Exhibit 32.1

                            Certification Pursuant to
                        Section 906 of the Sarbanes-Oxley
              Act of 2002 (Subsections (a) and (b) of Section 1350,
                   Chapter 63 of Title 18, United States Code)

     Pursuant to section 906 of the  Sarbanes-Oxley Act of 2002 (Subsections (a)
and (b) of Section 1350,  Chapter 63 of Title 18,  United States Code),  I, S.P.
Johnson, IV, President and Chief Executive Officer of Carrizo Oil & Gas, Inc., a
Texas corporation (the "Company"), hereby certify, to my knowledge, that:

     (1)  the Company's Quarterly Report on Form 10-Q for the three months ended
          September 30, 2004 (the "Report") fully complies with the requirements
          of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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


Dated:    November 15, 2004           /s/ S. P. JOHNSON IV
                                      --------------------------------------
                                      Name:  S.P. Johnson, IV
                                      President and Chief Executive Officer

The foregoing certification is being furnished solely pursuant to Section 906 of
the Sarbanes-Oxley Act of 2002 (Subsections (a) and (b) of Section 1350, Chapter
63 of Title 18, United States Code) and is not being filed as part of the Report
or as a separate disclosure document.

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