EXHIBIT 10.5.1 March 20, 2000 Via Facsimile and Regular Mail - ------------------------------ 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 - -------------------- HAROLD D. CARTER