EXHIBIT 99.1
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FOR IMMEDIATE RELEASE                                CONTACT: Caren W. Steffes
Wednesday, March 7, 2001                                      (281) 492-5393


                    DIAMOND OFFSHORE DRILLING, INC. TO REDEEM
                 3-3/4% CONVERTIBLE SUBORDINATED NOTES DUE 2007


Houston, Texas, March 7, 2001-Diamond Offshore Drilling, Inc. (NYSE: DO) today
announced its decision to redeem on April 6, 2001 all of its outstanding 3-3/4%
Convertible Subordinated Notes Due 2007 at a redemption price of 102.08% of the
principal amount thereof, in accordance with the Indenture under which the Notes
were issued. On April 6, 2001, the redemption price, together with interest
accrued to such date, will become due and payable and interest on the Notes will
cease to accrue.

The Notes are convertible, at any time on or before the close of business on
April 5, 2001, into the common stock, par value $.01 per share, of Diamond
Offshore at a conversion price of $40.50 per share, subject to adjustment in
certain circumstances.

$400,000,000 principal amount of the 3-3/4% Convertible Subordinated Notes Due
2007 were issued in February 1997. $399,980,000 principal amount are presently
outstanding.

Copies of the Notice of Redemption, which includes instructions for delivery of
3-3/4% Convertible Subordinated Notes Due 2007 for redemption or conversion, may
be obtained from The Chase Manhattan Bank, c/o Chase Bank of Texas, Corporate
Trust Services, P.O. Box 2320, Dallas, Texas 75221-2320, Telephone No. (212)
946-3068.

Diamond Offshore is a leader in deep water drilling. The Company's fleet of 45
offshore drilling rigs consists of 30 semisubmersibles, 14 jack-ups and one
drillship. The fleet operates in the waters of six of the world's seven
continents.