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                                                                       EXHIBIT H

                               ANCILLARY AGREEMENT

                                    RECITALS:

         A. Reference is made to that certain Amended and Restated Credit
Agreement (the "Senior Credit Agreement") dated as of February 17, 2000, among
Brigham Oil & Gas, L.P. ("Borrower"), Bank of Montreal, a Canadian bank, in its
individual capacity (in its individual capacity, "BMO"), and BMO, in its
capacity as agent (in such capacity, together with its successors in such
capacity, the "Senior Agent"), Societe Generale, Southwest Agency ("Soc-Gen")
and Shell Capital Inc. ("SCI"); all capitalized terms used but not defined
herein shall have the meanings assigned to them in the Senior Credit Agreement
or in the Equity Conversion Agreement, as such term is defined in the Senior
Credit Agreement.

         B. Borrower and SCI have reached an understanding concerning the
reduction of a portion of the Loans made by the SCI Lenders under the Senior
Credit Agreement, and desire to evidence such understanding by entering into
this Ancillary Agreement.

                                   AGREEMENT:

         1. In the event Borrower does not reduce the outstanding Loans of the
SCI Lenders under the Senior Credit Agreement by at least $15,000,000 on or
before January 31, 2001, Borrower shall permanently forfeit its right to force
conversion of the Tranche One Convertible Amount at $3.90 per share.

         2. Until such time as the Borrower reduces the outstanding Loans of the
SCI Lenders under the Senior Credit Agreement by $15,000,000 the Borrower shall
not have the right to force a conversion of the Tranche One Convertible Amount
pursuant to Section 2.02(a) of the Equity Conversion Agreement.

         3. The Borrower does not have the right to force conversion on any
tranche pursuant to Sections 2.02(a), (b) and (c) of the Equity Conversion
Agreement ("Tranche") prior to the release of first quarter 2001 financial
information unless the Guarantor's EBITDA to Interest as of December 31, 2000 is
at least .9:1.0 and it does not have the right to force conversion on any
Tranche after the release of the first quarter 2001 ratios and prior to the
release of second quarter 2001 financial information unless the Guarantor's
EBITDA to Interest as of the first quarter 2001 is at least 1.1:1.0.

                                 MISCELLANEOUS:

(a) Counterparts: This Ancillary Agreement is being executed in several
counterparts, all of which are identical; all such counter parts shall be
construed together as the same instrument.

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(b) CHOICE OF LAW: THIS ANCILLARY AGREEMENT SHALL, WITHOUT REGARD TO PRINCIPLES
OF CONFLICTS OF LAW, BE GOVERNED AND CONSTRUED UNDER AND IN ACCORDANCE WITH THE
LAWS OF THE STATE OF TEXAS.

(c) Entirety and Modification. This Ancillary Agreement constitutes the entire
agreement between the parties hereto with respect to the subject matter hereof
and supercedes any and all prior agreements and understandings, whether oral or
written, between the parties hereto relating to such subject matter.

         This Ancillary Agreement is executed and delivered on this 31st day of
October, 2000.


                                        SHELL CAPITAL INC.
                                        By: /s/ ROBERT L. ROBERTS
                                           -------------------------------------
                                        Name:  Robert L. Roberts
                                        Title: Vice President


                                        BRIGHAM OIL & GAS, L.P.

                                        By:    Brigham, Inc., as General Partner

                                        By: /s/ CURTIS F. HARRELL
                                           -------------------------------------
                                        Name:  Curtis F. Harrell
                                        Title: Chief Financial Officer