Exhibit 4.2



                                LOEWS CORPORATION
                                667 Madison Avenue
                             New York, NY 10021-8087



         Diamond Offshore Drilling, Inc.
         15415 Katy Freeway
         Houston, TX 77094

         Attention:     Richard L. Lionberger
                        Vice President, General Counsel and Secretary

         Gentlemen:

                   Reference is made to the Registration Rights
         Agreement dated October 16, 1995 (the "Agreement") between you
         (the "Company") and the undersigned ("Loews").  Capitalized
         terms used and not otherwise defined herein are used with
         meanings given thereto in the Agreement.

                   1.   Demand Registration.  This letter constitutes
         Loews's written request (being the first of three such requests
         to which Loews is entitled) pursuant to Section 2.1 of the
         Agreement that the Company prepare and file, and use its best
         efforts to cause to become effective as soon as practicable
         (but not later than September 30, 1998), one or more
         registration statements under the Act for a continuous offering
         by Loews of shares of Registerable Common Stock under Rule 415
         promulgated by the Commission under the Act (the "Registration
         Statement").  The shares of Registerable Common Stock covered
         by this request will underlie a proposed issuance by Loews of
         its Exchangeable Notes due 2007 ("Exchangeable Notes") through
         a public offering of such notes to be underwritten by Goldman,
         Sachs & Co. (the "Note Offering").  Loews expects to price the
         Note Offering on or about September 16, 1997 at which time
         Loews will advise the Company of the exact number of shares of
         Registerable Common Stock to be covered by this request and the
         Registration Statement.





                   2.   The Registration Statement.

                             (i)  Notwithstanding Section 5(h) of the
         Agreement, the Company agrees to keep effective the
         Registration Statement until the first to occur of (A)
         September 15, 2007 and (B) such time as no Exchangeable Notes
         remain outstanding.

                            (ii)  Loews agrees that the Company may, by
         giving one business day's written notice to Loews, and the
         trustee and the exchange agent for the Exchangeable Notes
         (which notice shall specify that it is given on behalf of Loews
         under the indenture for the Exchangeable Notes (the
         "Indenture")), defer filing the Registration Statement to a
         date later than September 30, 1998, or, at any time and from
         time to time after the Registration Statement has been filed
         and declared effective, require Loews to suspend use of any
         resale prospectus or prospectus supplement included in the
         Registration Statement (A) for a reasonable period of time, but
         not in excess of ninety (90) days, if the Company (x) is at
         such time conducting or about to conduct an underwritten public
         offering of its securities for its own account and the Board of
         Directors of the Company determines in good faith that such
         offering would be materially adversely affected by such use, or
         (y) would, in the opinion of the Company's counsel, be required
         to disclose in such Registration Statement information not
         otherwise then required by law to be publicly disclosed and, in
         the good faith judgment of the Board of Directors of the
         Company, such disclosure would reasonably be expected to
         adversely affect any material business transaction or
         negotiation in which the Company is then engaged or (B) for any
         period during which the Company has notified Loews and the
         exchange agent for the Exchangeable Notes of the occurrence of
         an event requiring the preparation of a supplement to the
         resale prospectus included in the Registration Statement or an
         amendment to the Registration Statement so that, as thereafter
         delivered to holders of the Exchangeable Notes exchanging such
         notes for shares of Registerable Common Stock, such prospectus
         will not contain an untrue statement of a material fact or omit
         to state any material fact required to be stated therein or
         necessary to make the statements therein, in light of the
         circumstances under which they were made, not misleading, and
         as promptly as practicable make available to Loews any such
         supplement or amendment.  Notwithstanding the foregoing, such
         suspensions of use of any such resale prospectus or prospectus
         supplement shall not be in effect for more than 120 days in any
         twelve-month period.

                           (iii)  Loews further agrees that the
         provisions of paragraph (ii) above shall apply to any future
         request for registration made by Loews under Section





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         2.1 of the Agreement if such request relates to a "shelf"
         registration requested to be filed by the Company pursuant to
         Rule 415 promulgated under the Act.

                   3.   Underwriting Agreement.  Pursuant to Section
         5(1) of the Agreement, the Company agrees to enter into the
         underwriting agreement, in the form attached hereto as Exhibit
         "A".

                   4.   Limitations on Suspension Periods.
         Notwithstanding the provisions of Section 2(ii) hereof, the
         Company agrees with Loews that it will not suspend the use of
         any resale prospectus or prospectus supplement included in the
         Registration Statement (i) during the 14-day period preceding
         the final maturity date of the Exchangeable Notes or, subject
         to compliance by Loews with the provisions of this Section 4,
         during the 14-day period preceding any Redemption Date (as
         defined in Loews's prospectus supplement for the Exchangeable
         Notes (the "Prospectus Supplement")) with respect to the
         Exchangeable Notes.  Loews agrees not to give notice under the
         Indenture to the holders of Exchangeable Notes of any proposed
         optional redemption at any time when use of any such prospectus
         or prospectus supplement has been suspended by the Company in
         accordance with this letter.  Prior to giving notice under the
         Indenture to the holders of Exchangeable Notes of any proposed
         optional redemption, Loews agrees to provide the Company with
         at least three full Trading Days' (as defined in the Prospectus
         Supplement) written notice (or such shorter period as the
         Company may agree) of such proposed optional redemption (the
         "Redemption Notice").  On or before the close of business on
         the third Trading Day following actual receipt by the Company
         of the Redemption Notice, the Company will notify Loews if the
         Company elects to suspend the use of any resale prospectus or
         prospectus supplement pursuant to Section 2(ii) above.  If the
         Company elects to suspend use of any resale prospectus or
         prospectus supplement, the Company will effect such suspension
         promptly and Loews will not give notice of any proposed
         optional redemption until the suspension period has terminated
         or expired.

                   5.   Effect Hereof.  This letter agreement
         constitutes an amendment to the Agreement pursuant to Section
         12.5 thereof and the general provisions of such agreement apply
         to this letter agreement (except the notice provisions hereof
         will control over Section 12.7 thereof in the event of any
         inconsistency).  As amended hereby, the Agreement is hereby
         confirmed to be and remain in full force and effect.

                   If this letter correctly sets forth our mutual
         understanding regarding the amendment to the Agreement proposed
         to be effected hereby, please so indicate by





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         executing each copy hereof, whereupon this letter shall
         constitute an agreement between us to amend the Agreement, and
         otherwise as set forth above.


                                       LOEWS CORPORATION


                                       By: /s/ Barry Hirsch              
                                          ------------------------
                                       Name:   Barry Hirsch             
                                       Title:  Sr. Vice President       


         Agreed and accepted
         this 16th day of September, 1997

         DIAMOND OFFSHORE DRILLING, INC.


         By: /s/ Richard L. Lionberger   
            -----------------------------  
            Name:  Richard L. Lionberger
            Title:  Vice President


































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