EXHIBIT 99.2
                                                                    ------------


FOR IMMEDIATE RELEASE                                CONTACT: Caren W. Steffes
Thursday, June 1, 2000                                        (281) 492-5393


                         DIAMOND OFFSHORE DRILLING, INC.
                    ANNOUNCES PRICING OF CONVERTIBLE OFFERING


Houston, Texas, June 1, 2000 -- Diamond Offshore Drilling, Inc. (NYSE:DO) today
announced that yesterday it priced a private placement of 20-year zero coupon
convertible debentures at a 42% conversion premium to yesterday's closing price
on the New York Stock Exchange of $40 7/8. The debentures are convertible into
shares of Diamond Offshore common stock at a fixed conversion rate of 8.6075
shares per debenture.

At closing, the debentures will be issued at a price of $499.60 per debenture,
which represents a yield to maturity of 3.5% per annum to reach an accreted
value at maturity of $1,000 per debenture.

Diamond Offshore has the right to redeem the debentures after five years for a
price equal to the issuance price plus accrued original issue discount through
the date of redemption. Holders have the right to require Diamond Offshore to
repurchase the debentures on the fifth, tenth and fifteenth anniversaries of
issuance at the accreted value through the date of repurchase. Diamond Offshore
may pay such repurchase price with either cash or shares of Diamond Offshore
common stock or a combination of cash and shares of common stock.

The transaction is expected to result in net proceeds to the Company of
approximately $392 million, which the Company intends to use for general
corporate purposes.

Closing of the transaction is scheduled for June 6, 2000, subject to
satisfaction of customary closing conditions.

The securities have not been registered under the Securities Act of 1933 and may
not be offered or sold in the United States absent registration or an applicable
exemption from registration requirements.

Statements in this press release that contain "forward-looking statements"
within the meaning of the Private Securities Litigation Reform Act of 1995
include, but are not limited to, statements regarding the timing of and
conditions to closing and the amount and use of proceeds. Such statements are
inherently subject to a variety of risks and uncertainties that could cause
actual results to differ materially from those projected. A discussion of the
risk factors that could impact these areas and the Company's overall business
and financial performance can be found in the Company's reports filed with the
Securities and Exchange Commission. Given these concerns, investors and analysts
should not place undue reliance on forward-looking statements.


                                       7