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                                                                   EXHIBIT 10.12

                            CONVEYANCE OF ADJUSTABLE
                        TERM OVERRIDING ROYALTY INTEREST

         This Conveyance of Adjustable Term Overriding Royalty Interest (this
"Conveyance"), is by and between Brigham Oil & Gas, L.P., a Delaware limited
partnership (the "Grantor"), and ECT Merchant Investments Corp., a Delaware
corporation ("ECT Merchant") and Joint Energy Development Investments II
Limited Partnership, a Delaware limited partnership ("JEDI-II and, together
with ECT Merchant, the "Grantee").

                                   RECITALS:

         1. Brigham Exploration Company ("Brigham Parent") and Chase Bank of
Texas, National Association, as Trustee, have entered into an Indenture dated
as of August 20, 1998, as amended by a First Amendment to Indenture dated as of
March 26, 1999, and a Second Amendment to Indenture dated as of even date
herewith (as amended, the "Indenture"), pursuant to which Brigham Parent issued
certain Notes (as defined in the Indenture).

         2. In accordance with the terms of the Indenture, Brigham Parent
agreed to convey, and to cause its Subsidiaries to convey, to the Noteholders
(as defined in the Indenture), Term ORRI's (as defined below), as an absolute
assignment, and not as collateral, such conveyance to be made pursuant to one
or more Term ORRI Conveyances (as defined in the Indenture).

         3. This Conveyance constitutes one of the Term ORRI Conveyances
contemplated by the Indenture.

                                   ARTICLE I.

                                 DEFINED TERMS

         Section 1. Defined Terms and References. Reference is hereby made to
the Indenture for all purposes. Unless otherwise defined herein, all
capitalized terms used herein shall have the meaning attributed to such term in
the Indenture. In addition, as used in this Conveyance, the following
capitalized terms shall have the following meanings:

         "Accrued PIK Amount" means, as of any particular day, the aggregate
dollar amount of all accrued interest on the Notes, that has been paid in kind
(and not in cash) as of such day in accordance with the Indenture.

         "Applicable Percentage" shall mean, with respect to any Subject
Reserves, Grantor's actual net revenue interest (expressed as a percentage) in
the production of oil, gas and/or other minerals in, under and/or that may be
produced from any Subject Reserves, (including without limitation any
net revenue interest attributable to an overriding royalty interest or acquired
by virtue of a third party



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nonconsent election in any drilling, completion or other operation), subject to
the agreements and other matters set out in Exhibit B hereto, and the rights
afforded third parties (which are not affiliates or Subsidiaries of Brigham
Parent) thereunder.

         "Brigham Parent" is defined in the Recitals.

         "Effective Date" shall mean 7:00 a.m. local time on February 17, 2000.

         "Hydrocarbon Interests" means all rights, titles and estates of
Grantor in and to the oil and gas leases, oil, gas and mineral leases, or other
liquid or gaseous hydrocarbon leases, mineral fee interests, overriding royalty
and royalty interests, net profit interests and production payment interests
identified on Exhibit A attached hereto or otherwise owned by Grantor,
including any reserved or residual interest of whatever nature.

         "Indenture" is defined in the Recitals.

         "Marketing Terms and Conditions" shall have the meaning assigned to it
in Section 4.1.

         "Non-Proved Reserves" means any category of oil and gas reserves other
than Proved Reserves.

         "ORRI Hydrocarbons" shall have the meaning assigned to it in Section
4.1.

         "ORRI Percentage" shall be defined as follows:

                  (a)      Until the occurrence of the Recalculation Event, the
                           ORRI Percentage shall be four percent (4%).

                  (b)      Under circumstances more particularly described in
                           Section 2.3, effective from and after the occurrence
                           of the Recalculation Event, the ORRI Percentage
                           shall be adjusted downward to three percent (3%).

         "ORRI Term" means the period from the Effective Date to a date that is
the earliest to occur of (a) the date on which there is a payment in full of
the Accrued PIK Amount and all other Obligations under the Indenture or (b) the
date on or after November 21, 2000, on which there is a payment in full of the
Accrued PIK Amount.

         "Overproduced Position" shall mean a position that arises as a result
of a party (and/or its predecessors in title) taking more production from a
property than its ownership interest in such property would, but for a gas
balancing or similar agreement, entitle it to take.

         "Permissible Charges" shall mean (i) all production, severance, ad
valorem or similar taxes assessed against or measured by production and
severance of ORRI Hydrocarbons or the value and (ii) with respect to each well
not operated by the Grantor or any Affiliate thereof, the Term ORRI's allocable
share of any reasonable post production expenses, costs, charges, and fees
incurred in



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transporting, processing, gathering, treating, separating, dehydrating and
marketing the Subject Reserves allocable to such well.

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

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

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

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

         "Recalculation Event" shall have the meaning assigned to it in Section
2.3.

         "Subject Reserves" means (a) any PDP Reserves and PDNP Reserves
identified by Grantor or Brigham Parent (or any Subsidiary thereof) as of the
date hereof as being produced or producible in paying quantities out of wells
now located on the Hydrocarbon Interests as of the date hereof including those
listed on the attached Exhibit A or (b) any PDP Reserves and PDNP Reserves
identified by Grantor or Brigham Parent (or any Subsidiary thereof) following
the date hereof and on or before December 31, 2000, as being produced or
producible in paying quantities out of any well spudded or acquired by Grantor
or Brigham Parent (or any Subsidiary thereof) on or before December 31, 2000,
(c) in the event only that Brigham Parent's Consolidated Interest Coverage
Ratio calculated as of September 30, 2000 (in accordance with the Indenture),
is less than 1.1 to 1.0, any PDP Reserves and PDNP Reserves identified by
Grantor or Brigham Parent (or any Subsidiary thereof) following December 31,
2000 and on or before December 31, 2001, as being produced or producible in
paying quantities out of any well spudded or acquired after December 31, 2000
but on or before December 31, 2001, and (d) in the cases of (a), (b) and (c),
above, a sufficient interest in the Hydrocarbon Interests to afford Grantor or
the Brigham Parent as applicable the right, prior to giving effect hereto or to
any Term ORRI Conveyance, to secure the maximum authorized share of production
that is allocable to PDP Reserves and, when applicable, PDNP Reserves found in
each Subject Well. Under no circumstances, and notwithstanding any provision
hereof to the contrary, shall the term "Subject Reserves" include (1) any PUD
Reserves or any Non-Proved Reserves or (2) any PDP Reserves and/or PDNP
Reserves beneficially or legally owned (whether in a vested or contingent
manner) by a third party (which is not an Affiliate of the Brigham Parent)
under or pursuant to any agreement or other matter disclosed in Exhibit B
hereto, or (3) any PDP Reserves or PDNP Reserves identified by Brigham Parent
or Grantor as a result of the deepening or sidetracking of a Subject Well after
December 31, 2000 (in the event item (c) of the definition of Subject Reserves
is not triggered) and after December 31, 2001, (in the event item (c) of the
definition of Subject Reserves is triggered). Under no circumstances shall the
term "Subject Reserves" include reserves that are not either producing or
capable of producing (or being made in



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the case of PDNP Reserves to produce or capable of producing) in "paying
quantities," as such term is defined under the Texas common law (regardless of
the jurisdiction in which the subject Oil and Gas Properties are located).

         "Term ORRI" shall have the meaning assigned to it in Section 2.1.

         "Underproduced Position" shall mean a position that arises as a result
of a party (and/or its predecessors in title) taking less production from a
property than its ownership interest in such property would, but for a gas
balancing or similar agreement, entitle it to take.

                                  ARTICLE II.

                              GRANTING PROVISIONS

         Section  2.1      Granting Clause. For a good and valuable
                           consideration, the receipt and sufficiency of which
                           is hereby acknowledged, Grantor does hereby GRANT,
                           BARGAIN, SELL, TRANSFER, ASSIGN, CONVEY, WARRANT and
                           DELIVER, for and during the ORRI Term only, to each
                           Grantee according to their Participations, an
                           overriding royalty interest (collectively, the "Term
                           ORRI") equal to the ORRI Percentage of the
                           Applicable Percentage of each of the Subject
                           Reserves.

         Section  2.2      Adjustment of the Term ORRI; Further Assurances.
                           Upon the occurrence of the Recalculation Event,
                           Grantor and Grantee agree, at Grantor's expense, to
                           execute (or cause to be executed) any such
                           instruments as may be necessary or appropriate in
                           order to evidence of record in the appropriate
                           filing jurisdictions that the ORRI Percentage has
                           been adjusted.

         Section 2.3       Adjustment of ORRI Percentage. The ORRI Percentage
                           shall be automatically decreased from four (4%) to
                           three (3%) on the first to occur of the following
                           (the "Recalculation Event"):

               (a)  Brigham Parent sells common or preferred equity securities
                    of Brigham Parent resulting in net proceeds received by
                    Brigham Parent (after deducting all costs and expenses
                    incurred in such sale) of at least $10,000,000;

               (b)  Grantor and/or Brigham Parent acquires, in exchange for
                    common or preferred equity securities of Brigham Parent,
                    Oil and Gas Properties containing PDP Reserves and/or PDNP
                    Reserves with a net present value, discounted at 10% per
                    annum, of at least $10,000,000 (in Grantees' reasonable
                    judgement); or



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               (c)  through a combination of (a) and (b) above, Brigham Parent
                    and/or Grantor receives net proceeds and newly acquired Oil
                    and Gas Properties, which (as valued above), total at least
                    $10,000,000 in net present value;

provided that, on or before August 31, 2000, the Recalculation Event shall have
closed and (a) Brigham Parent shall have received the $10,000,000 of cash
and/or properties as provided above, and (b) either the Chief Financial Officer
or President of Brigham Parent shall have delivered a certificate to Grantor to
that effect.

         Section 2.4       Term. The Term ORRI shall automatically terminate at
                           the end of the ORRI Term. Upon such event, Grantee
                           shall execute such instruments as Grantor shall
                           reasonably request to evidence such termination,
                           and/or reassigning such Term ORRI, free and clear of
                           all liens, encumbrances and other burdens created
                           by, through or under Grantee.

         Section 2.5       Permissible Charges. The Term ORRI shall be free of
                           any expense for exploration, drilling, development,
                           operating, marketing and other costs incident to the
                           production and sale of oil and gas other than
                           Permissible Charges. Notwithstanding any provision
                           hereof to the contrary, the Term ORRI shall not
                           apply to (a) any oil, gas and/or other minerals as
                           are (i) unavoidably lost in operations on or
                           relating to the Subject Reserves or in marketing of
                           oil, gas and/or other minerals from or attributable
                           to the Subject Reserves, or (ii) consumed or
                           utilized (e.g., as part of a re-injection program)
                           in prudent operations conducted on the Subject
                           Reserves with a reasonable expectation of increasing
                           ultimate recovery of oil, gas and/or other minerals
                           from the Subject Reserves; provided that, to the
                           extent any oil, gas and/or other minerals utilized
                           in operations conducted on the Subject Reserves are
                           subsequently re-produced, the Term ORRI shall apply
                           to such re-produced volumes.

         Section 2.6       Pooling Issues. Prior to the date hereof, certain of
                           the Hydrocarbon Interests may have been pooled or
                           unitized for the production of oil, gas and/or
                           minerals and without the joinder of Grantee with
                           respect to the Term ORRI, Grantor shall, from and
                           after the date hereof, have the right and power to
                           unitize, communitize or pool any portion or portions
                           of the Term ORRI. If pursuant to any law, rule,
                           regulation or order of any governmental body or
                           official, any portion of the Hydrocarbon Interests
                           is automatically or involuntarily pooled,
                           communitized or unitized in any manner, the Term
                           ORRI, insofar as it affects such Hydrocarbon
                           Interests, shall also be pooled, communitized and
                           unitized. With respect to each existing pool or
                           unit, and with respect to each pool or unit in which
                           the Term ORRI is hereafter included in accordance
                           with the


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                           foregoing, the Term ORRI in each portion of the
                           Hydrocarbon Interests included in such pool or unit
                           shall apply to the portion of production from such
                           pool or unit which is attributable to such portion
                           of the Hydrocarbon Interests under and by virtue of
                           the applicable pooling, communitization and
                           unitization agreements, designations and/or orders.
                           Nothing in this Section 2.6 shall be construed to
                           afford Grantee rights in PDP Reserves or PDNP
                           Reserves identified in wells that are not now
                           located on the Hydrocarbon Interests.


         Section 2.7       Renewals and Extensions. The Term ORRI shall apply
                           to all renewals and extensions of any oil, gas
                           and/or mineral lease, deed or any other interest
                           included, in part or in whole, in the Subject
                           Reserves.

         Section 2.8       Gas Imbalances. It is hereby recognized that certain
                           of the Subject Reserves are or may be subject to
                           Underproduced Positions. It is hereby further
                           recognized and stipulated that the Term ORRI does
                           and shall apply to the volumes of oil, gas or other
                           hydrocarbons taken by Grantor in reducing or making
                           up an Underproduced Position (which volumes and any
                           make-up rights relating thereto shall for all
                           purposes hereof be included within the Subject
                           Reserves), whether the subject Underproduced
                           Position arose before, or arises after, the
                           Effective Date hereof.

         Section 2.9       Fee, Royalty and Similar Interests. It is hereby
                           recognized that certain of the Hydrocarbon Interests
                           may constitute or include (a) unleased mineral fee
                           interests and unleased mineral rights or servitudes
                           (the "Unleased Mineral Interests"), (b) mineral fee
                           interests and mineral rights or servitudes that are
                           owned by Grantor but subject to an existing oil, gas
                           and/or mineral lease or similar agreement in favor
                           of a third party or parties, which oil, gas and/or
                           mineral lease or similar agreement entitles Grantor
                           to be paid a royalty, either in kind or in money
                           (the "Leased Mineral Interests"), and (c) perpetual
                           or term royalty or overriding royalty interests
                           carved out of and burdening a mineral fee, right,
                           servitude or lease owned by a third party or third
                           parties (the "Royalty Interests") (the Unleased
                           Mineral Interests, the Leased Mineral Interests and
                           the Royalty Interests are herein collectively called
                           the "Non-Working Interest Properties"). It is hereby
                           recognized and stipulated that the Term ORRI is
                           payable out of and shall burden the Non-Working
                           Interest Properties, to the extent they constitute
                           Subject Reserves, just as it is payable out of and
                           burdens the balance of the Hydrocarbon Interests. By
                           way of example (and not by way of limitation):



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                  (i)      If Grantor owns an Unleased Mineral Interest that
                           constitutes a 50% undivided mineral fee interest in
                           a particular tract of land, the Term ORRI payable
                           relative to such tract of land would, until the
                           occurrence of the Recalculation Event, be equal to
                           and measured by an undivided 4% of 50% of the oil,
                           gas and/or other minerals in, under and/or that may
                           be produced from the subject tract of land;

                  (ii)     If Grantor owns a Leased Mineral Interest that
                           constitutes an undivided 50% mineral fee interest in
                           a particular tract of land that is subject to a
                           lease entitling Grantor to a 20% royalty interest,
                           proportionately reduced, the Term ORRI payable
                           relative to such tract of land would, until the
                           occurrence of the Recalculation Event, be equal to
                           and measured by an undivided 4% of 10% of the oil,
                           gas and/or other minerals in, under and/or that may
                           be produced from the subject tract of land; and

                  (iii)    If Grantor owns a Royalty Interest that constitutes
                           a 1/32nd nonparticipating royalty interest in a
                           particular tract of land, the Term ORRI payable
                           relative to such tract of land would, until the
                           occurrence of the Recalculation Event, be equal to
                           and measured by an undivided 4% of 1/32nd of the
                           oil, gas and/or other minerals in, under and/or that
                           may be produced from the subject tract of land.

         Section 2.10      Habendum Clause and Subrogation. TO HAVE AND TO HOLD
                           the Term ORRI unto Grantee, its successors and
                           assigns, during the ORRI Term. This Conveyance is
                           made with full substitution and subrogation of
                           Grantee in and to all covenants and warranties by
                           others heretofore given or made.

                                  ARTICLE III.

                           ASSIGNMENTS AND TRANSFERS

         Section 3.1       Assignment and Transfer by Grantee. Subject to
                           Section 7.12(e) of the Indenture, nothing herein
                           contained shall in any way limit or restrict the
                           right of Grantee to sell, convey, assign, mortgage
                           or otherwise dispose of the Term ORRI (including its
                           rights, titles, interests, estates, remedies, powers
                           and privileges appurtenant or incident to the Term
                           ORRI under this Conveyance), in whole or in part.

         Section 3.2       Assignment and Transfer by Grantor.


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         (A) In the event any of the Subject Reserves are sold, farmed out or
otherwise transferred by the Grantor in a bona fide transaction with a
third-party that is not an Affiliate of Grantor, the Term ORRI conveyed herein
in the Subject Reserves so sold, farmed out or otherwise transferred shall
automatically terminate and merge into the interest so sold, farmed-out or
otherwise transferred upon the final closing of such transaction; provided that
the Grantor pays or otherwise affords to Grantee, in accordance with their
Participations, (a) the ORRI Percentage of all net cash proceeds or other
consideration received (or credited) to Grantor as a result of such
transaction, to the extent only such net cash proceeds are allocable to the
Subject Reserves out of which the subject Term ORRI is carved and (b) the ORRI
Percentage of the Applicable Percentage secured by (in a contemporaneous
exchange of properties) or reserved to (e.g., in the form of an override or
back-in) Grantor as a result of such transaction, to the extent only the
properties exchanged or the interests reserved are allocable to the Subject
Reserves out of which the subject Term ORRI is carved. Where requested by the
purchaser, farmee, exchange counterparty or transferee, Grantee shall join in
any instrument of sale, farm-out, exchange or transfer.

         (B) In the event any of the Hydrocarbon Interests not constituting
Subject Reserves at the time of sale, farm-out or other transfer (the
"NonSubject Reserves") are sold, farmed out, or otherwise transferred by the
Grantor in a bona fide transaction with a third party that is not an affiliate
of Grantor, the Term ORRI conveyed herein in the NonSubject Reserves so sold,
farmed-out or otherwise transferred shall automatically terminate and merge
into the interest so sold, farmed-out or otherwise transferred upon the final
closing of such transaction; and the Grantee shall not be entitled to any of
the cash proceeds or other consideration received by Grantor on account of the
sale, farm-out or other transfer (either as an Applied Payment or otherwise).
When requested by the purchaser, farmee or transferee on NonSubject Reserves,
Grantee shall join in any instrument of sale, farm-out exchange or transfer.


                                  ARTICLE IV.

          MARKETING OF ORRI HYDROCARBONS AND DISTRIBUTION OF PROCEEDS

         Section 4.1       Nature of Marketing Arrangements. Grantor shall have
                           the obligation to market, or cause to be marketed,
                           the oil, gas and other minerals attributable to the
                           Term ORRI (the "ORRI Hydrocarbons") on behalf of and
                           for the account of Grantee in arm's-length
                           transactions with purchasers who are not Affiliates,
                           on the same terms upon which Grantor markets its own
                           Subject Reserves from the same Subject Well. Grantor
                           shall have no express or implied obligation to sell
                           or otherwise to market or render marketable or more
                           valuable the ORRI Hydrocarbons on any terms better
                           or otherwise different than those pursuant to which
                           it sells, markets or renders marketable or more
                           valuable its own Subject Reserves from the same
                           Subject Well. As to any third parties, all acts of
                           Grantor in marketing the ORRI Hydrocarbons and all
                           sales or other marketing agreements executed by
                           Grantor in accordance herewith shall be binding on
                           Grantee and the Term ORRI; it being understood that
                           the right and obligation to



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                           market the ORRI Hydrocarbons is at all times vested
                           in Grantor, and Grantee does not have any such right
                           or obligation or any possessory interest in all or
                           part of the ORRI Hydrocarbons. Accordingly, it shall
                           not be necessary for Grantee to join in any
                           production sales or marketing agreements or any
                           amendments to existing production sales or marketing
                           agreements.

         Section 4.2       Distribution of Funds. Until notified by Grantee to
                           the contrary, Grantor shall receive all payments for
                           (or on account of) ORRI Hydrocarbons and shall, on
                           or before the last day of each calendar month,
                           distribute any such payments received during the
                           previous calendar month, net only of Permissible
                           Charges, to Agent, on behalf of and for further
                           distribution to Grantee, by wire transfer to such
                           account(s) or location(s) as Agent may direct from
                           time to time in writing. Any monies received by
                           Agent for or on account of ORRI Hydrocarbons shall
                           constitute trust funds in Agent's hands. Except as
                           provided otherwise in the Indenture, Grantee shall
                           have the right at all times, upon thirty (30) days'
                           written notice sent to Grantor, to begin receiving
                           payment for (or on account of) all ORRI Hydrocarbons
                           directly from the purchasers thereof or from any
                           other parties obligated to make payment therefor. In
                           the event Grantee exercises its right to receive
                           payment for (or on account of) ORRI Hydrocarbons
                           directly, Grantor shall immediately cause to be
                           prepared and executed such division orders, transfer
                           orders, or instructions in lieu thereof, as Grantee
                           (or any third party) may reasonably require from
                           time to time to cause payments to be made directly
                           to Grantee; in the event that, for any reason,
                           Grantee cannot (or does not) receive such payments
                           directly, the same shall be collected by Grantor and
                           shall constitute trust funds in Grantor's hands, to
                           be immediately paid over to Grantee by wire transfer
                           to such account or location as Grantee may direct
                           from time to time in writing (or by such other form
                           of transfer reasonably specified by Grantee).

         Section 4.3       Notification to Production Purchasers. ANY AND ALL
                           PURCHASERS OF ORRI HYDROCARBONS SHALL HAVE THE RIGHT
                           TO ASSUME THAT THE TERM ORRI IS STILL VALID AND
                           EXISTING - CALCULATED UTILIZING AN ORRI PERCENTAGE
                           OF 4% UNTIL THE OCCURRENCE OF THE RECALCULATION
                           EVENT - UNTIL SUCH TIME AS SUCH PURCHASER IS
                           NOTIFIED IN WRITING BY GRANTEE TO BEGIN MAKING
                           PAYMENTS ON SOME OTHER BASIS. UNTIL RECEIVING SUCH
                           WRITTEN NOTIFICATION, ALL PURCHASERS OF PRODUCTION
                           SHALL CONTINUE MAKING PAYMENTS IN ACCORDANCE WITH
                           THE FOREGOING ASSUMPTIONS (AND OTHERWISE IN
                           ACCORDANCE WITH




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                           THE DIRECTIVES SET OUT IN SECTION 4.2 HEREOF), AND
                           SHALL NOT PLACE THE FUNDS IN SUSPENSE.

         Section 4.4       Ad Valorem and Severance Taxes. For so long as
                           Grantor is receiving payments and making
                           distributions on account of ORRI Hydrocarbons to
                           Grantee under Section 4.2 hereof, Grantor shall, as
                           an administrative convenience to Grantee and to the
                           extent only that funds are on hand on account of
                           sales of ORRI Hydrocarbons, timely pay and discharge
                           (a) all ad valorem taxes assessed against the
                           Subject Reserves (or the Hydrocarbon Interests
                           directly allocable thereto, including the Term ORRI)
                           or any part thereof, and (b) all production,
                           severance, excise and other taxes assessed against,
                           or measured by, the ORRI Hydrocarbons or the value,
                           or proceeds, of the ORRI Hydrocarbons (the "Taxes").
                           Grantor shall have the right to net Taxes payable
                           under this and any other Term ORRI Conveyance on
                           account of the Term ORRI and the ORRI Hydrocarbons
                           hereunder and thereunder against amounts otherwise
                           distributable on account of the sale of ORRI
                           Hydrocarbons under this and any other Term ORRI
                           Conveyance. Nothing contained in this Section 4.4
                           shall, however, create a personal obligation on the
                           part of Grantor to pay any Taxes on behalf of
                           Grantee to the extent amounts in the possession of
                           Grantee on account of the ORRI Hydrocarbons are
                           insufficient to cover the payment of Taxes on
                           account of the Term ORRI and/or the ORRI
                           Hydrocarbons. Without limitation of the generality
                           of the foregoing, in the event that, in Grantor's
                           reasonable discretion, distributions owing to
                           Grantee will be insufficient to fully cover any ad
                           valorem or similar Taxes allocable to the Term ORRI,
                           Grantee agrees to pay the difference to the
                           appropriate taxing authority within twenty (20) days
                           after receipt from Grantor of the applicable ad
                           valorem or similar Tax assessment. Grantor shall
                           have the right to offset against any distributions
                           owing or to become owing to Grantee the full amount
                           of any Taxes so paid on behalf of Grantee. In the
                           event Grantee elects pursuant to Section 4.2 hereof
                           to receive payment on account of ORRI Hydrocarbons
                           directly, it shall be responsible to pay all Taxes
                           allocable to the Term ORRI directly, for its own
                           account.


                                   ARTICLE V.

                              COVENANTS OF GRANTOR

         Grantor hereby covenants for the benefit of Grantee that Neither
Brigham Parent or Grantor, will allow any Subsidiary to transfer any assets to
Quest Resources LLC or Venture Acquisitions, L.P.



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                                  ARTICLE VI.

                            MISCELLANEOUS PROVISIONS

         Section 6.1       Further Assurances. Grantor agrees to execute and
                           deliver to Grantee, and, to the extent it is
                           reasonably within Grantor's power to do so, to cause
                           any third parties to execute and deliver to Grantee,
                           all such other and additional instruments and to do
                           all such further acts and things as may be necessary
                           or appropriate to more fully vest in and assure to
                           Grantee all of the rights, titles, interests,
                           remedies, powers and privileges herein granted or
                           intended so to be, Grantee agrees to execute and
                           deliver to Grantor all such other and additional
                           instruments and to do all such further acts and
                           things as may be necessary or appropriate to more
                           fully vest in and assure to Grantor all of the
                           rights, titles, interests, remedies, powers and
                           privileges herein granted or intended so to be.

         Section 6.2       Termination. Upon Grantor's request, Grantee will
                           confirm to Grantor in writing reasonably acceptable
                           to Grantor the occurrence of the Recalculation Event
                           and the termination of the Term ORRI (as to all or
                           any one or more Hydrocarbon Interests).

         Section 6.3       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 other obligation hereunder.

         Section 6.4       Applicable Law. THIS CONVEYANCE AND THE RIGHTS AND
                           OBLIGATIONS OF THE PARTIES HEREUNDER SHALL, WITHOUT
                           REGARD TO PRINCIPLES OF CONFLICTS OF LAWS, BE
                           GOVERNED BY AND INTERPRETED, CONSTRUED AND ENFORCED
                           IN ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS,
                           EXCEPT TO THE EXTENT THE LAWS OF ANY STATE IN WHICH
                           ANY PART OF THE HYDROCARBON INTERESTS IS LOCATED
                           NECESSARILY, GOVERNS WITH RESPECT TO SUCH PART OF
                           THE HYDROCARBON INTERESTS LOCATED IN SUCH STATE.


                                     -11-


<PAGE>   12




         Section 6.5       Severability. Every provision in this Conveyance is
                           intended to be severable. If any term or provision
                           hereof is determined to be invalid, illegal or
                           unenforceable for any reason whatsoever, such
                           invalidity, illegality or unenforceability shall not
                           affect the validity, legality and enforceability of
                           the remainder of this Conveyance.

         Section 6.6       No Personal Liability of Grantee/Indemnities.
                           NOTWITHSTANDING ANYTHING TO THE CONTRARY CONTAINED
                           IN THIS CONVEYANCE, GRANTEE SHALL NEVER PERSONALLY
                           BE RESPONSIBLE FOR PAYMENT OF ANY PART OF THE COSTS,
                           EXPENSES OR LIABILITIES INCURRED IN CONNECTION WITH
                           THE EXPLORING, DEVELOPING, OPERATING, OWNING AND/OR
                           MAINTAINING OF THE HYDROCARBON INTERESTS. GRANTOR
                           AGREES TO INDEMNIFY AND HOLD GRANTEE AND ITS
                           DIRECTORS, OFFICERS, EMPLOYEES, REPRESENTATIVES,
                           AGENTS AND AFFILIATES, HAS FROM AND AGAINST ALL SUCH
                           COSTS, EXPENSES AND LIABILITIES (WITH SUCH INDEMNITY
                           TO ALSO COVER ALL COSTS AND EXPENSES OF GRANTEE,
                           INCLUDING REASONABLE LEGAL FEES AND EXPENSES, WHICH
                           ARE INCURRED INCIDENT TO THE MATTERS INDEMNIFIED
                           AGAINST); PROVIDED, HOWEVER; THAT PERMISSIBLE
                           CHARGES SHALL, TO THE EXTENT THE SAME RELATE TO
                           PERIODS AFTER THE EFFECTIVE DATE, NEVERTHELESS BE
                           CHARGEABLE AGAINST THE TERM ORRI OR OTHERWISE
                           PAYABLE AND/OR BORNE DIRECTLY BY GRANTEE UNDER
                           CIRCUMSTANCES DESCRIBED HEREIN, AS AND TO THE EXTENT
                           HEREIN PERMITTED. EXPRESSLY WITHOUT LIMITATION OF
                           THE GENERALITY OF THE FOREGOING, GRANTOR HEREBY
                           AGREES TO INDEMNIFY AND HOLD GRANTEE AND ITS
                           DIRECTORS, OFFICERS, EMPLOYEES, REPRESENTATIVES,
                           AGENTS AND AFFILIATES, HARMLESS FROM AND AGAINST ALL
                           CLAIMS, DEMANDS, LIABILITIES, LOSSES, DAMAGES, COSTS
                           AND EXPENSES (A) ARISING FROM ANY FAILURE OF GRANTOR
                           TO PERFORM OR COMPLY WITH ANY OF THE PROVISIONS OF
                           THIS CONVEYANCE, (B) ARISING OUT OF THE CONDITION OF
                           THE HYDROCARBON INTERESTS (WHETHER KNOWN OR UNKNOWN,
                           LATENT OR PATENT) ON, BEFORE OR AFTER THE DATE
                           HEREOF, AND/OR (C) ARISING UNDER ANY ENVIRONMENTAL
                           LAWS, WHETHER NOW IN EXISTENCE OR HEREINAFTER



                                     -12-

<PAGE>   13




                           ENACTED. THE INDEMNITIES AND HOLD HARMLESS
                           PROVISIONS CONTAINED IN THIS SECTION 7.6 SHALL APPLY
                           WHETHER OR NOT THE INDEMNIFIED PARTY WAS WHOLLY OR
                           PARTIALLY NEGLIGENT (OTHER THAN GROSSLY NEGLIGENT).

         Section 6.7       Counterparts. This Conveyance is being executed in
                           several counterparts, all of which are identical,
                           except that, to facilitate recordation, in certain
                           counterparts hereof only that portion of Exhibit A
                           which contains specific descriptions of the
                           Hydrocarbon Interests located in the recording
                           jurisdiction in which the counterpart is to be
                           recorded shall be included, and all other portions
                           of Exhibit A shall be included by reference only.
                           All of such counterparts together shall constitute
                           one and the same instrument. Complete copies of this
                           Conveyance, containing the entire Exhibit A, have
                           been retained by Grantor and Grantee.



                                     -13-


<PAGE>   14


         THIS CONVEYANCE IS EXECUTED this 17th day of February, 2000, and made
effective as of the Effective Date.

                                       BRIGHAM OIL & GAS, L.P.

                                       By:  Brigham, Inc. a Nevada corporation,
                                            its General Partner

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


ADDRESS OF GRANTOR:                         ADDRESS OF GRANTEE:
6300 Bridge Point Parkway                   1400 Smith Street
Austin, Texas 78730                         Houston, Texas 77002


This instrument prepared by:
Gray H. Muzzy
Bracewell & Patterson, L.L.P.
711 Louisiana
Houston, Texas 77002
(713) 221-1406

<PAGE>   15

                                 ACKNOWLEDGMENT


STATE OF TEXAS                    )
                                  )
COUNTY OF HARRIS                  )

                                     KANSAS

         The foregoing instrument was acknowledged before me on February 17,
2000, by Karen Lynch, Vice President of Brigham, Inc., a Nevada corporation, as
general partner of Brigham Oil & Gas, L.P., a Delaware limited partnership, on
behalf of the corporation, as general partner of the limited partnership.

                                   LOUISIANA

         This instrument was acknowledged by me on February 17, 2000 by Karen
Lynch, Vice President of Brigham, Inc., a Nevada corporation, as general
partner of Brigham Oil & Gas, L.P., a Delaware limited partnership, on behalf
of the corporation, as general partner of the limited partnership.

                                    MONTANA

         The foregoing instrument was acknowledged before me on February 17,
2000, by Karen Lynch, Vice President of Brigham, Inc., a Nevada corporation, as
general partner of Brigham Oil & Gas, L.P., a Delaware limited partnership, on
behalf of the corporation, as general partner of the limited partnership.

                                   NEW MEXICO

         The foregoing instrument was acknowledged before me on February 17,
2000, by Karen Lynch, Vice President of Brigham, Inc., a Nevada corporation, as
general partner of Brigham Oil & Gas, L.P., a Delaware limited partnership, on
behalf of the corporation, as general partner of the limited partnership.

                                    OKLAHOMA

         Before me, a Notary Public in and for said county and state, on this
17th day of February, 2000, personally appeared Karen Lynch, to me know to be
the identical person who subscribed the name of the maker thereof to the
foregoing instrument as Vice President of BRIGHAM, INC., as general partner of
BRIGHAM OIL & GAS, L.P., a Delaware limited partnership, and acknowledged to me
that she executed the same as her free and voluntary act and deed, and as the
free and voluntary act and deed of such corporation for the uses and purposes
therein set forth.




<PAGE>   16

                                     TEXAS

         This instrument was acknowledged before me on February 17, 2000 by
Karen E. Lynch, Vice President of BRIGHAM, INC., a Nevada corporation, as
general partner of BRIGHAM OIL & GAS, L.P., a Delaware limited partnership, on
behalf of such corporation, as general partner of the limited partnership.


                                       ----------------------------------------
                                       NOTARY PUBLIC IN AND FOR
                                       THE STATE OF TEXAS

                                       Notarial Seal:



<PAGE>   17




                                   EXHIBIT A


            [Describe leases and wells - to be provided by Brigham]






<PAGE>   18

                                   EXHIBIT B

                                  TITLES, ETC.

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

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

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

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

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

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



<PAGE>   19



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