1
                                                                    EXHIBIT 10.4

                                PROMISSORY NOTE

$3,500,000                      Houston, Texas                 December 20, 1995

                 FOR VALUE RECEIVED and WITHOUT GRACE, the undersigned
("Maker") promises to pay to the order of COMPASS BANK-HOUSTON ("Payee"), at
its banking quarters in Houston, Harris County, Texas, the sum of THREE MILLION
FIVE HUNDRED THOUSAND DOLLARS ($3,500,000), or so much thereof as may be
advanced against this Note pursuant to the Credit Agreement dated of even date
herewith by and between Maker and Payee (as amended, restated, or supplemented
from time to time, the "Credit Agreement"), together with interest at the rates
and calculated as provided in the Credit Agreement.

                 Reference is hereby made to the Credit Agreement for matters
governed thereby, including, without limitation, certain events which will
entitle the holder hereof to accelerate the maturity of all amounts due
hereunder.  Capitalized terms used but not defined in this Note shall have the
meanings assigned to such terms in the Credit Agreement.

                 This Note is issued pursuant to, is the "Note" under, and is
payable as provided in the Credit Agreement.  Subject to compliance with
applicable provisions of the Credit Agreement, Maker may at any time pay the
full amount or any part of this Note without the payment of any premium or fee,
but such payment shall not, until this Note is fully paid and satisfied, excuse
the payment as it becomes due of any payment on this Note provided for in the
Credit Agreement.

                 Without being limited thereto or thereby, this Note is secured
by the Security Instruments.

                 THIS NOTE SHALL BE GOVERNED AND CONTROLLED BY THE LAWS OF THE
STATE OF TEXAS WITHOUT GIVING EFFECT TO PRINCIPLES THEREOF RELATING TO
CONFLICTS OF LAW; PROVIDED, HOWEVER, THAT VERNON'S TEXAS CIVIL STATUTES,
ARTICLE 5069, CHAPTER 15 (WHICH REGULATES CERTAIN REVOLVING CREDIT LOAN
ACCOUNTS AND REVOLVING TRIPARTY  ACCOUNTS) SHALL NOT APPLY TO THIS NOTE.

                                        SOUTHERN MINERAL CORPORATION


                                        By: /s/ STEVEN H. MIKEL
                                            ------------------------------------
                                            Steven H. Mikel
                                            President and CEO





                      (Signatures Continued on Next Page)
   2
                                          SMC PRODUCTION CO.

                                          SAN SALVADOR DEVELOPMENT COMPANY, INC.

                                          VENTURE RESOURCES, INC.

                                          VENTURE PIPELINE COMPANY

                                          VENGAS PIPELINE COMPANY

                                          SPRUCE HILLS PRODUCTION COMPANY, INC.


                                          By: /s/ STEVEN H. MIKEL
                                              ----------------------------------
                                              Steven H. Mikel
                                              President and CEO