tigre Project as set forth
                          below) within the A Lands, BOG shall pay for all of
                          the costs  allocable to the Additional A Lands
                          Ownership Interest acquired from RIMCO and Tigre and
                          related to such operations until such time as payout
                          is reached ("BPO") with respect to all of the costs
                          incurred by BOG within the A Lands other than the
                          licensing and processing costs incurred by BOG with
                          respect to 30 square miles of the Project Data as
                          described in Section 2 above.

                 *        In the event that BOG elects to acquire the
                          Additional A Lands Ownership Interest from Tigre and
                          RIMCO, BOG shall cause the drilling of an initial
                          test well to be commenced within the A Lands prior to
                          the expiration of nine months from the A Lands
                          Election Date; provided, however, that in the event
                          that BOG also elects to acquire additional ownership
                          interests in the B Lands as set forth in Section 4
                          below, BOG shall only be required to drill one
                          initial test well within either the A Lands or the B
                          Lands within such nine month period, but in the event
                          that BOG does not elect to cause the drilling of an
                          initial test well to be commenced within the other
                          portion of the RIMCO/Tigre Project (being either the
                          A Lands or the B Lands on which BOG did not drill the
                          first initial test well) within one year from the B
                          Lands Election Date, BOG shall assign back to RIMCO
                          and Tigre the additional ownership interests (being
                          either the Additional A Lands Ownership Interest or
                          the Additional B Lands Ownership Interest) that were
                          to be earned under this Section 3 or Section 4 below,
                          as applicable, in all of the interests located within
                          such undrilled portion.

                 *        The payout determination for the 20% back-in APO
                          shall be based upon all of the expenditures (other
                          than the licensing and processing costs incurred by
                          BOG with respect to 30 square miles of the 3-D data
                          as described in Section 2 above) BOG has incurred
                          (including, without limitation, the reimbursements
                          paid to RIMCO and Tigre for their sunk costs
                          allocated to the A Lands and an





    
<PAGE>   4
RIMCO/Tigre Project
Proposed Trade Structure
Page 4




                          interpretational charge of $1,750 per square mile of
                          seismic data licensed within the A Lands) within the
                          A Lands up to that point in time versus the oil
                          and/or gas sales revenues received by BOG from the A
                          Lands up to that specific point in time.  Once a
                          point in time is reached when oil and/or gas sales
                          revenues received by BOG from the A Lands have
                          exceeded BOG's expenditures, payout shall be deemed
                          to have occurred and all future costs incurred within
                          the A Lands shall be borne and paid for on a heads-up
                          basis in accordance with the parties' respective
                          ownership interests after the back-in.


4)       Within 90 days of BOG's receipt of the fully merged and processed Geco
Data (being merged and processed with the Fairfield Data) that is licensed in
accordance with the terms of Section 2 above, but in no event later than July
1, 1997 (the end of such period being referred to as the "B Lands Election
Date"), BOG has the exclusive option to acquire all of Tigre's remaining 37.5%
ownership interest and 12.5% out of RIMCO's remaining 37.5% ownership interest
in that part of the RIMCO/Tigre Project which is outlined on the plat which is
attached hereto as Attachment 3 (the lands described on Attachment 3 being
referred to herein as the "B Lands" and the additional ownership interests in
the B Lands to be acquired by BOG from Tigre and RIMCO being referred to herein
as the "Additional B Lands Ownership Interest"), by committing to the
following:

                 *        On or before the B Lands Election Date, BOG shall
                          notify Tigre and RIMCO, in writing, whether BOG is
                          electing to acquire the Additional B Lands Ownership
                          Interest.  The Additional B Lands Ownership Interest
                          shall only be subject to (i) a proportionately
                          reduced share of the 3% ORRI due to Huerfano (being
                          reduced in proportion to the Additional B Lands
                          Ownership Interest being acquired  -- i.e. 37.5% +
                          12.5% = 50%), (ii) a proportionately reduced share of
                          the 2% ORRI due to RIMCO and Tigre, and (iii) a
                          proportionately reduced share of the 20% back-in APO
                          ownership interest due to RIMCO and Tigre.  By way of
                          example, if BOG elects to acquire the full Additional
                          B Lands Ownership Interest (i.e. 37.5% from Tigre and
                          12.5% from RIMCO), the Additional B Lands Ownership
                          Interest acquired by BOG would be subject to its
                          proportionate share of the 3% Huerfano ORRI and the
                          2% ORRI reserved to RIMCO and Tigre and the parties'
                          total respective ownership interests in the B Lands
                          within the RIMCO/Tigre Project would be as follows:

<TABLE>
<CAPTION>
                                  Ownership Interest BPO
                                  ----------------------
                                  <S>             <C>
                                  BOG              75%
                                  RIMCO            25%
</TABLE>

<TABLE>
<CAPTION>
                                  Ownership Interest APO
                                  ----------------------
                                  <S>             <C>
                                  BOG              65%
                                  RIMCO            27.5%
                                  Tigre            7.5%.
</TABLE>

                 *        In the event that BOG elects to acquire the
                          Additional B Lands Ownership Interest from Tigre and
                          RIMCO as set forth in this Section 4, a proportionate
                          part (being in proportion to the 37.5% additional
                          interest acquired from Tigre and the 12.5% additional
                          interest acquired from RIMCO) of BOG's interest in
                          all subsequently acquired leases and mineral
                          interests covering the B Lands shall be subject to
                          the same proportionately reduced (i) 3% ORRI due to
                          Huerfano, (ii) 2% ORRI due to RIMCO and Tigre, and
                          (iii) 20% back-in ownership interest APO due to RIMCO
                          and Tigre.

                 *        In the event that BOG elects to acquire the
                          Additional B Lands Ownership Interest from Tigre and
                          RIMCO, BOG shall reimburse each of Tigre and RIMCO
                          for a proportionate





    
<PAGE>   5
RIMCO/Tigre Project
Proposed Trade Structure
Page 5




                          (being a percentage equal to the amount of additional
                          ownership interest that is to be acquired by BOG from
                          such party) part of the sunk costs allocated to the B
                          Lands (the sunk costs allocated to the B Lands being
                          set forth on Attachment 4).  In addition, in the
                          event that BOG elects to acquire the Additional B
                          Lands Ownership Interest as aforesaid, with respect
                          to all prospect costs, including but not limited to
                          leasing, delay rentals, drilling and completion
                          operations (including the initial test well
                          operations) in which BOG elects to participate
                          (recognizing that BOG has the obligation to
                          participate in at least one initial test well within
                          the RIMCO/Tigre Project as set forth below) within
                          the B Lands, BOG shall pay for all of the costs
                          allocable to the Additional B Lands Ownership
                          Interest acquired from RIMCO and Tigre and related to
                          such operations BPO with respect to all of the costs
                          incurred by BOG within the B Lands other than the
                          licensing and processing costs incurred by BOG with
                          respect to 30 square miles of the Project Data as
                          described in Section 2 above.

                 *        In the event that BOG elects to acquire the
                          Additional B Lands Ownership Interest from Tigre and
                          RIMCO, BOG shall cause the drilling of an initial
                          test well to be commenced within the B Lands prior to
                          the expiration of nine months from the B Lands
                          Election Date; provided, however, that in the event
                          that BOG also elects to acquire the Additional A
                          Lands Ownership Interest as set forth in Section 3
                          above, BOG shall only be required to drill one
                          initial test well within either the A Lands or the B
                          Lands within such nine month period, but in the event
                          that BOG does not elect to cause the drilling of an
                          initial test well to be commenced within the other
                          portion of the RIMCO/Tigre Project (being either the
                          A Lands or the B Lands on which BOG did not drill the
                          first initial test well) within one year from the B
                          Lands Election Date, BOG shall assign back to RIMCO
                          and Tigre the additional ownership interests (being
                          either the Additional A Lands Ownership Interest or
                          the Additional B Lands Ownership Interest) that were
                          to be earned under this Section 4 or Section 3 above,
                          as applicable, in all of the interests located within
                          such undrilled portion.

                 *        The payout determination for the 20% back-in APO
                          shall be based upon all of the expenditures (other
                          than the licensing and processing costs incurred by
                          BOG with respect to 30 square miles of the 3-D data
                          as described in Section 2 above) BOG has incurred
                          (including, without limitation, the reimbursements
                          paid to RIMCO and Tigre for their sunk costs
                          allocated to the B Lands and an





    
<PAGE>   6
RIMCO/Tigre Project
Proposed Trade Structure
Page 6




                          interpretational charge of $1,750 per square mile of
                          seismic data licensed within the B Lands) within the
                          B Lands up to that point in time versus the oil
                          and/or gas sales revenues received by BOG from the B
                          Lands up to that specific point in time.  Once a
                          point in time is reached when oil and/or gas sales
                          revenues received by BOG from the B Lands have
                          exceeded BOG's expenditures, payout shall be deemed
                          to have occurred and all future costs incurred within
                          the B Lands shall be borne and paid for on a heads-up
                          basis in accordance with the parties' respective
                          ownership interests after the back-in.

5)       The parties will establish an AMI covering the entire RIMCO/Tigre
Project (being the lands which are described and outlined on Attachment 1).
The parties shall each have the right to participate with their ownership
interest share (as it exists at the time of the acquisition of the acquired
interest) of any interests acquired within the AMI by paying their ownership
interest share of the costs incurred to acquire such interests.  In the event
that a party elects not to acquire its ownership interest share of an acquired
interest, such party shall own no interest in the acquired interest.  However,
with respect to all additional interests (being any land or mineral interests
that are acquired by BOG and which were not already held, owned or controlled
by Tigre or RIMCO prior to the date of this letter agreement and being
hereinafter referred to as "Newly Acquired Interests") acquired by BOG prior to
the Election Date, BOG shall also initially pay for all of Tigre's remaining
37.5% ownership interest share and 12.5% out of RIMCO's ownership interest
share of the costs incurred to obtain such Newly Acquired Interests.  However,
in the event that BOG does not elect to acquire the additional ownership
interests from Tigre and RIMCO in the A Lands or the B Lands as set forth in
Sections 3 and 4 above, and Tigre or RIMCO subsequently assign or convey any of
their interests within the RIMCO/Tigre Project for any consideration whatsoever
(regardless of form or character), all of such consideration shall be paid to
BOG but only until such time as BOG has recouped such party's (being the
assigning party -- either RIMCO or Tigre) original ownership interest share of
the costs incurred to obtain Newly Acquired Interests within the portion(s)
(being the A Lands and/or B Lands) not selected by BOG together with an
interpretation charge of $1,750 per square mile of the Project Data which
covers lands in the portion of the RIMCO/Tigre Project not selected by BOG.  If
any party hereto desires to release, surrender, abandon, or let expire any
prospect leases, the releasing party ("Releasing Participant") shall give all
of the other parties seventy-five (75) days advance written notice thereof and
the remaining parties shall have the right, at their option, to the Releasing
Participant's interest in such leases at no cost to the remaining parties.
Should such written notice not be given as provided above, then the Releasing
Participant shall be obligated to keep the lease in force by paying its
ownership interest share of the rental payments or other costs necessary to
keep the lease in effect.

6)       BOG, RIMCO and Tigre have reviewed and approved the terms of the
         License Agreements with Geco and Fairfield.

7)       A separate JOA shall govern each individual geological prospect area
that is identified within the separate portions (A Lands or B Lands) of the
RIMCO/Tigre Project.  This proposal is subject to BOG, RIMCO and Tigre reaching
agreement as to the terms of a mutually acceptable form JOA.  However, the JOA
shall provide that if BOG is not obligated to carry such party for their share
of drilling costs under





    
<PAGE>   7
RIMCO/Tigre Project
Proposed Trade Structure
Page 7




Section 3 or 4 above, and such party elects not to participate in the drilling
of the initial test well within the prospect area, such party shall relinquish
and assign all of its present and future interests in the applicable prospect
area to the parties participating in the initial test well.  With respect to
subsequent wells drilled within a prospect area, the JOA shall provide that if
a party elects not to participate in the drilling of the well, such party shall
relinquish and assign all of its interests in the in the proration unit
established for such well to the parties participating in the initial test well
until such time as a 600% payout is reached with respect to all of the costs
and expenses incurred to drill, complete, equip and operate the well.


8)       BOG or its designee shall be named as the initial drilling operations
         operator under each JOA.

         The parties are in agreement with proceeding with good faith efforts
toward the negotiation and execution of a formal agreement containing the above
general concepts and additional detail as evidenced by their signature below.


                             TIGRE ENERGY CORPORATION                   
                                                                        
                                                                        
                             By:  /s/ JEFFREY W. WHEELOCK
                                ----------------------------------------
                             (name printed)  JEFFREY W. WHEELOCK
                                           -----------------------------
                             Its:         President 
                                 ---------------------------------------
                                                                        
                                                                        
                                                                        
                                                                        
                             RESOURCE INVESTORS MANAGEMENT COMPANY      
                                                                        
                                                                        
                             By:/s/ M. LEE JORDEN                       
                                ----------------------------------------
                             (name printed) M. LEE JORDEN               
                                           -----------------------------
                             Its:     Vice President                    
                                 ---------------------------------------
                                                                        
                                                                        
                                                                        
                                                                        
                             BRIGHAM OIL & GAS, L.P.                    
                                                                        
                                                                        
                             By:   /s/ BEN M. BRIGHAM
                                ----------------------------------------
                             Ben M. Brigham                             
                             President / CEO                            
                                                                        
                                                                        
                                                                        
                                                                        

<PAGE>   1




                                                                 EXHIBIT 10.36.1

January 31, 1997



Mr. David T. Brigham
Brigham Oil & Gas, L.P.
5949 Sherry Lane, Suite 1616
Dallas, TX  75225

RE:      PROPOSED TRADE STRUCTURE
         RIMCO/TIGRE PROJECT AGREEMENT

Dear Mr. Brigham:

Pursuant to your letter of January 24, we concur with the above referenced
Agreement with the exception of section "1)".  We request that all future
formal documents separately apportion the "Party/Ownership Interest" for the
RIMCO entities, as follows:

                          Party                         Ownership Interest
                          -----                         ------------------
         RIMCO Exploration Partners, L.P.I                      22.500%
         RIMCO Exploration Partners, L.P. II                    3.750%
         RIMCO Production Company, Inc.                         11.250%

We have enclosed the corrected original signature pages and further request
that all future signature blocks be prepared as follows:

         RIMCO Exploration Partners, L.P. I & II,
         By RIMCO Holdings Corp., Its General Partner
                 and
         RIMCO Production Company, Inc.

If you have any questions, please call.

Sincerely,


/s/ A. LEE JORDEN

A. Lee Jorden
Sr. Vice President


ALJ:acs

Enclosures

<PAGE>   1
                                                                  EXHIBIT 10.37


                                 ANADARKO BASIN
                        SEISMIC OPERATIONS AGREEMENT II


         This Anadarko Basin Seismic Operations Agreement II (this "Agreement")
is dated effective as of the 1st day of April, 1997, and is by and between
BRIGHAM OIL & GAS, L.P. ("BOG") and VERITAS DGC LAND, INC. ("Veritas") (BOG and
Veritas being sometimes individually referred to herein as a "Party" and
collectively referred to herein as the "Parties");

         WHEREAS, BOG and Veritas Geophysical, Ltd. (being the predecessor in
interest to Veritas) entered into that certain Anadarko Basin Seismic
Operations Agreement dated February 15, 1996 (the "Previous Agreement")
providing for Veritas' acquisition of 3-D seismic operations for BOG within the
areas described therein; and

         WHEREAS, BOG has designated the last project area within which Veritas
is to perform 3-D seismic operations for BOG under the Previous Agreement and
that the Previous Agreement shall terminate by its own terms upon the
completion of Veritas' 3-D seismic operations for such last project area; and

         WHEREAS, BOG has identified a number of additional project areas
within the lands described in Exhibit A which is attached hereto and
incorporated herein for all purposes (the lands described in Exhibit A being
hereinafter referred to as the "Alliance Area"), within which BOG desires to
pursue oil and gas exploration and/or development operations with project
participants; and

         WHEREAS, BOG desires to have Veritas to continue to conduct
three-dimensional seismic operations within the Alliance Area as provided in
this Agreement; and

         WHEREAS, Veritas desires to perform such three-dimensional seismic
operations within the Alliance Area pursuant to the terms set forth  in this
Agreement;

         NOW, THEREFORE, for and in consideration of the mutual covenants
contained herein and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Parties hereto agree as
follows:

                                   ARTICLE I.
                            RELATIONSHIP OF PARTIES
                       AND EFFECT UPON PREVIOUS AGREEMENT

         Section 1.1.     No Partnership.  The liabilities of the Parties
hereunder shall be several, not joint or collective.  It is not the intention
of the Parties to create, nor shall this Agreement be deemed as creating, a
mining, tax or other partnership or association or to render the Parties liable
as partners.  However, if for federal income tax purposes, this Agreement and
the operations hereunder are regarded as a partnership, each Party thereby
affected elects to be excluded from the application of all of the provisions of
Subchapter "K," Chapter 1, Subtitle "A," of the Internal Revenue Code of 1986,
as amended (hereinafter referred to as the "Code"), as permitted and authorized
by Section 761 of the Code and the regulations promulgated thereunder.  Should
there be any requirement that each Party hereby affected give further evidence
of this election, each such Party shall execute such documents and furnish such
other evidence as may be required by the Federal Internal Revenue Service or as
may be necessary to evidence this election.  No Party shall give any notice or
take any other action inconsistent with the election made hereby.  In making
the foregoing election, each Party states that the income derived by such Party
from operations hereunder can be adequately determined without the computation
of partnership taxable income.

         Section 1.2.     Effect Upon Previous Agreement.  The Parties
recognize and agree that, except as provided in Section 3.6 below this
Agreement shall not effect the Parties' rights and responsibilities under the
Previous Agreement and the Parties' rights and responsibilities with respect to
the 3-D operations which were conducted under and pursuant to the Previous
Agreement shall be governed solely by the Previous Agreement.  Similarly,
except as provided in Section 3.6 below the Previous Agreement shall not effect
or in any way apply to the 3-D operations which are conducted pursuant to the
terms of this Agreement.
<PAGE>   2
                                  ARTICLE II.
                         CONDUCT OF SEISMIC OPERATIONS

         Section 2.1.BOG Project Areas.  The Parties recognize and acknowledge
that BOG will be designating geographic areas within the Alliance Area (the
separate geographic areas being herein referred to as "Project Areas") for the
conduct of three-dimensional seismic operations (hereinafter referred to as
"3-D Operations") hereunder for the benefit of BOG and its participants.  For
purposes of this Agreement BOG's participants (hereinafter referred to as "BOG
Participants") shall mean (i) those parties that have entered into an agreement
with BOG providing for such parties' joint participation with BOG in an entire
Project Area, and (ii) those entities in which BOG either owns more than fifty
one percent (51%) of the ownership equity in such entity or controls the day to
day operations of such entity.  The Parties recognize and acknowledge that
third parties that enter into agreements with BOG under which such parties
either assign or are assigned interests covering less than an entire Project
Area are not BOG Participants for purposes of this Agreement.  For example, in
the event that BOG simply enters into a farm-in agreement with the owner of an
oil and gas leasehold estate covering less than an entire Project Area, such
party will not be considered a BOG Participant for purposes of this Agreement.

         Section 2.2.     BOG Commitment to 1000 Square Miles.

         A.      Subject to the other terms and provisions which are contained
in this Agreement, within a period of thirty-six months (to be reduced to
twenty-two months in the event that Veritas gives the notice described in
Section 2.6 below) of the date on which Veritas commences field seismic
acquisition operations for the first Project Area which is the subject of this
Agreement (such time period being hereinafter referred to as the "Agreement
Term"), BOG agrees to utilize a Veritas seismic crew  (hereinafter referred to
as the "Alliance Seismic Crew") to conduct 3-D Operations within Project Areas
covering a total of at least one thousand square miles (to be reduced to five
hundred square miles in the event that Veritas gives the notice described in
Section 2.6 below) within the Alliance Area (such number of square miles to be
covered by 3-D Operations under this Agreement being hereinafter referred to as
the "Contract Mileage"); provided, however, that at BOG's option the Agreement
Term shall be extended for any days during which the Alliance Seismic Crew does
not conduct operations hereunder due to weather conditions or any other causes
which are not the fault of BOG.  The Parties recognize and acknowledge that in
order to complete 3-D Operations across the entire final Project Area which is
to be shot  pursuant to the terms of  this Agreement, at BOG's option, the
Contract Mileage may be increased in size, provided that it is not increased by
more than one hundred square miles without Veritas' consent.  The Parties also
agree that two Alliance Seismic Crews shall be utilized simultaneously to
conduct the field seismic operations for the first two Project Areas which are
the subject of this Agreement and that upon the Parties' mutual agreement, two
Alliance Seismic Crews may be utilized simultaneously at other times during the
Agreement term to conduct field seismic acquisition operations within the
Project Areas.

         B.      For purposes of this Agreement the number of square miles
which are covered by the 3-D Operations shall be determined by the total number
of source and receiver points which are shot as part of the 3-D Operation for
the Project Area.

         (i)     For the 1,320' receiver line spacing parameters one hundred
         ninety two total source and receiver points shall be deemed to be one
         square mile;  provided, however, that in the event that the total
         number of receiver points are greater than fifty-one percent of the
         total source and receiver points for any Project Area, any receiver
         points exceeding such fifty-one percent amount shall not be counted
         for purposes of determining the number of square miles covered by the
         3-D Operations, and in the event that the total number of source
         points are greater than fifty-one percent of the total source and
         receiver points for the Project Area, any source points exceeding such
         fifty-one percent amount shall not be counted for purposes of
         determining the number of square miles covered by the 3-D Operations.
         However, in the event that the total number of receiver points exceed
         fifty-one percent of the total source and receiver points for a
         Project Area and BOG approves such excess receiver points, though
         those excessive receiver points will not be





Anadarko Basin
Seismic Operations Agreement II       2
<PAGE>   3
         counted for purposes of determining the number of square miles which
         are covered by the 3-D Operations, BOG shall be charged for the number
         of receiver points exceeding such fifty-one percent of total points at
         a rate of sixty-seven dollars ($67.00) per additional receiver point.
         In the event that the total number of source points exceed fifty-one
         percent of the total source and receiver points for a Project Area and
         BOG approves such excessive source points, though those excessive
         source points will not be counted for purposes of determining the
         number of square miles which are covered by the 3-D Operations, BOG
         shall be charged for the number of source points exceeding such
         fifty-one percent of total points at a rate of one hundred twelve
         dollars ($112.00) per additional source point.  In the event that
         Veritas must cable around a tract that is to be excluded from the 3-D
         Operations and the amount of cable which is utilized to cable around
         such tract would normally have more than five receiver points on it,
         then the number of receiver points along the cable length which is
         used to cable around such tract shall be counted as receiver points
         for purposes of determining the number of square miles which are
         covered by the 3-D Operations.

         (ii)    For the 660' receiver line spacing parameters two hundred
         eighty-eight total source and receiver points shall be deemed to be
         one square mile; provided, however, that in the event that the total
         number of receiver points are greater than sixty-seven and one-half
         percent of the total source and receiver points for any Project Area,
         any receiver points exceeding such sixty-seven and one-half percent
         amount shall not be counted for purposes of determining the number of
         square miles covered by the 3-D Operations, and in the event that the
         total number of source points are greater than sixty-seven and
         one-half percent of the total points for the Project Area, any source
         points exceeding such sixty-seven and one-half percent amount shall
         not be counted for purposes of determining the number of square miles
         covered by the 3-D Operations.  However, in the event that the total
         number of receiver points exceed sixty-seven and one-half percent of
         the total source and receiver points for a Project Area and BOG
         approves such excess receiver points, though those excessive receiver
         points will not be counted for purposes of determining the number of
         square miles which are covered by the 3-D Operations, BOG shall be
         charged for the number of receiver points exceeding such sixty-seven
         and one-half percent of total points at a rate of seventy-nine dollars
         ($79.00) per additional receiver point.  In the event that the total
         number of source points exceed sixty-seven and one-half percent of the
         total source and receiver points for a Project Area and BOG approves
         such excessive source points, though those excessive source points
         will not be counted for purposes of determining the number of square
         miles which are covered by the 3-D Operations, BOG shall be charged
         for the number of source points exceeding such sixty-seven and
         one-half percent of total points at a rate of one hundred thirty-two
         dollars ($132.00) per additional source point.  In the event that
         Veritas must cable around a tract that is to be excluded from the 3-D
         Operations and the amount of cable which is utilized to cable around
         such tract would normally have more than five receiver points on it,
         then the number of receiver points along the cable length which is
         used to cable around such tract shall be counted as receiver points
         for purposes of determining the number of square miles which are
         covered by the 3-D Operations.

         Section 2.3.     Parameters and Equipment.  For each Project Area BOG
shall select: 1) the seismic parameters that are to be utilized for the 3-D
Operations to be conducted within such Project Area from the parameters which
are set forth in Exhibit D; and 2) the equipment which is to be utilized for
the 3-D Operations to be conducted within such Project Area from the equipment
list which is set forth in Exhibit E.  However, if for any Project Area BOG
desires to utilize parameters other than those which are set forth in Exhibit D
or equipment other than that which is listed in Exhibit E, BOG and Veritas
shall attempt to mutually agree upon the reasonable charges to be incurred for
such parameters or equipment.  Should the Parties fail to reach agreement on
such charges, such Project Area shall be removed from this Agreement and shall
not be considered part of the Contract Mileage which is set forth in this
Agreement; such Contract Mileage commitment amount shall not, however, be
reduced as the result of any such removal of a Project Area.





Anadarko Basin
Seismic Operations Agreement II       3
<PAGE>   4
         Section 2.4.     Notification of Project Area Outline and Parameters
and Equipment.  No less than twenty-one days prior to the expected commencement
of the field seismic acquisition operations for each of its Project Areas, BOG
will notify Veritas in writing of 1) the location and general outline of the
specific Project Area, 2) the parameters to be utilized for the Project Area,
3) the equipment to be utilized for the Project Area, and 3) the approximate
patch to be used for source and receiver lines within the Project Area.  In no
event, without BOG's prior consent, shall Veritas commence surveying in source
and receiver locations more than thirty days prior to the date that field
seismic acquisition operations are expected to commence for the Project Area.
Following the notice described in this Section 2.4 and continuing until the
field seismic acquisition operations for the applicable Project Area have been
completed, BOG and Veritas shall stay in regular contact and utilize all
reasonable efforts to continue to work with each other in their efforts to
permit the lands that BOG desires to include in the Project Area and conduct
the field seismic operations across all of the lands which BOG and/or Veritas
are able to permit prior to the completion of such field seismic acquisition
operations for the Project Area.

         Section 2.5.     Veritas 3-D Seismic Crew Commitment.  During the
Agreement Veritas hereby agrees to give BOG priority use of one Alliance
Seismic Crew for the continuous conduct of 3-D Operations covering the Contract
Mileage as provided in Section 2.2 above; provided, however, that Veritas
agrees to utilize two Alliance Seismic Crews for the simultaneous conduct of
field seismic operations for the first two Project Areas that are designated by
BOG hereunder.  Veritas shall commence field seismic acquisition operations for
the first Project Area designated hereunder no earlier than July 1, 1997 and no
later than July 21, 1997 and shall commence field seismic operations for the
second Project Area designated hereunder no earlier than July 7, 1997 and no
later than August 7, 1997.  Following the commencement of field seismic
operations for the first two Project Areas as described above, BOG shall make a
reasonable effort to have Project Areas ready for surveying and field
acquisition such that one Alliance Seismic Crew may go directly from the
completion of 3-D Operations within one Project Area to the start of 3-D
Operations for the next Project Area.  As long as BOG has a Project Area ready
for surveying and field seismic acquisition, Veritas agrees that the Alliance
Seismic Crew will go from Project Area to Project Area without interruption
unless and until such time as BOG does not have a Project Area ready for
surveying and field seismic acquisition.  In the event that BOG notifies
Veritas that BOG will not have a Project Area ready for surveying in source and
receiver points upon the completion of the current Project Area, Veritas shall
make every reasonable effort to place the Alliance Seismic Crew on a
third-party project area with as little stand-by time as possible incurred
prior to the commencement of the next BOG Project Area.  However, in the event
that following the completion of 3-D Operations for a BOG Project Area the
Alliance Seismic Crew is moved to a third-party project area as provided above,
at BOG's request, Veritas will schedule the Alliance Seismic Crew to move to a
designated BOG Project Area as soon as possible following the completion of the
intervening third-party project areas which have been scheduled by Veritas
prior to its receipt of BOG's notice.  In the event that following the
completion of 3-D Operations for a BOG Project Area a subsequent BOG Project
Area is not ready for surveying and, despite Veritas' efforts to place the
Alliance Seismic Crew on a third-party project area, the Alliance Seismic Crew
experiences stand-by time, unless BOG has given Veritas at least sixty days
advance notice, as provided below in this Section 2.5, that no Project Area
will be ready, BOG shall compensate Veritas for stand-by time incurred by the
Alliance Seismic Crew as follows  (a) for the first three days of stand-by time
BOG shall pay Veritas fifteen thousand dollars per day, and (b) for any
stand-by time incurred after three days, BOG shall pay Veritas ten thousand
dollars per day; provided, however, in no event shall BOG be required to pay
Veritas more than four hundred fifty thousand dollars in total stand-by charges
for stand-by time incurred between the completion of any one BOG Project Area
and the commencement of the next succeeding BOG Project Area.  Anything to the
contrary contained herein notwithstanding, in the event that BOG gives Veritas
at least sixty days advance notice that BOG will not have any Project Areas
ready for field seismic acquisition, anything to the contrary contained in this
Section 2.5 notwithstanding, BOG shall not be required to pay any stand-by time
charges for any stand-by time that may be incurred by Veritas more than sixty
days after Veritas' receipt of such notice.  In the event that BOG gives
Veritas sixty days notice that BOG will not have any Project Areas ready for
field seismic acquisition, after such sixty day time period BOG shall not be
responsible for stand-by charges, unless and until BOG gives Veritas written
notice of a date by which BOG will have a Project Area ready for 3-D Operations





Anadarko Basin
Seismic Operations Agreement II       4
<PAGE>   5
and then BOG subsequently fails to have a Project Area ready for surveying
within the time frame BOG has given Veritas.  Any stand-by charges incurred
pursuant to this Section 2.5 shall be invoiced by Veritas on a monthly basis
and paid in full by BOG within thirty days of its receipt of an invoice
correctly reflecting the amount of such charges.

         Section 2.6.     Veritas Option to Reduce Contract Mileage.  In the
event that, and only in the event that, Veritas has not received payments under
Sections 3.4, 3.5 and/or 4.2 of the Previous Agreement totaling at least  two
million seven hundred thousand dollars ($2,700,000.00) on or before December
31, 1997, Veritas shall have the option to reduce the Contract Mileage to five
hundred square miles (subject to increase by up to one hundred square miles to
finish the last Project Area designated as provided in Section 2.5 above).  To
exercise the option described in this Section 2.6, Veritas must notify BOG in
writing that it is exercising the option on or before 5:00 p.m. CST on January
15, 1998.  In the event that Veritas has either (i) received at least
$2,700,000.00 of total payments pursuant to Sections 3.4, 3.5 and/or 4.2 of the
Previous Agreement prior to December 31, 1997, or (ii) Veritas fails to give
the written notice described in this Section 2.6 on or before the 5:00 p.m. CST
on January 15, 1998, then in either of such events, the Contract Mileage shall
remain to be one thousand square miles (subject to increase by up to one
hundred square miles to finish the last Project Area designated as provided in
Section 2.5 above).

         Section 2.7.     Excessive Weather Delays.  Anything to the contrary
contained in Section 2.5 above notwithstanding, in the event that weather
problems prevent the Alliance Seismic Crew from conducting field seismic
acquisition operations within a Project Area for more than two continuous days
and it does not reasonably appear that the Alliance Seismic Crew will be able
to begin conducting field seismic acquisition operations for at least another
six days, unless BOG  notifies Veritas that BOG desires to have the Alliance
Seismic Crew stay on location at the Project Area, Veritas shall utilize all
reasonable efforts to move the Alliance Seismic Crew to a third-party project
area, however, unless BOG agrees otherwise, the Alliance Seismic Crew shall
return to the abandoned  Project Area no later than twenty days after it left
such Project Area.  In the event that the Alliance Seismic Crew is moved to a
third-party project area as provided above, anything to the contrary contained
in this Agreement notwithstanding, BOG shall not incur any weather day delay
charges until after the Alliance Seismic Crew returns to the abandoned Project
Area and has commenced field seismic acquisition for such Project Area and
additional weather delays are incurred.

         Section 2.8.     General Terms and Provisions for 3-D Operations.  All
3-D Operations provided for herein shall be conducted by Veritas in accordance
with the general terms and provisions which are set forth in Exhibit F which is
attached hereto and incorporated herein for all purposes.  However, in the
event that there are any ambiguities or conflicts between the terms, provisions
and/or conditions which are set forth in the body of this Agreement and the
terms, provisions and/or conditions which are contained in Exhibit F, the
terms, provisions and conditions set forth in the body of this Agreement shall
control.  Veritas covenants and warrants to BOG that during the term of this
Agreement the Alliance Seismic Crew shall use all reasonable efforts to keep
and maintain all of the equipment, supplies and personnel necessary to
efficiently perform the operations described in this Article II on a continuous
basis, including, without limitation, the equipment, supplies and personnel
described on Exhibit E which are selected by BOG for the applicable Project
Area.

         Section 2.9.     Veritas Failure to Perform.  Anything to the contrary
contained herein notwithstanding, in the event that at any time the Alliance
Seismic Crew fails or is unable to perform seismic operations in full
compliance with all of the requirements set forth in this Agreement for more
than ten continuous days, in addition to and without limitation of any other
remedies which may be available to BOG at law or in equity, BOG shall have the
right to terminate this Agreement as to all future obligations to utilize the
Alliance Seismic Crew; provided, however, that if such failure to perform
seismic operations is due solely to weather or surface conditions which are
beyond Veritas' control or if BOG causes the nonperformance, BOG shall not have
the right to terminate this Agreement as provided herein.





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Seismic Operations Agreement II       5
<PAGE>   6
         Section 2.10.    Definition of Completion of 3-D Operations.  The
Parties agree that for all  purposes of this Agreement, the 3-D Operations for
a Project Area shall be deemed to have been completed when BOG receives from
Veritas: 1) all of the final correlated field tapes resulting from all of the
3-D Operations conducted within the Project Area on 9-track tape or 3480
cartridges in a state that is suitable for processing; 2) all survey
information obtained within the Project Area in Seg-P1 format and on a hard
copy and digital format, including without limitation all shot and receiver
point locations and GPS stations located within the Project Area and all
non-seismic survey points obtained; and 3) all observor reports, field notes,
and any other survey and support data obtained.  For each Project Area Veritas
agrees to provide all of the data and information which is described in this
Section 2.10 as soon as same is available and Veritas agrees to make every
reasonable effort to cause all of such data and information to be made
available as soon as is possible.


                                  ARTICLE III
                          CONSIDERATION DUE TO VERITAS

         Section 3.1.     Payment of One-Third Seismic Acquisition Costs.  For
each Project Area for which Veritas conducts and completes 3-D Operations as
provided herein, BOG shall owe Veritas one-third of 1) the turnkey charge which
is calculated as provided in Section 3.2 below based on the parameters,
dimensions and size of the applicable Project Area which are selected by BOG
for the applicable Project Area (hereinafter referred to as the "Turnkey
Charge") for the number of square miles over which 3-D Operations are conducted
within such Prospect Area, 2) the mobilization fee which is set forth in
Exhibit B for the number of road miles between the Project Area and the
previous Project Area (hereinafter referred to as the "Mobilization Fee"), and
3) the reimbursable costs which are not included in the Turnkey Charge as
reflected in Exhibit B, save and except any third-party line clearance charges
and permitting and surface damage settlement costs (the Turnkey Rate, the
Mobilization Fee and all of the reimbursable costs described in Exhibit B, save
and except any third-party line clearance charges and permitting and surface
damage settlement costs, being hereinafter collectively referred to as "Seismic
Acquisition Costs").  BOG shall pay such one-third share of the Seismic
Acquisition Costs within thirty days of BOG's receipt of an invoice correctly
indicating the costs which have been incurred.

         Section 3.2.     Determining the Turnkey Charge.  The Turnkey Charge
for each Project Area shall be determined as follows:

         A.      The number of square miles which are covered by the 3-D
Operations within the Project Area are to be determined by the total number of
source and receiver points that are included within such Project Area as
provided in Section 2.2 above.  The total number of square miles which are
covered by the 3-D Operations within the applicable Project Area being referred
to in this Section 3.2 as the "TA."

         B.      BOG shall determine the source and receiver line spacing
(either 1320' or 660'), the patch (10x96 or 8x120) and the source and receiver
line directions.

         C.      The various lengths of the receiver lines within the Project
Area shall be determined, each individual receiver line length being rounded to
the nearest one-half mile.  Each receiver line length for the applicable
Project Area being referred to in this Section 3.2 as a "RLLN",  with "N" being
the length of the applicable receiver line rounded to the nearest one-half
mile.  For example, if a Project Area has receiver line lengths that are five
and one- tenth miles wide, such receiver lines would be RLL5s.  The same
Project Area could also have receiver lines that are three miles in width, or
RLL3s, as well as other receiver line lengths of any variation.

         D.      The hypothetical source line length for each RLLN shall be
determined by dividing the receiver line length of a specific RLLN (rounded to
the nearest one-half mile) into the TA.  Each individual hypothetical source
line length being rounded to the nearest one-half mile and being referred to in
this Section 3.2 as a "HSLN", with "N" being the length of the





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Seismic Operations Agreement II     6
<PAGE>   7
receiver line rounded to the nearest one-half mile.  For example, if the
Project Area's TA equals 16 square miles, the HSL5 would equal sixteen divided
by five, or three point two, which would then be rounded to three.

         E.      The Turnkey Charge per square mile shall be determined for
each RLLN utilizing the applicable Master Rate Table set forth in Exhibit B for
the parameters selected by BOG and the HSLN for such RLLN.  The Turnkey Charge
per square mile for a RLLN being found at the intersection of the receiver line
length for the applicable RLLN and the HSLN for such RLLN on the applicable
Master Rate Table.  Such per square mile Turnkey Charge for each RLLN shall be
referred to in this Section 3.2 as "RRLLN."

         F.      The total number of square miles covered by each RLLN shall be
determined.  The total number of square miles covered by a RLLN being referred
to in this Section 3.2 as a "SMRLLN."  For example, if five mile long receiver
lines cover a total of twenty-two square miles within the applicable Project
Area, SMRLL5 for the Project Area would be twenty-two square miles.  It being
understood that all of the SMRLLNs for a Project Area, added together, total
the TA for the Project Area.

         G.      The total Turnkey Charge for each RLLN shall then be
determined by multiplying the RRLLN for such RLLN times its SMRLLN.  The total
Turnkey Charge for a RLLN being referred to in this Section 3.2 as "TCRLLN."

         H.      The sum of all of the TCRLLNs is then determined by adding
together all of the TCRLLNs for the Project Area.  The sum of all of the
TCRLLNs for a Project Area being referred to in this Section 3.2 as the "SUM."

         I.      The average of all of the TCRLLNs for a Project Area is then
obtained by dividing the SUM by the TA for the Project Area.  The average of
all of the TCRLLNs for a Project Area being referred to in this Section 3.2 as
the "AVG."

         J.      The Total Turnkey Charge per square mile for a Project Area is
then determined by adding together (i) twenty-five percent (25%) of the AVG,
(ii) seventy-five percent (75%) of the RRLLN for the longest receiver line in
the Project Area, (iii) in the event that 1320' receiver line spacing is
utilized, $365.00, and in the event that 660' receiver line spacing is utilized
$570.00, and (iv) in the event and only to the extent that the part of the
Project Area is located within the State of Oklahoma, $1,100.00.  It being
understood that in the event that a Project Area is located only partially
within the State of Oklahoma, the $1,100.00 amount shall only be added to the
Total Turnkey Charge with respect to the square miles that are located within
the State of Oklahoma.  The Total Turnkey Charge per square mile for a Project
Area being referred to in this Section 3.2 as the "TTCPM."

         K.      The Total Turnkey Charge for a Project Area is then determined
by multiplying the TTCPM for the Project Area times the TA for the Project
Area.

See Exhibit C for example determinations of the Turnkey Charges for
hypothetical Project Areas with different configurations.

         Section 3.3.     Right to Pay All Seismic Acquisition Costs and
Receive Full Ownership.  Anything to the contrary contained herein
notwithstanding, prior to the commencement of field seismic acquisition for the
3-D Operations for a Project Area BOG shall have the right to designate in
writing all or any part of the Project Area for which it desires to pay one
hundred five percent of the Turnkey Charge for the applicable Project Area and
one hundred percent of all of the other Seismic Acquisition Costs related to
such selected lands (the lands for which BOG elects to pay one hundred five
percent of the Turnkey Charge and one hundred percent of other Seismic
Acquisition Costs as provided in this Section 3.3 being hereinafter referred to
as "Excluded Lands") in order to receive all of the ownership interest in the
seismic data obtained across the Excluded Lands.  In the event that BOG
designates Excluded Lands covering all or part of a Project Area, BOG shall pay
one hundred five percent of the Turnkey Charge and one hundred percent of the
other Seismic Acquisition Costs related to such Excluded Lands within





Anadarko Basin
Seismic Operations Agreement II     7
<PAGE>   8
thirty days of BOG's receipt of an invoice correctly indicating the costs which
have been incurred.  The Parties recognize and acknowledge that with respect to
the Excluded Lands, BOG's obligation to pay one hundred five percent of the
Turnkey Charge and one hundred percent of the other Seismic Acquisition Costs
related to such Excluded Lands as provided in this Section 3.3 is in lieu of
and complete substitution for what would have otherwise been an obligation to
pay one-third of the Seismic Acquisition Costs as provided in Section 3.1 above
and the additional compensations set forth in Sections 3.4 and 3.5 below, and
not in addition to those obligations.  The Parties also recognize and agree
that in the event that Excluded Lands are designated for a Project Area
covering part, but not all of the Project Area, the payment provided for in
this Section 3.3 shall not include any part of the Mobilization Fee related to
the applicable Project Area as BOG shall still be required to pay such
mobilization fee for the Project Area in accordance with the terms and
provisions of Sections 3.1 above and Sections 3.4 and 3.5 below.  Anything to
the contrary contained herein notwithstanding, the Parties recognize and agree
that if Excluded Lands are designated hereunder such Excluded Lands shall not
be counted as part of BOG's commitment to utilize the Veritas Seismic Crew to
conduct 3-D Operations across the Contract Mileage as set forth in Section 2.2
above and thus the Contract Mileage shall not be reduced by the number of
square miles which are included within Excluded Lands.

         Section 3.4.     Payment of 2/3rd Seismic Acquisition Cost Balance.
Until the earlier to occur of 1) the expiration of two years following the
completion of all of the 3-D Operations conducted for the last Project Area
covered by this Agreement (the period of time commencing with the effective
date of this Agreement and continuing until the expiration of two years
following the completion of all of the 3-D Operations conducted for the last
Project Area covered by this Agreement being hereinafter referred to as the
"Exclusivity Period"), or 2) such time as BOG has paid Veritas a total amount
under this Section 3.4 and/or Section 4.2 below equal to the remaining
two-thirds of all Seismic Acquisition Costs (determined in accordance with the
provisions of Exhibit B for each of the applicable Project Areas) incurred in
conducting 3-D Operations within BOG Project Areas less and except the Excluded
Lands (such amount  being hereinafter referred to as the "First Payout Amount"
and such time as BOG has paid Veritas the First Payout Amount being hereinafter
referred to as the "First Payout"), BOG shall pay Veritas an amount equal to
twenty percent of: (a) all actual lease bonus costs  paid by BOG and the BOG
Participants to mineral interest owners in order to lease mineral interests
within Project Areas (other than within Excluded Lands) after 3-D Operations
have been completed within such Project Area; and (b) all costs incurred by BOG
and the BOG Participants in drilling and completing oil and/or gas wells within
Project Areas (other than within Excluded Lands) after 3-D Operations have been
completed within such Project Area.  For the costs described in (a) above,
within ten working days following the end of a calendar month, BOG shall pay
Veritas the twenty percent fee on all actual lease bonus costs which were paid
out by BOG and the BOG Participants during such calendar month.  For the costs
described in (b) above, within ten days of reaching casing point in a well, BOG
shall pay Veritas the twenty percent fee on drilling (and completion if BOG
elects to participate in completing such well) costs for such well based upon
the AFE prepared for such well; provided, however, that on a calendar quarter
basis BOG shall review all drilling and completion fees which have been paid to
Veritas during the calendar quarter to reconcile Veritas' account based on
actual drilling and completion costs incurred in drilling and completing wells
during the calendar quarter.

         Section 3.5.     Payments Following the First Payout.  Following the
occurrence of the First Payout and continuing until the earlier to occur of 1)
the expiration of the Exclusivity Period, or 2) such time as BOG has paid
Veritas a total amount under this Section 3.5 and/or Section 4.2 below equal to
the product obtained by multiplying the Contract Mileage times two thousand
five hundred dollars (such product being hereinafter referred to as the "Final
Payout Amount" and such time as BOG has paid Veritas the Final Payout Amount
being hereinafter referred to as "Final Payout"), BOG shall pay Veritas an
amount equal to ten percent of (i) all actual lease bonus costs paid by BOG and
the BOG Participants to mineral interest owners in order to lease mineral
interests within Project Areas (other than within Excluded Lands) after 3-D
Operations have been completed within such Project Area and (ii) all costs
incurred by BOG and the BOG Participants in drilling and completing oil and/or
gas wells within Project Areas (other than within Excluded Lands) after 3-D
Operations have been completed within such Project Area.  For the costs
described in (i) above, within ten working days following the end of





Anadarko Basin
Seismic Operations Agreement II     8
<PAGE>   9
a calendar month, BOG shall pay Veritas the ten percent fee on all actual lease
bonus costs which were paid out by BOG and the BOG Participants during such
calendar month.  For the costs described in (ii) above, within ten days of
reaching casing point in a well, BOG shall pay Veritas the ten percent fee on
drilling (and completion if BOG elects to participate in completing such well)
costs for such well based upon the AFE prepared for such well; provided,
however, that on a calendar quarter basis BOG shall review all drilling and
completion fees which have been paid to Veritas during the calendar quarter to
reconcile Veritas' account based on actual drilling and completion costs
incurred in drilling and completing wells during the calendar quarter.
Anything to the contrary contained herein notwithstanding, in the event that
Excluded Lands have been designated by BOG in accordance with Section 3.3
above, the Parties recognize and acknowledge that the number of square miles
covered by the Excluded Lands are not part of the Contract Mileage and
therefore are excluded from the calculation of Final Payout Amount.  As such,
the Contract Mileage utilized for purposes of calculating the Final Payout
Amount is equal to the number of square miles that have been covered by 3-D
Operations conducted hereunder, less and except the number of square miles that
are covered by the Excluded Lands.  The Parties also recognize and acknowledge
that in the event that more than the Contract Mileage minimum number of square
miles are covered by the 3-D Operations hereunder pursuant to Section 2.5 above
in order to finalize the last Project Area which is designated hereunder, for
purposes of calculating the Final Payout Amount, the Contract Mileage shall
include the number of square miles added to the minimum in order to finalize
the last Project Area as provided in Section 2.5.  Finally, in the event that
BOG's obligation to continue to use the Alliance Seismic Crew is terminated
prior to the completion of 3-D Operations covering the Contract Mileage as
provided in Section 2.9, the Final Payout Amount shall be reduced by an amount
equal to the product obtained by multiplying 1) the number obtained by dividing
(a) the difference obtained by subtracting the number of square miles covered
by 3-D Operations which have been completed within Project Areas prior to such
termination from the minimum Contract Mileage, by (b) the Contract Mileage,
times 2) the product obtained by multiplying the Contract Mileage times two
thousand five hundred dollars.  For example, assuming that the Contract Mileage
has not been reduced pursuant to the terms of Section 2.6 above, if 3-D
Operations have been completed covering seven hundred square miles and BOG's
obligation to continue to utilize the Alliance Seismic Crew is subsequently
terminated in accordance with the terms of Section 2.9 above, then the Final
Payout Amount shall be reduced by seven hundred fifty thousand dollars
([[1,000-700]/1,000] x [1,000 x $2,500] = $750,000).

         Section 3.6.     Leasing and Drilling Costs Covering Overlap Lands.
Anything to the contrary contained in Sections 3.4 and 3.5 above
notwithstanding, in the event that BOG designates a Project Area hereunder
which overlaps with a project area which was designated under the Previous
Agreement (the lands located within the overlap area being referred to as
"Previous Agreement Overlap Lands"), no payments shall be made under Sections
3.4 or 3.5 of this Agreement to Veritas for lease bonus costs and/or drilling
or completion costs which are related to the Previous Agreement Overlap Lands.
Veritas' compensation for such operations shall be governed solely by the
Previous Agreement.  In addition, anything to the contrary contained in
Sections 3.4 and 3.5 above notwithstanding, in the event that BOG designates a
Project Area hereunder (for purposes of this Section 3.6 such Project Area is
referred to as the "Prior Project Area") and then subsequently designates
another Project Area hereunder (for purposes of this Section 3.6 such
subsequently designated Project Area is referred to as the "Subsequent Project
Area") which overlaps with the Prior Project Area (the lands located within
such overlap area being referred to as "Project Area Overlap Lands"), BOG shall
only be required to make the payments described in Sections 3.4 and 3.5 above
once, even though the Project Area Overlap Lands are covered by two separate
Project Areas and 3-D operations are conducted twice over such Project Area
Overlap Lands.  However, the Parties agree that, without Veritas' prior
consent, in no event shall 3-D Operations conducted for a Subsequent Project
Area overlap more than one mile in one orthogonal direction into lands which
were covered by 3-D Operations which were conducted for a Prior Project Area
hereunder or for a project area that was designated under the Previous
Agreement.  For example, in the event that a Subsequent Project Area is
designated hereunder and is to overlap with the 3-D Operations conducted for a
Prior Project Area which overlaps with such Subsequent Project Area on the East
side of such Subsequent Project Area, the 3-D Operations for such Subsequent
Project Area may overlap no





Anadarko Basin
Seismic Operations Agreement II     9
<PAGE>   10
more than one mile to the East into the lands which were covered by the 3-D
Operations conducted for the Prior Project Area.  The Parties recognize and
agree, however, that in the example above, the 3-D Operations for the
Subsequent Project Area may overlap into the lands which were covered by the
3-D Operations conducted for the Prior Project Area in a North / South
direction across the entire West boundary line of the 3-D Operations that were
conducted for the Prior Project Area regardless of how long that boundary line
is, provided that the 3-D Operations do not penetrate such West boundary line
by more than one mile.

         Section 3.7.     Monthly Lease Bonus and Drilling and Completion Cost
Reports.  Commencing with the completion of 3-D Operations for the first
Project Area hereunder and continuing until such time as the Final Payout has
occurred, within thirty days of the end of each calendar month BOG shall
provide Veritas with a report setting forth the amount of lease bonus costs and
drilling and completion costs which have been incurred by BOG within each
Project Area following the completion of 3-D Operations for such Project Area.

         Section 3.8.     Exclusion of Production Purchases.  Anything to the
contrary contained in this Agreement notwithstanding, it is recognized and
agreed that in the event that subsequent to the date of this Agreement BOG or
any BOG Participant acquires an interest in oil and/or gas leasehold, mineral
or royalty interests that are already producing oil and/or gas, or that are
held by production which was in existence prior to the completion of 3-D
Operations covering such lands, BOG shall not be required to pay any
consideration to Veritas under the terms of Section 3.4 or 3.5 above as the
result of such acquisition with respect to the consideration paid for the
acquisition.  However, in the event that following the completion of 3-D
Operations on the lands which are the subject of the acquisition, BOG or any
BOG Participant subsequently participates in the drilling of a well involving
the interests that were acquired in the acquisition, the terms and provisions
of Sections 3.4 or 3.5 (whichever is the applicable) shall apply with respect
to any drilling and completion costs incurred with respect to the drilling of
such well.

         Section 3.9.     Reimbursement for Permitting, Surface Damage
Settlements and Line Clearance Costs.  Veritas shall pay all BOG approved
third-party line clearance costs, permitting costs and surface damage
settlement payments.  Veritas shall submit to BOG an invoice on a monthly basis
for all third-party line clearance, permitting costs and surface damage
settlement payments incurred during the month and BOG shall reimburse Veritas
for one hundred percent of all of such costs within ten days of BOG's receipt
of the invoice.

         Section 3.10.    Compensation for BOG Failure to Minimum Contract
Mileage.  In the event that BOG fails, for any reason, to make sufficient
Project Areas ready for 3-D Operations in order to cause 3-D Operations to be
conducted by the Alliance Seismic Crew covering at least the minimum Contract
Mileage within the Alliance Area within the Agreement Term (as same may be
extended as provided in Section 2.2 above) as provided in Sections 2.2 and 2.5
above, BOG shall pay Veritas an amount (hereinafter referred to as the "Pay Off
Amount") equal to the difference obtained by subtracting 1) all amounts already
paid by BOG to Veritas pursuant to the terms of Sections 3.1, 3.4 and 3.5
above, from 2) the sum of (A) all Seismic Acquisition Costs (determined in
accordance with the provisions of Exhibit B for each of the applicable Project
Areas) incurred in conducting the 3-D Operations during the Agreement Term
within BOG Project Areas, less and except any Seismic Acquisition Costs related
to the Excluded Lands, and (B) an amount equal to the product obtained by
multiplying (i) the number obtained by dividing (a) the number of square miles
which were covered by 3-D Operations that were conducted hereunder during the
Agreement Term by (b) the Contract Mileage, times (ii) the product obtained by
multiplying the Contract Mileage times two thousand five hundred dollars.  In
such event, such payment shall be made to Veritas within thirty (30) days of
the expiration of the Agreement Term and shall be in full and complete
settlement and satisfaction of all obligations hereunder.  Upon making the
payment described in this Section 3.10, BOG shall own all interest in the
Program Data (as defined below) which has resulted from the 3-D Operations
conducted within the Alliance Area.  The payment by BOG to Veritas hereunder of
the Pay Off Amount shall be the sole and exclusive remedy of Veritas for the
failure of BOG to make sufficient Project Areas ready for 3-D Operations
hereunder, and Veritas hereby waives any other remedy, damages and/or cause of
action it may otherwise have had against BOG, whether in law or in equity.  The
Parties recognize and agree that BOG's payment of the Pay Off Amount will not





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Seismic Operations Agreement II      10
<PAGE>   11
extinguish BOG's responsibility to reimburse Veritas for all actual third-party
line clearance, permitting costs and damage settlement payments incurred prior
to the termination of this Agreement as set forth in Section 3.9 above and BOG
shall remain responsible for such payments in accordance with the terms of
Section 3.9 above.


                                   ARTICLE IV
                       OWNERSHIP AND USE OF SEISMIC DATA

         Section 4.1.     Ownership of the Program Data.  Except as provided
above in Section 3.10 and below with respect to seismic data that covers
Excluded Lands, and subject to the other terms of this Article IV, Veritas
shall own one hundred percent of the ownership interest in the seismic data
that results from the 3-D Operations (hereinafter referred to as "Program
Data") conducted within Project Areas hereunder until such time as the First
Payout occurs.  Once the First Payout occurs BOG and Veritas shall each own an
undivided fifty percent interest in all of the Program Data.  Then, if Final
Payout occurs prior to the expiration of the Exclusivity Period, upon the
occurrence of Final Payout BOG shall own one hundred percent of the ownership
interest in all of the Program Data.  Anything to the contrary contained in
this Agreement notwithstanding, in the event that BOG designates Excluded Lands
and pays for the costs described in Section 3.3 above, BOG shall own one
hundred percent of the ownership interest in the Program Data covering such
Excluded Lands.  In addition, anything to the contrary contained in this
Agreement notwithstanding, in the event that BOG is required to make the
payment which is described in Section 3.10 above, BOG shall own one hundred
percent of the ownership interest in the Program Data which has resulted from
all of the 3-D Operations conducted hereunder.

         Section 4.2.     BOG Right to Contribute Toward First Payout and Final
Payout.  In the event that Final Payout has not been reached prior to the
expiration of the Exclusivity Period, BOG shall nonetheless have the option to
acquire one hundred percent of the ownership interest in the Program Data by
paying Veritas the amount which is necessary to cause Veritas to have received
the Final Payout Amount.  To exercise such option, BOG must notify Veritas in
writing that it is exercising such option prior to the expiration of the
Exclusivity Period.  In the event that BOG exercises the option to acquire all
interest in the Program Data as provided herein, BOG shall remit payment for
the amount necessary to cause Veritas to have received the Final Payout Amount
within thirty days of the expiration of the Exclusivity Period.  In addition,
at BOG's option, to be exercised in BOG's sole discretion, BOG shall also have
the right at any time, and from time to time, to make payments to Veritas to go
toward the First Payout Amount or the Final Payout Amount before actually
incurring the lease bonus or drilling and/or completion costs within the
Project Areas which would otherwise result in the need for such payments.  In
the event that BOG, at its option, elects to make advance payments to Veritas
toward the First Payout Amount or the Final Payout Amount as provided in this
Section 4.2, such payments shall be credited against the next lease bonus
payments and/or drilling and/or completion cost payments which would otherwise
be due to Veritas under the terms of Section 3.4 or 3.5 above (as applicable).

         Section 4.3.     Program Data to Remain Clear of Liens and
Encumbrances.  Anything to the contrary contained herein notwithstanding,
Veritas shall not allow its interest in the Program Data to be burdened or
encumbered with any liens, mortgages or other burdens of any kind unless, until
and to the extent that Veritas has retained ownership interest in the Program
Data after the expiration of the Exclusivity Period.  Anything to the contrary
contained herein notwithstanding, BOG shall not burden or encumber the Program
Data with any liens, mortgages or other burdens of any kind unless and until
BOG has received an ownership interest in the Program Data.  The Parties agree
that in exercising their rights to have liens, mortgages or other burdens
attached to the Program Data as allowed in this Section 4.3, neither Party
shall have the right to burden or encumber the other Party's ownership interest
in the Program Data.

         Section 4.4.     Veritas' Rights to Sell, Exchange and/or Disclose the
Program Data.  Anything to the contrary contained herein notwithstanding,
Veritas agrees that it will not sell, license, trade, exchange or in any way
disclose the Program Data (or any part thereof) or any information related to
the Program Data, in any format or manner, or negotiate or advertise for





Anadarko Basin
Seismic Operations Agreement II      11
<PAGE>   12
the potential sale, license, trade, exchange or other disclosure of the Program
Data (or any part thereof), prior to the expiration of the Exclusivity Period.
In addition, in the event that BOG ends up owning one hundred percent of the
ownership interest in all or part of the Program Data as provided herein,
Veritas shall not ever have the right to sell, license, trade, exchange or
otherwise disclose the Program Data or any information related to the Program
Data.

         Section 4.5.     Proceeds resulting from Sale or Licensing of Program
Data.  In the event that after the expiration of the Exclusivity Period BOG and
Veritas each own an undivided fifty percent interest in the Program Data, if
either BOG or Veritas subsequently sells or licenses the Program Data for cash
consideration, the Parties shall each receive fifty percent of the cash
consideration received as the result of such sale or licensing; provided,
however, that the Party that licenses or sells the Program Data as aforesaid
shall have the right to deduct from the other Party's share of the cash
consideration fifty percent of the reasonable costs and expenses which have
been incurred in licensing or selling such Program Data.  In the event that
either Party hereto trades, exchanges or licenses the Program Data in
conformance with the other terms that are contained in this Article IV, as long
as such exchange, trade or licensing does not involve the payment of cash
consideration, the trading, exchanging or licensing Party will not owe any
consideration of any kind to the other Party hereto as a result of such
transaction, even though such other Party may own part of the ownership
interest in the Program Data.

         Section 4.6.     BOG's and BOG Participants' Right to Utilize the
Program Data.  Whether or not BOG owns any ownership interest in the Program
Data, at all times BOG and the BOG Participants shall have all rights to
utilize, copy, trade, exchange and disclose the Program Data in pursuit of
their oil and gas exploration and/or development operations within the
applicable Project Areas.  In the event that Veritas owns an interest in the
Program Data following the expiration of the Exclusivity Period as provided
herein, BOG shall provide Veritas with a list of the names of the companies
with whom BOG has traded or exchanged all or parts of the Program Data as
allowed hereunder, together with a description of the Program Data which has
been traded or exchanged with each such company.


                                   ARTICLE V.
                              VERITAS NON-COMPETE

         Section 5.1.     Veritas Agreement Not to Compete.  Veritas hereby
agrees that for a period of six years from the date of this Agreement neither
Veritas, its successors or assigns or any of their affiliated companies
(hereinafter referred to as the "Veritas Group") shall compete with BOG or any
of the BOG Participants within one mile of the outside perimeter of any Project
Areas which are designated by BOG hereunder, by owning or acquiring any
leasehold, mineral or royalty interest within such area, either directly or
indirectly, through any agents, nominees, or representatives, unless purchased
or acquired from BOG or a BOG Participant.  In the event that any member of the
Veritas Group breaches the non-compete provisions contained in this Section
5.1, in addition to any other remedies that may be available to BOG and each
BOG Participant at law or in equity, upon BOG's or any BOG Participant's
request, Veritas shall cause the interests that have been acquired in breach of
the provisions contained in this Section 5.1, to be assigned to BOG or such BOG
Participant without reimbursement for any costs incurred in obtaining such
interests.  The Parties agree that for purposes of this Section 5.1 the
"outside perimeter of each Project Area" shall include all lands that are
located within the outside perimeter of the area that is depicted on the final
bin/fold map resulting from the 3-D Operations which is provided by the seismic
processor.  Following the completion of final processing of the Program Data
resulting from a Project Area BOG shall prepare a legal description of the
acreage which is located within the outside perimeter depicted on the final
bin/fold map for such Project Area and the Parties agree that such legal
description shall constitute the outside perimeter of the Project Area for
purposes of this Section 5.1.  BOG shall use reasonable efforts to cause the
legal description to depict the outside perimeter of the area that is depicted
on the final bin/fold map which is provided by the seismic processor; however,
the Parties recognize that in order to provide a legal description of such area
BOG shall not be required to have a survey conducted on the ground and may
approximate, in its sole and reasonable discretion, the location of the outside
perimeter depicted on the final bin/fold map for purposes of aiding BOG in the
preparation of the legal





Anadarko Basin
Seismic Operations Agreement II      12
<PAGE>   13
description.  Anything to the contrary contained in this Section 5.1
notwithstanding, in the event that following the expiration of the Exclusivity
Period Veritas owns an interest in the Program Data as provided herein, the
terms and provisions of this Section 5.1 shall not be construed to impede
Veritas' ability to sell, license, trade or exchange the Program Data in
accordance with the provisions of Article IV above.


                                  ARTICLE VI.
                                 MISCELLANEOUS

         Section 6.1.     Assignments.  BOG shall have the right to assign or
convey all or any part of its rights, obligations or interests under this
Agreement provided that such assignment is made subject to all of the terms and
provisions of this Agreement; provided, however, that prior to the expiration
of the Exclusivity Period BOG shall not assign or convey all of its interests
under this Agreement.  Veritas shall not have the right to assign or convey all
or any part of its rights, obligations or interests under this Agreement.

         Section 6.2.     Merger.  This Agreement supersedes any and all prior
and existing agreements, whether oral or in writing, between any of the Parties
hereto with respect to the subject matter hereof and contains all of the
covenants and agreements between the Parties with respect to the subject matter
hereof.

         Section 6.3.     Notices.  All notices and other communications
required or permitted under this Agreement shall be in writing, and shall be
delivered personally, or by telecopier or delivery service, to the addresses
set forth opposite the signatures of the Parties below, and shall be considered
delivered upon the date of receipt.  Each Party may specify its proper address
or any other address by giving notice to other Parties, in the manner provided
in this section, at least ten days prior to the effective date of such change
of address.

         Section 6.4.     Right to Specific Performance.  Each Party
acknowledges  1) that its obligations under this Agreement are unique and 2)
that the other Parties would be irreparably damaged and would not have an
adequate remedy at law for damages if such Party defaults in its obligations
hereunder.  Each Party expressly waives the defense that a remedy in damages
will be adequate.  If any Party should default in its obligations hereunder,
each non-defaulting Party, in addition to any other available rights or
remedies, may sue in equity for specific performance or injunctive relief.

         Section 6.5.     Governing Law.  THIS AGREEMENT AND ALL MATTERS
PERTAINING THERETO, INCLUDING, BUT NOT LIMITED TO, MATTERS OF PERFORMANCE,
NON-PERFORMANCE, BREACH, REMEDIES, PROCEDURES, RIGHTS, DUTIES, AND
INTERPRETATIONS OR CONSTRUCTION, SHALL, WITHOUT REGARD TO PRINCIPLES OF
CONFLICTS OF LAW, BE GOVERNED BY THE LAWS OF THE STATE OF TEXAS.  THE PARTIES
AGREE THAT THE EXCLUSIVE VENUE FOR ANY DISPUTES OR CLAIMS ARISING HEREUNDER OR
IN ANY WAY RELATED HERETO SHALL BE IN DALLAS COUNTY, TEXAS.

         Section 6.6.     Counterparts.  This Agreement may be executed in
multiple counterparts, each of which shall be binding upon the signing Party or
Parties thereto as fully as if all Parties had executed one instrument, and all
of such counterparts shall constitute one and the same instrument.  If
counterparts of this Agreement are executed, the signatures of the Parties, as
affixed hereto, may be combined in and treated and given effect for all
purposes as a single instrument.





Anadarko Basin
Seismic Operations Agreement II      13
<PAGE>   14
         IN WITNESS WHEREOF this Agreement is executed by the Parties on the
dates set forth opposite their respective signatures below but is effective for
all purposes as of the date first set forth above.

   
Address:                                   VERITAS DGC LAND, INC.
         860 West Airport Freeway
         Suite 509
         Hurst, Texas  76054
         Phone: (817) 498-1383
         Fax:  (817) 498-1256
Dated:   3/19/97                           By:/s/ EDWARD COMPTON         
      ------------------------                 -----------------------------
                                           (name printed) Edward Compton
                                                         -------------------
                                           Its: General Manager          
                                               -----------------------------
    



   
Address:                                   BRIGHAM OIL & GAS, L.P.,
         5949 Sherry Lane                  by Brigham, Inc.
         Suite 1616                        its Managing General Partner
         Dallas, Texas  75225
         Phone: (214) 360-9182
         Fax:  (214) 360-9825
Dated:   3/21/97                           By: /s/ JON L. GLASS          
      ------------------------                 -----------------------------
                                              Jon L. Glass                   
                                              Vice President - Exploration
    




Anadarko Basin
Seismic Operations Agreement II      14
<PAGE>   15
                                LIST OF EXHIBITS




Exhibit A -- Alliance Area

Exhibit B -- Turnkey Amount and Other Seismic Acquisition Costs

Exhibit C -- Example Turnkey Charge Determinations

Exhibit D -- Alternative Seismic Parameters

Exhibit E -- Description of Equipment and Personnel

Exhibit F -- General Terms and Provisions





Anadarko Basin
Seismic Operations Agreement II      15

<PAGE>   1


                                                                 EXHIBIT 10.37.1




   
                                 MARCH 20, 1997
    

Via Facsimile and Hand Delivery
Mr. Ed Compton
Veritas DGC Land, Inc.
Suite 509, 860 West Airport Fwy.
Hurst, Texas 76054
Fax # (817) 498-1256

                 Re:      Anadarko Basin Seismic Operations Agreement II, dated
                          April 1, 1997, by and between Brigham Oil
                          & Gas, L.P. ("BOG") and Veritas DGC Land, Inc.
                          ("Veritas") (hereinafter referred to as the
                          "Alliance Agreement II")

Gentlemen:

         Anything to the contrary contained in the Alliance Agreement II
notwithstanding, in consideration for Veritas' commitment to utilize two
Alliance Seismic Crews to simultaneously conduct seismic operations for the
first two BOG Project Areas that are designated under the Alliance Agreement
II, BOG hereby agrees to advance pay $200,000 of the amounts which would
otherwise not be due under Section 3.4 of the Alliance Agreement II until such
time as BOG has incurred lease bonus and drilling and completion costs within
the Project Areas.  Such advance payment shall be made within thirty (30) days
of BOG's receipt of an invoice for such amount from Veritas; provided, however
that Veritas shall not submit such invoice until field seismic operations have
commenced for both of such first two designated Project Areas.

         BOG and Veritas recognize, acknowledge and agree that  the $200,000
payment to be made to Veritas as provided in this letter agreement shall be
applied toward the First Payout Amount and shall be credited against the first
lease bonus payments and drilling and/or completion cost payments which would
otherwise be due to Veritas under the terms of Section 3.4.

         If this letter agreement correctly sets forth your company's agreement
and understanding with respect to the subject matter hereof, we ask that you
have an authorized representative of your company execute the duplicate
originals of same below and return one of such fully executed duplicate
originals to our offices.

                                         Sincerely,
                                         BRIGHAM OIL & GAS, L.P.
                                         by Brigham, Inc.,
                                         its Managing General Partner
                               
                               
   
                                         /s/ BEN M. BRIGHAM
                                         -------------------------------
                                         Ben M. Brigham, President / CEO
    

ACCEPTED AND AGREED:

VERITAS DGC LAND, INC.
   

By:/s/ EDWARD COMPTON
   ------------------------------
(name printed) Edward Compton
              -------------------
Its:  General Manager
    -----------------------------
    


<PAGE>   1
                                                                    EXHIBIT 11.1

Exhibit 11.1 -- Computation of pro forma net loss per common share for the year
                ended December 31, 1996 (in thousands, except per share data)

<TABLE>
<CAPTION>

<S>                                                                             <C>               <C>
                                                                                                    Pro Forma
                                                                                Pro Forma          As Adjusted
                                                                                ---------          -----------

Pro forma net income (loss)...................................................   $(56)               $   190
                                                                                =====                =======

Number of shares outstanding after the Exchange ..............................  8,929                  8,929

Number of shares issued pursuant to the Offering .............................                         3,000                

Employee stock options granted under the 1997 Incentive Plan .................    644                    644

Shares assumed to be repurchased under the treasury stock method: 
        $3,220,485 (1)/$10.50 Per share (2) ..................................   (307)                  (307)
                                                                                -----                -------

Pro forma weighted average number of common shares outstanding ...............  9,266                 12,266
                                                                                =====                =======

Pro forma net income (loss) per common share ................................. $ 0.00                $  0.02  
                                                                               ======                =======
</TABLE>

Notes:
- ------

(1)--     Calculated by multiplying employee stock options granted under the
          1997 Incentive Plan (644,097) by their exercise price ($5.00).

(2)--     Assumed initial public offering price.     

<PAGE>   1

                                                                      EXHIBIT 21


                 SUBSIDIARIES OF BRIGHAM EXPLORATION COMPANY



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

Brigham, Inc., a Texas corporation

Quest Resources, L.L.C., a Texas limited liability company









<PAGE>   1
 
                                                                    EXHIBIT 23.2
 
                       CONSENT OF INDEPENDENT ACCOUNTANTS
 
   
     We hereby consent to the use in the Prospectus constituting part of this
Registration Statement on Form S-1 of our report dated February 26, 1997, except
as to Notes 1 and 4 which are as of February 27, 1997, relating to the financial
statements of Brigham Oil & Gas, L.P., which appears in such Prospectus.
Additionally, we hereby consent to the use in the Prospectus constituting part
of this Registration Statement on Form S-1 of our report dated February 26,
1997, except as to Notes 1 and 3 which are as of February 27, 1997, relating to
the Balance Sheet of Brigham Exploration Company, which appears in such
Prospectus. We also consent to the reference to us under the heading "Experts"
in such Prospectus.
    
 
PRICE WATERHOUSE LLP
 
Houston, Texas
   
April 21, 1997
    

<PAGE>   1
 
                                                                    EXHIBIT 23.3
 
   
                                 April 21, 1997
    
Brigham Exploration Company
5949 Sherry Lane, Suite 1616
Dallas, Texas 75225
 
Gentlemen:
 
     In connection with the offering of shares of common stock, par value $.01
per share ("Common Stock"), of Brigham Exploration Company (the "Corporation"),
we delivered a letter dated February 14, 1997 to Brigham Oil & Gas, L.P. (the
"Partnership") with respect to an estimate of the reserves, future production
and income attributable to certain interests of the Partnership, as of December
31, 1996.
 
   
     We understand that you intend that our letter be included in a Registration
Statement on Form S-1 and any amendments thereto, as well as a Prospectus to be
provided to potential purchasers of Common Stock, and we hereby consent to such
use. We also consent to the references in the Registration Statement on Form S-1
(and any amendments thereto) or Prospectus to our firm and to the information
provided therein.
    
 
                                            Very truly yours,
                                            Cawley, Gillespie & Associates, Inc.
 
                                                    /s/ AARON CAWLEY
                                            ------------------------------------
                                                     Aaron Cawley, P.E.
                                                  Executive Vice President


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