EXHIBIT 32.1

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, I. Jon Brumley, Chief Executive Officer of Encore Acquisition Company (the “Company”), in connection with the filing of the Company’s Annual Report of Company on Form 10-K with the Securities and Exchange Commission on the date hereof (the “Report”), for the period ending December 31, 2003, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, certify that:

     (1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

     (2) The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

/s/ I. Jon Brumley

I. Jon Brumley
Chief Executive Officer
March 11, 2004