Exhibit 32.1

Section 1350 Certification

     In connection with the Quarterly Report of Encore Acquisition Company (“EAC”) on Form 10-Q for the period ended June 30, 2008 as filed with the Securities and Exchange Commission (the “SEC”) on the date hereof (the “Report”), I, Jon S. Brumley, Chief Executive Officer of EAC, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 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 results of operations of EAC.

Date: August 8, 2008	/s/ Jon S. Brumley
	Jon S. Brumley
	Chief Executive Officer and President

     A signed original of this written statement required by Section 906 has been provided to EAC and will be retained by EAC and furnished to the SEC or its staff upon request.

Note:      The certification of the registrant furnished in this exhibit is not deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended, or otherwise subject to the liabilities of that Section. Registration statements or other documents filed with the SEC shall not incorporate this exhibit by reference, except as otherwise expressly stated in such filing.