EXHIBIT 20.4

                         [ZYDECO LETTERHEAD APPEARS HERE]




                             FOR IMMEDIATE RELEASE



CONTACT:  MR. SAM B. MYERS, JR.
          CHIEF EXECUTIVE OFFICER
          (713) 659-2222


                     ZYDECO REPORTS EMPLOYEE TERMINATIONS

     December 14, 1998 (Houston) -- Zydeco Energy, Inc. (NASDAQ National Market
System trading symbol "ZNRG") reported today that cost cutting measures have
resulted in the terminations and resignations of 13 Zydeco employees, or
approximately 52% of its total workforce. Mr. Sam Myers, Company Chairman and
CEO, remarked, "Regrettably, we had to take this action. Our recent spending
levels could not be supported during the near term." Coupled with other overhead
reductions, the Company is repositioning itself in order to weather the current
downturn in the oil and gas industry. Furthermore, the Company announced that
the terminations included Mr. John O. Smith, President and Chief Operating
Officer, who also resigned from the Board of Directors. In addition, the Company
accepted the resignation of Mr. John W. McTigue, Jr., Vice President of
Exploration Technology.

     Discussing the impact of these employee reductions on the Company's
operations, Mr. Myers stated, "The cutbacks will not hamper our ability to
continue marketing our prospects situated within our West Cameron Seismic
Project. Over the past year, we have acquired approximately 12,000 gross acres
within the Project area and intend to sell interests in these prospects or an
interest in the Project." This Project, located within a 230 square mile area of
a narrow trend paralleling the Louisiana coastline known as the Louisiana
Transition Zone, has been the principal focus of the Company's exploratory
efforts. Mr. Myers further stated that the Company's marketing efforts to date
had been hampered by its litigation with Cheniere Energy, Inc. He said, "With
the final arbitration ruling made last week by the arbitration panel, both
companies are now keenly focused on resolving differences and having wells
drilled. We have an excellent inventory of prospects and believe that drilling
will commence sometime in the first quarter of 1999."

     This news release may contain forward-looking statements that are based on
assumptions that in the future may prove not to be accurate. Those statements,
and Zydeco Energy, Inc.'s business and prospects, are subject to a number of
risks including, but not limited to, the volatility of oil and gas prices,
environmental risks, operating risks and hazards, risks related to exploration
and development drilling, uncertainties about reserve estimates, competition,
governmental regulation and the ability of the Company to implement its business
strategy. These and other risks are described in the Company's periodic reports
that are filed with and available from the United States Securities and Exchange
Commission.

     Zydeco Energy, Inc. is an independent oil and gas exploration company
engaged in acquiring leases, drilling and producing reserves utilizing focused
geologic concepts and advanced 3D seismic and computer-aided exploration (CAEX)
technology, including enhanced structural and stratigraphic depth imaging and
attribute analysis. Zydeco's efforts are focused primarily in the Louisiana
Transition Zone.