Letter Agreement

EXHIBIT 10.4

AMENDMENT TO CONSULTING AGREEMENT

      Brigham Oil & Gas, L.P. (the “Company”) and Harold D. Carter (“Consultant”) hereby amend that certain Consulting Agreement dated May 1, 1997, as previously amended, by and between the Company and Consultant (the “Consulting Agreement”), as follows:

      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 shall continue until terminated by either party by giving notice of such termination to the other party hereto.

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

      In witness whereof the Company and Consultant have signed this Amendment below to evidence their acceptance and agreement to the terms contained herein.