EXHIBIT 10.5.1

                                 March 20, 2000

Via Facsimile and Regular Mail
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Mr. Harold D. Carter
5949 Sherry Lane, Suite 620
Dallas, Texas 75225
Phone (214) 692-7785
Fax (214) 692-7820

         Re:      Amendment to Consulting Agreement by and between
                  Harold D. Carter ("Consultant") and
                  Brigham Oil & Gas, L.P. (the "Company")

Dear Harold:

         This  letter  agreement  shall set forth the  agreement  by and between
Consultant and the Company to amend the above referenced  Consulting  Agreement,
effective as of January 1, 2000, as follows:

(1)  Section 3 of the Consulting Agreement is hereby deleted in its entirety and
     replaced with the following Section 3:

          3.  Compensation.  The Company shall pay  Consultant  for his services
     under this  Agreement a consulting  fee of $2,500 per month during the term
     of this Agreement.  All federal withholding and other employment and income
     related taxes shall be the responsibility of Consultant.

(2) Section 6 of the Consulting  Agreement is hereby deleted in its entirety and
replaced with the following Section 6:

          6. Term. The term of this Agreement  shall commence on the date hereof
     and terminate on December 31, 2000.

     All of the other terms and  provisions of the  Consulting  Agreement  shall
continue in force and effect.

     If  this  letter   amendment   correctly   reflects   your   agreement  and
understanding,  we ask that you  execute  the  duplicate  originals  of same and
return one of the duplicate originals to us for our records.

                                      Sincerely,
                                      BRIGHAM OIL & GAS, L.P.
                                      By Brigham, Inc.
                                      Its Managing General Partner

                                      /s/ David T. Brigham
                                      David T. Brigham
                                      Vice President

AGREED AND ACCEPTED:


/s/ Harold D. Carter
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HAROLD D. CARTER