EXHIBIT 32.1

                            CERTIFICATION PURSUANT TO
                    SECTION 1350 OF TITLE 18 OF THE U.S. CODE

I, Terence E. Hall, Chairman of the Board and Chief Executive Officer of
Superior Energy Services, Inc. (the "Company"), certify, pursuant to Section
1350 of Title 18 of the U.S. Code, adopted pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002 ("Section 906"), that:

1.        the annual report on Form 10-K of the Company for the year ended
          December 31, 2004 (the "Report"), as filed with the Securities and
          Exchange Commission on the date hereof, 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.

This certificate is being furnished solely for purposes of Section 906 and is
not being filed as part of the Report or as a separate disclosure document.

Date:  March 15, 2005
                               /s/ Terence E. Hall
                               -------------------------------------------------
                               Terence E. Hall
                               Chairman of the Board and Chief Executive Officer
                               Superior Energy Services, Inc.

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