Exhibit 10.9




                            STONE ENERGY CORPORATION

               AMENDMENT TO THE ANNUAL INCENTIVE COMPENSATION PLAN
                                JANUARY 15, 1997




    Exhibit II to the Annual Incentive  Compensation  Plan is amended to provide
that the  following  be used as the  criteria by the  Compensation  Committee in
determining  whether an  incentive  bonus pool should be awarded in any calendar
year and the amount of any such pool.


                                                   Bonus                           Bonus
                                                   Points                 Performance Parameters
                                                 Allocation             Minimum             Maximum
                                                -----------             -------             --------
                                                                                  
Annual change in shareholder value,
     using average December stock prices.....        15                    0%       to        20%

Superior performance percentage used by
     the original plan which compares SGY
     to the peer group by quarter............        20                    0%       to        20%

Earnings and cash flow per share.............        15                   10%       to        30%

Annual change in net asset value.............        20                   10%       to        30%

Discretionary................................        30
                                                     --

Total                                               100
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