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                                   EXHIBIT I
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                                            Contact:

                                            John Misitigh
                                            Vice President, Secretary
                                            & Treasurer
                                            (713) 872-7621


June 21, 1995
For Immediate Release


                          SOUTHERN MINERAL CORPORATION
                         ANNOUNCES ODD LOT TENDER OFFER

     Houston, June 21, -- Southern Mineral Corporation announced today that it
has offered to purchase outstanding shares of its common stock from 291
shareholders of record.  The odd lot tender has been made at a cash price of
$1.50 per share to such shareholders who owned less than 100 shares of its
stock on March 24, 1995 and will remain open until August 31, 1995 unless
earlier suspended by the Company.  These shareholders represent about 35% of the
total number of shareholders of record but less than 1% of the Company's
outstanding stock.

     Southern Mineral Corporation is an oil and gas acquisition, exploration and
production company that is listed in The NASDAQ SmallCap Market under the
trading symbol SMIN.



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