EXHIBIT 10.24



                                   January 8, 1997


Mr. Morton H. Meyerson
Suite 400
4514 Cole Avenue
Dallas, Texas 75205

     RE:  Restricted Stock Agreement

Dear Mr. Meyerson: 

     Reference is made to that certain Restricted Stock Agreement dated May
31,  1988 by and between you and ENSCO International Incorporated (formerly
Energy Service Company, Inc.), a Delaware corporation ( ENSCO ), as amended
(collectively,  the  Agreement ).   Under  the terms  of the  Agreement you
acquired  168,750 shares (the "Original Shares") of ENSCO common stock, par
value $.10 per share ( Common Stock ), subject to a right  of repurchase by
ENSCO  upon the occurrence of certain circumstances and under certain terms
and conditions.  You delivered  to ENSCO a promissory note  referred herein
as the  Promissory Note ,  dated July 19, 1988  in the aggregate  principal
amount  of $675,000  in  payment of  the purchase  price  for the  Original
Shares.  

     We have  previously discussed restructuring the terms of the Agreement
and  the Promissory Note  so that the  Promissory Note is  canceled and you
would  receive (i)  cash in an  amount necessary  to pay  the United States
income tax on the income recognized by  you resulting from this transaction
(the "Tax  Amount") and (ii)   shares  of Common Stock  (the "New  Shares")
equal to the  difference between the  value of the  Original Shares on  the
date the Promissory Note is canceled calculated using the Formula Price (as
defined in  the Agreement) less the sum of (A) the unpaid principal balance
of  the Promissory  Note and  (B) the  Tax Amount.   The Agreement  will be
terminated  and  the  New  Shares  will  not  be  subject  to  any  of  the
restrictions  in the Agreement.   Please note  that the New Shares will  be
deemed "restricted stock" as  that term is defined in  Rule 144 promulgated
under the Securities  Act of 1933, as amended, and  therefore the resale of
the New Shares will be subject to restrictions set forth in Rule 144.  

     Based on  these discussions ENSCO  and you  hereby agree  that on  the
Closing  Date (as defined  below), you shall  transfer to ENSCO  all right,
title and interest you have in the Original Shares and in exchange therefor
ENSCO  shall  cancel  the Promissory  Note  and  deliver  to  you  a  stock
certificate representing  the New Shares and an amount in cash equal to the
Tax  Amount.  The Agreement   shall be deemed terminated  as of the Closing
Date.   You shall advise ENSCO prior to the Closing Date of the calculation
of the Tax Amount, which shall be  subject to the prior review and approval
by ENSCO.    




     The number of New Shares shall be calculated in the following manner:

Number of New Shares = (168,750 x  Formula Price) - ($675,000 + Tax Amount)
                       ----------------------------------------------------
                                             Market Price

     Where,

                    Market Price       =     the price per share  of Common
               Stock based on the  average of the high and low  sale prices
               of  the Common  Stock  as reported  by  the New  York  Stock
               Exchange, Inc. on the Closing Date.

                    Formula Price     = the Formula Price referenced in the
               Agreement using the  Market Price as  the Trading Price  (as
               defined in the Agreement).

                    Tax Amount       =  cash  in an amount necessary to pay
               the United States income tax on the income recognized by you
               resulting from this transaction.

The Closing  Date shall  be a  date mutually agreed  between ENSCO  and you
occurring after the date the ENSCO Board of Directors approves the terms of
this letter.  This agreement is subject  to the prior approval of the ENSCO
Board of  Directors.  In the event the Board  of Directors does not approve
the terms  of this agreement, this letter shall be deemed terminated and of
no force or effect.

     If  the  foregoing correctly  sets  forth  our mutual  agreement  with
respect to the foregoing, please sign at the space provided below. 

                                   Yours very truly, 

                                   ENSCO International Incorporated

                                   /s/  CARL F. THORNE
                                   --------------------------------
                                   Carl F. Thorne
                                   Chairman and Chief Executive Officer 

AGREED AND ACCEPTED 
this 13th day of January, 1997.

/s/  MORTON H. MEYERSON
- ------------------------------                    
Morton H. Meyerson