EXHIBIT 10.4

                     [PRIDE INTERNATIONAL, INC. LETTERHEAD]


VIA FACSIMILE (303/382-1275)                                     June 21, 1999

First Reserve Fund VIII, Limited Partnership
c/o First Reserve Corp.
1801 California Street
Denver, Colorado 80202

Attention: Thomas R. Denison

Gentlemen:

            This letter sets forth certain agreements relating to the First
Closing of the transactions provided for in the Securities Purchase Agreement
between us dated as of May 5, 1999, as amended by that certain Letter Agreement
dated June 4, 1999 and that certain Letter Agreement dated June 18, 1999 (as so
amended, the "Purchase Agreement"). Capitalized terms used herein that are not
otherwise defined shall have the respective meanings given them in the Purchase
Agreement.

            1. The Company hereby acknowledges and agrees that a condition to
the Purchaser's obligations to consummate the transactions contemplated by the
Purchase Agreement to be effected at the First Closing is the receipt by the
Purchaser of an opinion of British Virgin Islands counsel to the Company in form
and substance satisfactory to the Purchaser substantially to the effect of the
representations of the Company set forth in paragraph 4 hereof. The parties also
agree that the delivery of such opinion shall be a condition to the Purchaser's
obligations to consummate the transactions contemplated by the Purchase
Agreement to be effected at the Second Closing.

            2. The Company hereby acknowledges and agrees that, until the
earlier to occur of (i) the receipt by the Purchaser of the opinion set forth in
paragraph 1 hereof and (ii) the exercise by the Purchaser of its right of
rescission pursuant to paragraph 3 hereof, the Purchase Price payable by the
Purchaser to Twin Oaks Financial Ltd. ("Twin Oaks") pursuant to Section 2.1 of
the Purchase Agreement shall remain in the account of Twin Oaks maintained at
Wells Fargo Bank, San Francisco, or an affiliate bank thereof (or, with respect
to the Debentures, in an account mutually acceptable to the Purchaser and the
Company).

            3. On and after July 10, 1999, PROVIDED that the Purchaser shall not
have received the opinion set forth in paragraph 1 hereof, the Purchaser shall
have the right to rescind the transactions consummated at the First Closing
without liability by giving notice to the Company in accordance with the terms
of the Purchase Agreement, and upon such rescission, Twin Oaks shall immediately
deliver the Purchase Price to the Purchaser (together with interest thereon from
the date of receipt by the Company of such funds until the date of redelivery of
such funds to the Purchaser at 4.7% per annum) in exchange for the Purchaser's
delivery of the certificates representing the Shares.

            4. The Company hereby represents and warrants to the Purchaser that
all of the issued and outstanding capital stock of Twin Oaks has been duly and
effectively issued to Pride International, Inc. and that such stock has been
validly issued and is fully paid and nonassessable. This representation shall be
deemed a representation made by the Company pursuant to the Purchase Agreement.

First Reserve Fund VIII, Limited Partnership
c/o First Reserve Corp.             -2-                       June 21, 1999

            On the basis of and subject to the foregoing, the parties hereby
agree to consummate the transactions contemplated by the Purchase Agreement to
be effected at the First Closing, the effective date of which consummation shall
be June 21, 1999.

            Except to the extent otherwise expressly contemplated hereby, the
Purchase Agreement is hereby ratified and confirmed. This letter may be executed
in multiple counterparts, each of which shall constitute one and the same
instrument. This letter may be delivered by delivery of facsimile signature
pages.

            If the foregoing is in accordance with the agreements and
understandings between us, please so indicate by returning a signed counterpart
of this letter.

                                    Very truly yours,

                                    PRIDE INTERNATIONAL, INC.


                                    By:/s/PAUL A. BRAGG
                                          Paul A. Bragg
                                          President and Chief Executive Officer

AGREED TO AND ACCEPTED
AS OF THIS 21ST DAY OF JUNE 1999:

FIRST RESERVE FUND VIII, LIMITED PARTNERSHIP

By:   First Reserve GP VIII, L.P.
      its General Partner

By:   First Reserve Corporation
      its General Partner

By:/s/THOMAS R. DENISON
      Thomas R. Denison
      Managing Director