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                                                                     EXHIBIT 4.1

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

                               September 16, 1997

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.
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                 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: Senior 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, General 
            Counsel and Secretary
           ----------------------------





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