EXHIBIT 32.1

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


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

1. the Quarterly Report on Form 10-Q for the quarterly period ended March 31,
2004, as filed with the Securities and Exchange Commission on the date hereof
(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 for
the period covered by such Report.

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.

Date: May 7, 2004                     By: /s/ Terence E. Hall
                                      ------------------------------------------
                                      Terence E. Hall
                                      Chairman of the Board,
                                      Chief Executive Officer and President