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

In connection with the Quarterly Report of Cooper Cameron Corporation (the Company) for the quarter ended September 30, 2003 as filed with the Securities and Exchange Commission on the date hereof (the Report), I, Sheldon R. Erikson, Chairman, President and Chief Executive Officer of the Company, and I, Franklin Myers, Sr. Vice President, Finance and Chief Financial Officer of the Company, 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 the Company.

/s/ Sheldon R. Erikson

Name: Sheldon R. Erikson
Title: Chairman, President & CEO

/s/ Franklin Myers

Name: Franklin Myers
Title: Sr. Vice President, Finance & CFO

October 29, 2003

     A signed original of this written statement required by Section 906, or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Cooper Cameron Corporation and will be retained by Cooper Cameron Corporation and furnished to the Securities and Exchange Commission or its staff upon request.

     Note: The certification the registrant furnishes 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 Securities and Exchange Commission shall not incorporate this exhibit by reference, except as otherwise expressly stated in such filing.