BRIGHAM EXPLORATION CO
SC 13D/A, EX-99.G, 2000-11-06
CRUDE PETROLEUM & NATURAL GAS
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                                                                       EXHIBIT G


                               FIRST AMENDMENT TO
                          REGISTRATION RIGHTS AGREEMENT

     This First Amendment (the "Amendment") to the Registration Rights Agreement
dated as of February 17, 2000 (the "Registration Rights Agreement"), by and
between Brigham Exploration Company, a Delaware corporation (the "Company"), and
Shell Capital Inc. (the "Purchaser"), is effective as of October 31, 2000.
Capitalized terms used but not defined herein shall have the meanings assigned
to such terms in the Registration Rights Agreement.

                                    RECITALS

     WHEREAS, the Company and the Purchaser desire to amend the Registration
Rights Agreement in the manner set forth in this Amendment.

     NOW, THEREFORE, the parties hereto, intending legally to be bound, hereby
agree as follows:

                                   AGREEMENTS

     1. The second recitals paragraph of the Registration Rights Agreement shall
be amended and restated in its entirety to read as follows:

     "WHEREAS, the Company has agreed to issue certain capital stock of the
Company ("Common Stock") in connection with the exercise of certain equity
conversion rights pursuant to that certain Equity Conversion Agreement of even
date herewith among the Company, Purchaser and BOG (the "Equity Conversion
Agreement") and in connection with Warrants issued pursuant to those certain
Warrant Agreements dated as of February 17, 2000 and October 31, 2000, in each
case between the Company and the Purchaser (the "Warrants")."

     2. As amended hereby, the Registration Rights Agreement is hereby
specifically ratified and reaffirmed.

     IN WITNESS WHEREOF, the parties hereto have executed this Amendment
effective for all purposes as of October 31, 2000.

                                       BRIGHAM EXPLORATION COMPANY

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

                                       SHELL CAPITAL INC.

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


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