DIAMOND OFFSHORE DRILLING INC
8-K, 1997-09-19
DRILLING OIL & GAS WELLS
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<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549


                                 _____________

                                    FORM 8-K

                                 CURRENT REPORT
                     PURSUANT TO SECTION 13 OR 15(D) OF THE
                        SECURITIES EXCHANGE ACT OF 1934


Date of report:                  SEPTEMBER 19, 1997
               ----------------------------------------------------------------

Date of earliest event reported: SEPTEMBER 16, 1997
                                -----------------------------------------------

                       DIAMOND OFFSHORE DRILLING, INC.
- -------------------------------------------------------------------------------
             (Exact Name of Registrant as Specified in Charter)
                                            


<TABLE>
<S>                                        <C>                                                        <C>
DELAWARE                                                 1-13926                                           76-0321760    
- -------------------------------------------------------------------------------------------------------------------------
(State or Other Jurisdiction                     (Commission File Number)                                (IRS Employer
of Incorporation)                                                                                     Identification No.)


                                           15415 KATY FREEWAY, HOUSTON, TEXAS                                       77094
- -------------------------------------------------------------------------------------------------------------------------
(Address of Principal Executive Offices)                                                                       (Zip Code)
</TABLE>


Registrant's telephone number, including area code       (281) 492-5300
                                                   ----------------------------

                                NOT APPLICABLE
- --------------------------------------------------------------------------------
         (Former name or former address, if changed since last report)
<PAGE>   2

                    INFORMATION TO BE INCLUDED IN THE REPORT

ITEM 5.  OTHER EVENTS

         On September 16, 1997, Diamond Offshore Drilling, Inc. ("Diamond
Offshore") entered into an Underwriting Agreement (the "Underwriting
Agreement") with Loews Corporation ("Loews") and Goldman, Sachs & Co. (the
"Underwriter") in connection with the sale by Loews of $1,000,000,000 principal
amount of its 3-1/8% Exchangeable Subordinated Notes due September 15, 2007
(the "Notes") pursuant to an underwritten offering (the "Offering").  Pursuant
to a 30-day option that Loews granted the Underwriter, the Underwriter may
purchase up to an additional $150,000,000 principal amount of the Notes to
cover over-allotments.  The Notes are exchangeable into shares of Diamond
Offshore's common stock, par value $.01 per share, at any time from October 1,
1998 to, and including, September 15, 2007.  Also in connection with the
Offering, Diamond Offshore and Loews entered into an agreement, dated as of
September 16, 1997 (the "Registration Rights Agreement Amendment"), amending
the Registration Rights Agreement, dated as of October 16, 1995, between
Diamond Offshore and Loews.  Filed herewith are (i) the Underwriting Agreement
and (ii) the Registration Rights Agreement Amendment.





                                       2

<PAGE>   3

ITEM 7.  FINANCIAL STATEMENTS AND EXHIBITS

         (c)     Exhibits.

     Exhibit number                 Description
     --------------                 -----------
          1.1            Underwriting Agreement.
          4.1            Registration Rights Agreement Amendment.





                                       3
<PAGE>   4
                                   SIGNATURES

                 Pursuant to the requirements of the Securities Exchange Act of
1934, as amended, the Registrant has duly caused this report to be signed on
its behalf by the undersigned hereunto duly authorized.


                                        DIAMOND OFFSHORE DRILLING, INC.


                                        By: /s/ RICHARD L. LIONBERGER
                                           ------------------------------------
                                              Richard L. Lionberger
                                              Vice President, General Counsel
                                                     and Secretary


Dated: September 19, 1997





                                       4
<PAGE>   5
                                 EXHIBIT INDEX

     Exhibit number                   Description
     --------------                   -----------
          1.1            Underwriting Agreement.
          4.1            Registration Rights Agreement Amendment.





                                       5



<PAGE>   1
                                                                    EXHIBIT 1.1




                               LOEWS CORPORATION

                            (a Delaware corporation)

                   $1,000,000,000 aggregate principal amount
                3-1/8% Exchangeable Subordinated Notes due 2007

                             UNDERWRITING AGREEMENT



                                                              September 16, 1997


To the Representatives named in Schedule I hereto
     of the Underwriters named in Schedule II hereto

Ladies and Gentlemen:

         Loews Corporation, a Delaware corporation (the "Company"), proposes to
issue and sell to the underwriters named in Schedule II hereto (the
"Underwriters"), for whom you are acting as representatives (the
"Representatives"), the principal amount of its securities identified in
Schedule I hereto (the "Securities"), which may be senior or subordinated debt
securities (the "Debt Securities") or any combination thereof.

         The Debt Securities will be issued in one or more series as senior
indebtedness (the "Senior Debt Securities") under an indenture, dated as of
March 1, 1986, between the Company and The Chase Manhattan Bank (National
Association), as trustee (the "Trustee"), as supplemented by a first
supplemental indenture, dated March 30, 1993, between the Company and the
Trustee and a second supplemental indenture, dated as of February 18, 1997,
between the Company and the Trustee (such Indenture, as supplemented, is
referred to as the "Senior Indenture"), or as subordinated indebtedness (the
"Subordinated Debt Securities") under an indenture, dated as of December 1,
1985, between the Company and the Trustee, as supplemented by a first
supplemental indenture, dated as of February 18, 1997, between the Company and
the Trustee, a second supplemental indenture, dated as of February 18, 1997,
between the Company and the Trustee and a third supplemental indenture, dated
as of September 19, 1997, between the Company and the Trustee (such Indenture,
as supplemented, is referred to as the "Subordinated Indenture," and
collectively with the Senior Indenture, the "Indentures," and each, an
"Indenture"). Each series of Debt Securities may vary, as applicable, as to
title, aggregate principal amount, rank, interest rate or formula and timing of
payments thereof, stated maturity date, redemption and/or repayment provisions,
sinking fund requirements, conversion provisions (and terms of the related
Underlying Securities) and any other variable terms established by or pursuant
to the applicable Indenture.
<PAGE>   2
         As used herein, "Securities" means the Senior Debt Securities or
Subordinated Debt Securities, or any combination thereof, initially issuable by
the Company and, if Securities are convertible or exchangeable, "Underlying
Securities" means the securities (of the Company or another issuer) issuable
upon conversion or exchange of the Senior Debt Securities or Subordinated Debt
Securities, as applicable.

         Schedule I hereto specifies the number or aggregate principal amount,
as the case may be, of Securities to be initially issued (the "Initial
Underwritten Securities"), whether such offering is on a fixed or variable
price basis and, if on a fixed price basis, the initial offering price, the
price at which the Initial Underwritten Securities are to be purchased by the
Underwriters, the form, time, date and place of delivery and payment of the
Initial Underwritten Securities and any other material variable terms of the
Initial Underwritten Securities, as well as the material variable terms of any
related Underlying Securities.  In addition, if applicable, such Underwriting
Agreement shall specify whether the Company has agreed to grant to the
Underwriters an option to purchase additional Securities to cover
over-allotments, if any, and the number or aggregate principal amount, as the
case may be, of Securities subject to such option (the "Option Underwritten
Securities"). As used herein, the term "Underwritten Securities" shall include
the Initial Underwritten Securities and all or any portion of any Option
Underwritten Securities.

         The Company has filed with the Securities and Exchange Commission (the
"Commission") a registration statement on Form S-3 (No. 333-22113) for the
registration of the Securities under the Securities Act of 1933, as amended
(the "Act"), and the offering thereof from time to time in accordance with Rule
415 of the rules and regulations of the Commission under the Act (the "Act
Regulations"), and the Company has filed such post-effective amendments thereto
as may be required prior to the execution of this Underwriting Agreement.  Such
registration statement (as so amended, if applicable) has been declared
effective by the Commission and each Indenture has been duly qualified under
the Trust Indenture Act of 1939, as amended (the "Trust Indenture Act").  Such
registration statement (as so amended, if applicable), including the
information, if any, deemed to be a part thereof pursuant to Rule 430A(b) of
the Act Regulations (the "Rule 430A Information") or Rule 434(d) of the Act
Regulations (the "Rule 434 Information"), is referred to herein as the
"Registration Statement"; and the final prospectus and the final prospectus
supplement relating to the offering of the Underwritten Securities, in the form
first furnished to the Underwriters by the Company for use in connection with
the offering of the Underwritten Securities, are collectively referred to
herein as the "Final Prospectus"; provided, however, that all references to the
"Registration Statement" and the "Final Prospectus" shall also be deemed to
include all documents incorporated therein by reference pursuant to the
Securities Exchange Act of 1934, as amended (the "Exchange Act"), prior to the
execution of this Underwriting Agreement; provided further, that if the Company
files a registration statement with the Commission pursuant to Rule 462(b) of
the Act Regulations (the "Rule 462 Registration Statement"), then, after such
filing, all references to "Registration Statement" shall also be deemed to
include the





                                      -2-
<PAGE>   3
Rule 462 Registration Statement; and provided further, that if the Company
elects to rely upon Rule 434 of the Act Regulations, then all references to
"Final Prospectus" shall also be deemed to include the final or preliminary
prospectus and the applicable term sheet or abbreviated term sheet (the "Term
Sheet"), as the case may be, in the form first furnished to the Underwriters by
the Company in reliance upon Rule 434 of the Act Regulations, and all
references in this Underwriting Agreement to the date of the Final Prospectus
shall mean the date of the Term Sheet.  A "Preliminary Prospectus" shall be
deemed to refer to any prospectus used before the registration statement became
effective and any prospectus that omitted, as applicable, the Rule 430A
Information, the Rule 434 Information or other information to be included upon
pricing in a form of prospectus filed with the Commission pursuant to Rule
424(b) of the Act Regulations, that was used after such effectiveness and prior
to the execution and delivery of this Underwriting Agreement.  For purposes of
this Underwriting Agreement, all references to the Registration Statement,
Final Prospectus, Term Sheet or Preliminary Prospectus or to any amendment or
supplement to any of the foregoing shall be deemed to include any copy filed
with the Commission pursuant to its Electronic Data Gathering, Analysis and
Retrieval system ("EDGAR").  Notwithstanding anything to the contrary in this
Underwriting Agreement, if any revised Term Sheet, Preliminary Prospectus or
Final Prospectus, as the case may be, shall be provided to the Underwriters by
the Company for use in connection with the offering of the Securities which
differs from the prospectus on file at the Commission at the time the
Registration Statement becomes effective (whether or not such revised
prospectus is required to be filed by the Company pursuant to Rule 424(b) of
the Act Regulations), the terms "Term Sheet," "Preliminary Prospectus" or
"Final Prospectus," as the case may be, shall refer to such revised "Term
Sheet," "Preliminary Prospectus" or "Final Prospectus" from and after the time
it is first provided to the Underwriters for such use. Any reference herein to
the terms "amend," "amendment" or "supplement" with respect to the Registration
Statement, Term Sheet, any Preliminary Prospectus or the Final Prospectus,
unless otherwise expressly provided therein, shall be deemed to refer to and
include the filing of any document under the Exchange Act after the date of
this Underwriting Agreement, or the issue date of the Preliminary Prospectus or
the Final Prospectus, as the case may be, deemed to be incorporated therein by
reference.

         All references in this Underwriting Agreement to financial statements
and schedules and other information which is "contained," "included" or
"stated" (or other references of like import) in the Registration Statement,
Final Prospectus or Preliminary Prospectus shall be deemed to mean and include
all such financial statements and schedules and other information which is
incorporated by reference in the Registration Statement, Final Prospectus or
Preliminary Prospectus, as the case may be; and all references in this
Underwriting Agreement to amendments or supplements to the Registration
Statement, Final Prospectus or Preliminary Prospectus shall be deemed to mean
and include the filing of any document under the Exchange Act which is
incorporated by reference in the Registration Statement, Final Prospectus or
Preliminary Prospectus, as the case may be.





                                      -3-
<PAGE>   4
         1A.  Representations and Warranties of the Company.  The Company
represents and warrants to each Underwriter as of the date hereof and as of the
Closing Date that:

              (a)  The Company meets the requirements for use of Form S-3 
         under the Act.

              (b)  This Underwriting Agreement has been duly authorized,
         executed and delivered by the Company. The Indenture is substantially
         in the form filed as an exhibit to the Registration Statement at the
         time the Registration Statement became effective (other than insofar
         as the Indenture has been modified by a supplemental Indenture), and,
         has been duly authorized, executed and delivered by the Company and
         constitutes a legal, valid and binding agreement of the Company,
         enforceable against the Company in accordance with its terms, except
         that (A) the enforceability thereof may be subject to bankruptcy,
         insolvency, reorganization, moratorium or other similar laws now or
         hereafter in effect, relating to creditors' rights generally and (B)
         the remedy of specific performance and injunctive and other forms of
         equitable relief may be subject to equitable defenses and to the
         discretion of the court before which any proceeding therefor may be
         brought.  An Amendment to the Registration Rights Agreement, dated
         October 16, 1995, between the Company and Diamond Offshore Drilling,
         Inc. ("Diamond Offshore"), in the form of Exhibit A hereto, has been
         duly authorized by the Company and, as of the Closing Date, will be
         duly executed and delivered by the Company (as so amended, such
         Registration Rights Agreement is referred to as the "Amended
         Registration Rights Agreement").

              (c)  Each of the Registration Statement and any Rule 462(b)
         Registration Statement has become effective under the Act and no stop
         order suspending the effectiveness of the Registration Statement or
         any Rule 462(b) Registration Statement has been issued under the Act
         and no proceedings for that purpose have been instituted or are
         pending or, to the knowledge of the Company, are contemplated by the
         Commission, and any request on the part of the Commission for
         additional information has been complied with.  In addition, each
         Indenture has been duly qualified under the Trust Indenture Act.

              At the respective times the Registration Statement, any Rule
         462(b) Registration Statement and any post- effective amendments
         thereto (including the filing of the Company's most recent Annual
         Report on Form 10-K with the Commission (the "Annual Report on Form
         10-K")) became effective and as of the date hereof, the Registration
         Statement, any Rule 462(b) Registration Statement and any amendments
         and supplements thereto complied and will comply in all material
         respects with the requirements of the Act and the Act Regulations and
         the Trust Indenture Act and the rules and regulations of the
         Commission under the Trust Indenture Act (the "Trust Indenture Act
         Regulations") and did not and will not contain an untrue statement of
         a material fact or omit to state a material fact required to be stated
         therein or necessary





                                      -4-
<PAGE>   5
         to make the statements therein not misleading.  At the date of the
         Final Prospectus, at the Closing Date and at each Date of Delivery, if
         any, the Final Prospectus and any amendments and supplements thereto
         did not and will not include an untrue statement of a material fact or
         omit to state a material fact necessary in order to make the
         statements therein, in the light of the circumstances under which they
         were made, not misleading. If the Company elects to rely upon Rule 434
         of the Act Regulations, the Company will comply with the requirements
         of Rule 434. Notwithstanding the foregoing, the representations and
         warranties in this subsection (c) shall not apply to (i) statements in
         or omissions from the Registration Statement or the Final Prospectus
         made in reliance upon and in conformity with information furnished to
         the Company in writing by or on behalf of any Underwriter expressly
         for use in the Registration Statement or the Final Prospectus or (ii)
         that part of the Registration Statement which shall constitute the
         Statement of Eligibility and Qualification (Form T-1) under the Trust
         Indenture Act of the Trustee.

              Each preliminary prospectus and prospectus filed as part of the
         Registration Statement as originally filed or as part of any amendment
         thereto, or filed pursuant to Rule 424 under the Act, complied when so
         filed in all material respects with the Act Regulations and each
         Preliminary Prospectus and the Final Prospectus delivered to the
         Underwriters for use in connection with the offering of Underwritten
         Securities will, at the time of such delivery, be identical to any
         electronically transmitted copies thereof filed with the Commission
         pursuant to EDGAR, except to the extent permitted by Regulation S-T.

              (d)  The documents incorporated or deemed to be incorporated by
         reference in the Registration Statement and the Final Prospectus as of
         the date hereof, when they became effective or at the time they were
         or hereafter are filed with the Commission, complied and will comply
         in all material respects with the requirements of the Exchange Act and
         the rules and regulations of the Commission thereunder (the "Exchange
         Act Regulations").

              (e)  The Company has been duly organized and is validly existing
         as a corporation in good standing under the laws of the State of
         Delaware and has corporate power and authority to own, lease and
         operate its properties and to conduct its business as described in the
         Final Prospectus and to enter into and perform its obligations under,
         or as contemplated under, this Underwriting Agreement.  The Company is
         duly qualified as a foreign corporation to transact business and is in
         good standing in each other jurisdiction in which such qualification
         is required, whether by reason of the ownership or leasing of material
         property or the conduct of material business, except where the failure
         to so qualify or be in good standing would not result in a material
         adverse change in the condition (financial or other), earnings,
         business or properties of





                                      -5-
<PAGE>   6
         the Company and its subsidiaries, taken as a whole, whether or not
         arising from transactions in the ordinary course of business (a
         "Material Adverse Effect").

              (f)  The Underwritten Securities have been duly authorized by the
         Company for issuance and sale pursuant to this Underwriting Agreement.
         Such Underwritten Securities, when issued and authenticated in the
         manner provided for in the applicable Indenture and delivered against
         payment of the consideration therefor specified in this Underwriting
         Agreement, will constitute valid and legally binding obligations of
         the Company, enforceable against the Company in accordance with their
         terms, except as the enforcement thereof may be limited by bankruptcy,
         insolvency, reorganization, moratorium or other similar laws relating
         to or affecting creditors' rights generally or by general equitable
         principles, and except further as enforcement thereof may be limited
         by (A) governmental authority to limit, delay or prohibit the making
         of payments outside the United States and (B) the remedy of specific
         performance and injunctive and other forms of equitable relief may be
         subject to equitable defenses and to the discretion of the court
         before which any proceeding therefor may be brought. Such Underwritten
         Securities will be in the form contemplated by, and each registered
         holder thereof is entitled to the benefits of, the applicable
         Indenture.

              (g)  The Underwritten Securities being sold pursuant to this
         Underwriting Agreement and each applicable Indenture, as of the date
         of the Final Prospectus, will conform in all material respects to the
         statements relating thereto contained in the Final Prospectus.  The
         Underwritten Securities will be in substantially the form filed or
         incorporated by reference, as the case may be, as an exhibit to the
         Registration Statement.

              (h)  The execution and delivery of this Underwriting Agreement,
         each applicable Indenture, the Amended Registration Rights Agreement,
         and any other agreement or instrument entered into or issued or to be
         entered into or issued by the Company in connection with the
         transactions contemplated hereby or thereby or in the Registration
         Statement and the Final Prospectus and the consummation of the
         transaction contemplated herein and in the Registration Statement and
         the Final Prospectus (including the issuance and sale of the
         Underwritten Securities and the use of the proceeds from the sale of
         the Underwritten Securities as described under the caption "Use of
         Proceeds") and compliance by the Company with its obligations
         hereunder and thereunder have been duly authorized by all necessary
         corporate action and will not conflict with or constitute a breach of,
         or default under, or result in the creation or imposition of any lien,
         charge or encumbrance upon any property or assets of the Company or
         any of its subsidiaries pursuant to, any agreements or instruments,
         nor will such action result in any violation of the provisions of the
         charter or by-laws of the Company or any of its subsidiaries or any
         applicable law, administrative regulation





                                      -6-
<PAGE>   7
         or administrative or court decree which, in the aggregate, could
         reasonably be expected to result in a Material Adverse Effect.

              (i)  The statements set forth in the Final Prospectus under the
         captions "Description of Senior Debt Securities", "Description of
         Subordinated Debt Securities", "Description of Preferred Stock",
         "Description of Common Stock", "Description of the Notes" and
         "Description of Diamond Offshore Capital Stock", insofar as they
         purport to constitute a summary of the terms of the Securities, are
         accurate, complete and fair.

              (j)  Neither the Company nor any of its affiliates does business
         with the government of Cuba or with any person or affiliate located in
         Cuba within the meaning of Section 517.075, Florida Statutes.

         1B.  Representations and Warranties of Diamond Offshore.  Diamond
Offshore represents and warrants to each Underwriter as of the date hereof and
as of the Closing Date that:

              (a)  Diamond Offshore's annual report on Form 10-K for the fiscal
         year ended December 31, 1996 (the "Form 10-K"), its definitive proxy
         statement on Schedule 14A filed with the Commission on April 1, 1997,
         its quarterly reports on Form 10-Q for the quarters ended March 31,
         1997 and June 30, 1997 and any current reports on Form 8-K filed by
         Diamond Offshore subsequent to the Form 10-K are hereinafter referred
         to collectively as the "Exchange Act Reports".  The Exchange Act
         Reports, when they were filed with the Commission, conformed in all
         material respects to the applicable requirements of the Exchange Act
         and the applicable rules and regulations of the Commission thereunder,
         and did not, and on the date of the Final Prospectus, will not,
         contain an untrue statement of a material fact or omit to state a
         material fact necessary in order to make the statements therein, in
         the light of the circumstances under which they were made, not
         misleading.  To the extent that any statement made or omitted in the
         Registration Statement, the Final Prospectus or any amendment or
         supplement thereto are made or omitted in reliance upon and in
         conformity with written information furnished to the Company by
         Diamond Offshore expressly for use therein, such Registration
         Statement did, and the Final Prospectus and any further amendments or
         supplements to the Registration Statement and the Final Prospectus
         will, when they become effective or are filed with the Commission, as
         the case may be, conform in all material respects to the requirements
         of the Act and the Act Regulations and not contain any 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 not misleading.





                                      -7-
<PAGE>   8
              (b) Diamond Offshore has been duly incorporated and is an
         existing corporation in good standing under the laws of the State of
         Delaware, with power and authority (corporate and other) to own its
         properties and conduct its business as described in the Final
         Prospectus; and Diamond Offshore is duly qualified to do business as a
         foreign corporation in good standing in all other jurisdictions in
         which its ownership or lease of property or the conduct of its
         business requires such qualification, except where the failure of
         Diamond Offshore to be so qualified would not have a material adverse
         effect on the business, operations or financial condition of Diamond
         Offshore and its subsidiaries, taken as a whole.

              (c) Each subsidiary of Diamond Offshore has been duly
         incorporated and is an existing corporation in good standing under the
         laws of the jurisdiction of its incorporation, with power and
         authority (corporate and other) to own its properties and conduct its
         business as described in the Final Prospectus; and each subsidiary of
         Diamond Offshore is duly qualified to do business as a foreign
         corporation in good standing in all other jurisdictions in which its
         ownership or lease of property or the conduct of its business requires
         such qualification, except where the failure of such subsidiary to be
         so qualified would not have a material adverse effect on the business,
         operations or financial condition of Diamond Offshore and its
         subsidiaries, taken as a whole; all of the issued and outstanding
         capital stock of each subsidiary of Diamond Offshore has been duly
         authorized and validly issued and is fully paid and nonassessable,
         except where the failure of such capital stock to have been so
         authorized and issued would not have a material adverse effect on the
         business, operations or financial condition of Diamond Offshore and
         its subsidiaries, taken as a whole; and the capital stock of each
         subsidiary owned by Diamond Offshore, directly or through
         subsidiaries, is owned free from liens, encumbrances and defects,
         except where the failure of Diamond Offshore to so own such capital
         stock would not have a material adverse effect on the business,
         operations, properties or financial condition of Diamond Offshore and
         its subsidiaries, taken as a whole.

              (d)  The Amended Registration Rights Agreement has been duly
         authorized by Diamond Offshore and, on the Closing Date, will be duly
         executed and delivered by Diamond Offshore.

              (e)  The Underlying Securities deliverable upon exchange of the
         Underwritten Securities and all other outstanding shares of capital
         stock of Diamond Offshore have been duly authorized and are validly
         issued, fully paid and nonassessable; the Underlying Securities
         conform to the description thereof contained in the Final Prospectus
         and, when delivered in accordance with the terms of the related
         Underwritten Securities, will conform to the description thereof
         contained in the Final Prospectus as the same may be amended or
         supplemented; and the stockholders of





                                      -8-
<PAGE>   9
         Diamond Offshore have no preemptive rights with respect to the 
         Underlying Securities.

              (f)  Except as disclosed in the Final Prospectus, there are no
         contracts, agreements or understandings between Diamond Offshore and
         any person that would give rise to a valid claim against Diamond
         Offshore or any Underwriter for a brokerage commission, finder's fee
         or other like payment relating to the issuance of the Underwritten
         Securities or the exchange thereof for the Underlying Securities.

              (g)  Except for the Amended Registration Rights Agreement, there
         are no currently effective contracts, agreements or understandings
         between Diamond Offshore and any person granting such person the right
         to require Diamond Offshore to file a registration statement under the
         Act with respect to any securities of Diamond Offshore owned or to be
         owned by such person or to require Diamond Offshore to include such
         securities in any securities being registered pursuant to any
         registration statement filed by Diamond Offshore under the Act.

              (h)  The outstanding shares of common stock of Diamond Offshore,
         including the Underlying Securities, are listed on the New York Stock
         Exchange.

              (i)  No consent, approval, authorization, or order of, or filing
         with, any governmental agency or body or any court is required to be
         obtained by Diamond Offshore for the consummation of the transactions
         contemplated by this Underwriting Agreement or in connection with the
         exchange of the Underwritten Securities for the Underlying Securities,
         except such as have been (or, under the Amended Registration Rights
         Agreement, will have been) obtained and made under the Act and such as
         may be required under state securities laws.

              (j)  The execution, delivery and performance of the Amended
         Registration Rights Agreement and this Underwriting Agreement and
         compliance with the terms and provisions thereof will not conflict
         with or result in a breach or violation of any of the terms or
         provisions of, or constitute a default under, any indenture, mortgage,
         deed of trust, loan agreement or other agreement or instrument to
         which Diamond Offshore or any of its subsidiaries is a party or by
         which Diamond Offshore or any of its subsidiaries is bound, or to
         which any of the property or assets of Diamond Offshore or any of its
         subsidiaries is subject, nor will such action result in any violation
         of the provisions of the charter or bylaws of Diamond Offshore or any
         of its subsidiaries or any statute or any order, rule or regulation of
         any court or governmental agency or body having jurisdiction over
         Diamond Offshore or any of its subsidiaries or the property of Diamond
         Offshore or any of its subsidiaries except, in each case other than
         with respect to such charter or bylaws, which conflict, breach or
         default or violation would not impair Diamond Offshore's or any of its
         subsidiaries' ability to





                                      -9-
<PAGE>   10
         perform the obligations hereunder or have any material adverse effect
         upon the consummation of the transactions contemplated hereby or any
         Underwriter.

              (k)  This Underwriting Agreement has been duly authorized,
         executed and delivered by Diamond Offshore.

              (l)  Except as disclosed in the Exchange Act Reports or the Final
         Prospectus and except for Permitted Liens, as such term is defined
         below, Diamond Offshore and its subsidiaries have good and marketable
         title to all offshore drilling rigs described as being owned by them
         in the Exchange Act Reports or the Final Prospectus, and good and
         marketable title to all real property and all other properties and
         assets owned by them, in each case free from liens, encumbrances and
         defects that would materially affect the value thereof, taken as a
         whole, or materially interfere with the use made or to be made thereof
         by them; and except as disclosed in the Exchange Act Reports or the
         Final Prospectus, Diamond Offshore and its subsidiaries hold any
         leased real or personal property under valid and enforceable leases
         with no exceptions to such validity or enforceability that would
         materially interfere with the use made or to be made thereof by them.
         "Permitted Liens" means (i) liens for taxes not yet due or liens that
         have not been filed for taxes that are being contested in good faith
         and by appropriate proceedings diligently prosecuted; (ii) carriers',
         warehousemen's, mechanics', materialmen's, repairmen's, maritime,
         statutory or other like liens arising in the ordinary course of
         business that are not overdue for more than 30 days or that are being
         contested in good faith and by appropriate proceedings diligently
         prosecuted; (iii) pledges or deposits in connection with workmen's
         compensation, unemployment insurance and other social security
         legislation; and (iv) deposits to secure the performance of bids,
         contracts in the ordinary course of business (other than for borrowed
         money), leases, statutory obligations, surety and appeal bonds and
         performance bonds, and other obligations of a like nature that are
         incurred in the ordinary course of business.

              (m)  Diamond Offshore and its subsidiaries possess adequate
         certificates, authorities or permits issued by appropriate
         governmental agencies or bodies necessary to conduct the business now
         operated by them in all material respects and have not received any
         notice of proceedings relating to the revocation or modification of
         any such certificate, authority or permit that, if determined
         adversely to Diamond Offshore or any of its subsidiaries, would
         individually or in the aggregate have a material adverse effect on
         Diamond Offshore and its subsidiaries taken as a whole.

              (n)  No labor dispute with the employees of Diamond Offshore or
         any subsidiary exists or, to the knowledge of Diamond Offshore, is
         imminent that would reasonably be expected to have a material adverse
         effect on Diamond Offshore and its subsidiaries taken as a whole.





                                      -10-
<PAGE>   11
              (o)  Diamond Offshore and its subsidiaries own, possess or can
         acquire on reasonable terms, adequate trademarks, trade names and
         other rights to inventions, know-how, patents, copyrights,
         confidential information and other intellectual property
         (collectively, "intellectual property rights") necessary to conduct
         the business now operated by them, or presently employed by them, and
         have not received any notice of infringement of or conflict with
         asserted rights of others with respect to any intellectual property
         rights that, if determined adversely to Diamond Offshore or any of its
         subsidiaries, would individually or in the aggregate have a material
         adverse effect on Diamond Offshore and its subsidiaries taken as a
         whole.

              (p) Except as disclosed in the Exchange Act Reports or the Final
         Prospectus, neither Diamond Offshore nor any of its subsidiaries is in
         violation of any statute, any rule, regulation, decision or order of
         any governmental agency or body or any court, domestic or foreign,
         relating to the use, disposal or release of hazardous or toxic
         substances or relating to the protection or restoration of the
         environment or human exposure to hazardous or toxic substances
         (collectively, "environmental laws"), owns or operates any real
         property contaminated with any substance that is subject to any
         environmental laws, is liable for any off-site disposal or
         contamination pursuant to any environmental laws, or is subject to any
         claim relating to any environmental laws, which violation,
         contamination, liability or claim would individually or in the
         aggregate have a material adverse effect on Diamond Offshore and its
         subsidiaries taken as a whole; and Diamond Offshore is not aware of
         any pending investigation which might lead to such a claim.

              (q)  There are no pending actions, suits or proceedings against
         or affecting Diamond Offshore, any of its subsidiaries or any of their
         respective properties except as disclosed in the Exchange Act Reports
         or the Final Prospectus, or as individually or in the aggregate do not
         now have and, to the best knowledge of Diamond Offshore, are not
         reasonably expected in the future to have a material adverse effect on
         the condition (financial or other), business, properties or results of
         operations of Diamond Offshore and its subsidiaries taken as a whole,
         or would materially and adversely affect the ability of Diamond
         Offshore to perform its obligations under the Amended Registration
         Rights Agreement or this Underwriting Agreement, or which are
         otherwise material in the context of the sale of the Underwritten
         Securities; and no such actions, suits or proceedings are, to Diamond
         Offshore's knowledge, threatened or contemplated.

              (r)  The financial statements included in the Exchange Act
         Reports present fairly in all material respects the financial position
         of Diamond Offshore and its consolidated subsidiaries as of the dates
         shown and their results of operations and cash flows for the periods
         shown, and such financial statements have been prepared in conformity
         with generally accepted accounting principles in the United States
         applied on a consistent





                                      -11-
<PAGE>   12
         basis; any schedules included in the Exchange Act Reports present
         fairly the information required to be stated therein; and if pro forma
         financial statements are included in the Exchange Act Reports, the
         assumptions used in preparing the pro forma financial statements
         included in the Exchange Act Reports provide a reasonable basis for
         presenting the significant effects directly attributable to the
         transactions or events described therein, the related pro forma
         adjustments give appropriate effect to those assumptions in all
         material respects, and the pro forma columns therein reflect the
         proper application in all material respects of those adjustments to
         the corresponding historical financial statement amounts.

              (s)  Except as disclosed in the Exchange Act Reports, since the
         date of the latest audited financial statements included in the
         Exchange Act Reports there has been no material adverse change, nor
         any development or event involving a prospective material adverse
         change, in the condition (financial or other), business, properties or
         results of operations of Diamond Offshore and its subsidiaries taken
         as a whole, and there has been no dividend or distribution of any kind
         declared, paid or made by Diamond Offshore on any class of its capital
         stock.

              (t)  Diamond Offshore is not and, after giving effect to the
         transactions contemplated by this Underwriting Agreement, will not be
         (i) an "investment company" or a company "controlled" by an
         "investment company" within the meaning of the Investment Company Act
         of 1940, as amended, or (ii) a "holding company" or a "subsidiary
         company" or an "affiliate" of a holding company within the meaning of
         the Public Utility Holding Company Act of 1935, as amended.

              (u)  Neither Diamond Offshore nor any of its affiliates does
         business with the government of Cuba or with any person or affiliate
         located in Cuba within the meaning of Section 517.075, Florida
         Statutes.

              (v)  No consent or approval of any federal governmental agency
         with respect to any federal maritime law matter is required in
         connection with performance by Diamond Offshore of its obligations
         under this Underwriting Agreement, and the execution, delivery, and
         performance by Diamond Offshore and the consummation of the
         transactions contemplated thereby will not violate any existing
         federal maritime laws, including, without limitation, the Shipping
         Act, 1916, as amended, and the rules and regulations of the Maritime
         Administration (MarAd) and the United States Coast Guard.

         2.  Purchase and Sale.  Subject to the terms and conditions and in
reliance upon the representations and warranties set forth herein, the Company
agrees to sell to each Underwriter, and each Underwriter agrees, severally and
not jointly, to purchase from the Company, at the purchase price set forth in
Schedule I hereto the principal amount of the Underwritten Securities set forth
opposite such Underwriter's name in Schedule II hereto, except that, if
Schedule I





                                      -12-
<PAGE>   13
hereto provides for the sale of Securities pursuant to delayed delivery
arrangements, the respective principal amounts of Underwritten Securities to be
purchased by the Underwriters shall be as set forth in Schedule II hereto less
the respective amounts of Contract Securities (as hereinafter defined)
determined as provided below.  Securities to be purchased by the Underwriters
are herein sometimes called the "Underwritten Securities" and Securities to be
purchased pursuant to Delayed Delivery Contracts as hereinafter provided are
herein called "Contract Securities."

         In addition, subject to the terms and conditions herein set forth, the
Company may grant, if so provided in Schedule I, an option to the Underwriters,
severally and not jointly, to purchase up to the number or aggregate principal
amount, as the case may be, of the Option Underwritten Securities set forth
therein at a price per Option Underwritten Security equal to the price per
Initial Underwritten Security, less an amount equal to any dividends or
distributions declared by the Company and paid or payable on the Initial
Underwritten Securities but not payable on the Option Underwritten Securities.
Such option, if granted, will expire 30 days after the date of this
Underwriting Agreement, and may be exercised in whole or in part from time to
time only for the purpose of covering over-allotments which may be made in
connection with the offering and distribution of the Initial Underwritten
Securities upon notice by the Representatives to the Company setting forth the
number or aggregate principal amount, as the case may be, of Option
Underwritten Securities as to which the several Underwriters are then
exercising the option and the time, date and place of payment and delivery for
such Option Underwritten Securities.  Any such time and date of payment and
delivery shall be determined by the Representatives, but shall not be later
than seven full business days after the exercise of said option, nor in any
event prior to the Closing Date, unless otherwise agreed upon by the
Representatives and the Company.  If the option is exercised as to all or any
portion of the Option Underwritten Securities, each of the Underwriters,
severally and not jointly, will purchase that amount which shall bear the same
proportion to the total principal amount of Option Underwritten Securities as
the principal amount of Securities set forth opposite the name of such
Underwriter bears to the aggregate principal amount of Securities set forth in
Schedule II hereto, except to the extent that you determine that such reduction
shall be otherwise than in such proportion and so advise the Company in
writing.

         If so provided in Schedule I hereto, the Underwriters are authorized
to solicit offers to purchase Securities from the Company pursuant to delayed
delivery contracts ("Delayed Delivery Contracts"), substantially in the form of
Schedule III hereto but with such changes therein as the Company may authorize
or approve.  The Underwriters will endeavor to make such arrangements and, as
compensation therefor, the Company will pay to the Representatives, for the
account of the Underwriters, on the Closing Date, the percentage set forth in
Schedule I hereto of the principal amount of the Securities for which Delayed
Delivery Contracts are made.  Delayed Delivery Contracts are to be with
institutional investors, including commercial and savings banks, insurance
companies, pension funds, investment companies and educational and charitable
institutions.  The Company will enter into Delayed Delivery Contracts in all
cases





                                      -13-
<PAGE>   14
where sales of Contract Securities arranged by the Underwriters have been
approved by the Company but, except as the Company may otherwise agree, each
such Delayed Delivery Contract must be for not less than the minimum principal
amount set forth in Schedule I hereto and the aggregate principal amount of
Contract Securities may not exceed the maximum aggregate principal amount set
forth in Schedule I hereto.  The Underwriters will not have any responsibility
in respect of the validity or performance of Delayed Delivery Contracts.  The
principal amount of Securities to be purchased by each Underwriter as set forth
in Schedule II hereto shall be reduced by an amount which shall bear the same
proportion to the total principal amount of Contract Securities as the
principal amount of Securities set forth opposite the name of such Underwriter
bears to the aggregate principal amount of Securities set forth in Schedule II
hereto, except to the extent that you determine that such reduction shall be
otherwise than in such proportion and so advise the Company in writing;
provided, however, that, subject to Section 9 hereof, the total principal
amount of Securities to be purchased by all Underwriters shall be the aggregate
principal amount of Securities set forth in Schedule II hereto less the
aggregate principal amount of Contract Securities.

         3.  Delivery and Payment.  Delivery of and payment for the
Underwritten Securities shall be made at the office, on the date and at the
time specified in Schedule I hereto, which date and time may be postponed by
agreement between the Representatives and the Company or as provided in Section
9 hereof (such date and time of delivery and payment for the Underwritten
Securities being herein called the "Closing Date"). In addition, in the event
that the Underwriters have exercised their option, if any, to purchase any or
all of the Option Underwritten Securities, payment of the purchase price for,
and delivery of such Option Underwritten Securities, shall be made at the
location set forth on Schedule I, or at such other place as shall be agreed
upon by the Representatives and the Company, as specified in the notice from
the Representatives to the Company.

         Payment shall be made to the Company by wire transfer of immediately
available funds to a bank account designated by the Company, against delivery
to the Representatives for the respective accounts of the Underwriters of the
Underwritten Securities to be purchased by them.  It is understood that each
Underwriter has authorized the Representatives, for its account, to accept
delivery of, receipt for, and make payment of the purchase price for, the
Underwritten Securities which it has severally agreed to purchase.  The
Representatives, individually and not as representative of the Underwriters,
may (but shall not be obligated to) make payment of the purchase price for the
Underwritten Securities to be purchased by any Underwriter whose funds have not
been received by the Closing Date, as the case may be, but such payment shall
not relieve such Underwriter from its obligations hereunder.

         Certificates for the Underwritten Securities shall be registered in
such names and in such denominations as the Representatives may request not
less than two full business days in advance of the Closing Date.  The Company
agrees to have the Underwritten Securities available for inspection, checking
and packaging by the Representatives in New York, New York, not later





                                      -14-
<PAGE>   15
than 1:00 p.m. on the business day prior to the Closing Date.

         4.  Agreements.  (a)  The Company agrees with the several Underwriters
that:

                   (i)  Until the earlier of (X) the termination of the
              offering of the Underwritten Securities, and (Y) six months from
              the date of this Underwriting Agreement, the Company will not
              file any amendment (other than amendments resulting from the
              filing of the documents incorporated by reference pursuant to
              Item 12 of Form S-3 under the Act) of the Registration Statement
              or the Final Prospectus unless the Company has furnished you a
              copy for your review prior to filing and will not file any such
              proposed amendment or supplement to which you reasonably object.
              The Company will cause the Final Prospectus to be filed with the
              Commission pursuant to Rule 424. The Company will promptly advise
              the Representatives (A) when the Final Prospectus shall have been
              filed with the Commission pursuant to Rule 424, (B) when any
              amendment to the Registration Statement relating to the
              Underwritten Securities shall have become effective, (C) of any
              request by the Commission for any amendment of the Registration
              Statement or amendment of or supplement to the Final Prospectus
              or for any additional information, (D) of the issuance by the
              Commission of any stop order suspending the effectiveness of the
              Registration Statement or the institution or threatening of any
              proceeding for that purpose and (E) of the receipt by the Company
              of any notification with respect to the suspension of the
              qualification of the Underwritten Securities for sale in any
              jurisdiction or the initiation or threatening of any proceeding
              for such purpose.  The Company will use its best efforts to
              prevent the issuance of any such stop order and, if issued, to
              obtain as soon as possible the withdrawal thereof.

                   (ii)  If, at any time when a prospectus relating to the
              Underwritten Securities is required to be delivered under the
              Act, any event occurs as a result of which, the Final Prospectus
              as then amended or supplemented would include any untrue
              statement of a material fact or omit to state any material fact
              necessary to make the statements therein in the light of the
              circumstances under which they were made not misleading, or if it
              shall be necessary to amend or supplement the Final Prospectus to
              comply with the Act or the Exchange Act or the respective rules
              thereunder, the Company promptly will prepare and file with the
              Commission, subject to the first sentence of paragraph (a)(i) of
              this Section 4, an amendment or supplement which will correct
              such statement or omission or an amendment which will effect such
              compliance.

                   (iii)  The Company will comply with the Act and the Act
              Regulations and the Exchange Act and the Exchange Act Regulations
              so as to permit the completion of the distribution of the
              Underwritten Securities as contemplated in this Underwriting
              Agreement and in the Registration Statement and the Final
              Prospectus.  If at any





                                      -15-
<PAGE>   16
              time when the Final Prospectus is required by the Act or the
              Exchange Act to be delivered in connection with sales of the
              Underwritten Securities, any event shall occur or condition shall
              exist as a result of which it is necessary, in the opinion of
              counsel for the Underwriters or for the Company, to amend the
              Registration Statement in order that the Registration Statement
              will not contain an untrue statement of a material fact or omit
              to state a material fact required to be stated therein or
              necessary to make the statements therein not misleading or to
              amend or supplement the Final Prospectus in order that the Final
              Prospectus will not include an untrue statement of a material
              fact or omit to state a material fact necessary in order to make
              the statements therein not misleading in the light of the
              circumstances existing at the time it is delivered to a
              purchaser, or if it shall be necessary, in the opinion of such
              counsel, at any such time to amend the Registration Statement or
              amend or supplement the Final Prospectus in order to comply with
              the requirements of the Act or the Act Regulations, the Company
              will promptly prepare and file with the Commission, subject to
              Section 4(a)(i), such amendment or supplement as may be necessary
              to correct such statement or omission or to make the Registration
              Statement or the Final Prospectus comply with such requirements,
              and the Company will furnish to the Underwriters, without charge,
              such number of copies of such amendment or supplement as the
              Underwriters may reasonably request.

                   (iv)  The Company will make generally available to its
              securityholders and to the Representatives not later than 90 days
              after the end of the 12-month period beginning at the end of the
              current fiscal quarter of the Company an earnings statement or
              statements of the Company and its subsidiaries which will satisfy
              the provisions of Section 11(a) of the Act and Rule 158 under the
              Act.

                   (v)  The Company will furnish to the Representatives and
              counsel for the Underwriters, without charge, copies of the
              Registration Statement (including exhibits thereto or
              incorporated by reference therein and documents incorporated or
              deemed to be incorporated by reference therein), and each
              amendment to the Registration Statement which shall become
              effective on or prior to the Closing Date and, so long as
              delivery of a prospectus by an Underwriter or dealer may be
              required by the Act, as many copies of any Preliminary Prospectus
              and the Final Prospectus and any amendments thereof and
              supplements thereto as the Representatives may reasonably request
              and the Company hereby consents to the use of such copies for
              purposes permitted by the Act.  The Company will pay the expenses
              of printing or other production of all documents relating to the
              offering.  The Final Prospectus and copies of the Registration
              Statement and each amendment thereto furnished to the
              Underwriters will be identical to any electronically transmitted
              copies thereof filed with the Commission pursuant to EDGAR,
              except to the extent permitted by Regulation S-T.





                                      -16-
<PAGE>   17
                   (vi)  The Company will arrange for the qualification of the
              Underwritten Securities for sale under the laws of such
              jurisdictions as the Representatives may reasonably designate,
              will maintain such qualifications in effect so long as required
              for the distribution of the Underwritten Securities and will
              arrange for the determination of the legality of the Underwritten
              Securities for purchase by institutional investors; provided,
              however, the Company shall not be obligated to file any general
              consent to service of process under the laws of any such
              jurisdiction, subject itself to taxation as doing business in any
              such jurisdiction, or qualify to do business as a foreign
              corporation in any such jurisdiction.  The Company will pay all
              reasonable expenses (including fees and disbursements of counsel)
              in connection with such qualification (such expenses, fees and
              disbursements not to exceed in the aggregate $5,000).

                   (vii)  The Company, during the period when the Final
              Prospectus is required to be delivered under the Act or the
              Exchange Act, will file all documents required to be filed with
              the Commission pursuant to Section 13, 14 or 15 of the Exchange
              Act within the time periods required by the Exchange Act and the
              Exchange Act Regulations.

                   (viii)  During the period beginning from the date of the
              Final Prospectus and continuing to and including the date 90 days
              after the date of the Final Prospectus, neither the Company nor
              its subsidiaries will offer, sell, contract to sell or otherwise
              dispose of any shares of the Underlying Securities or any
              securities of Diamond Offshore or the Company which are
              substantially similar to the Underwritten Securities or the
              Underlying Securities or which are convertible into or
              exchangeable for the Underlying Securities or securities which
              are substantially similar to the Underwritten Securities or
              shares of the Underlying Securities (the "lock-up restriction")
              without the prior written consent of the Representatives (other
              than (i) pursuant to employee stock option plans existing, or on
              the conversion or exchange of convertible or exchangeable
              securities outstanding, on the date of the Final Prospectus or
              (ii) the issuance of securities registered on Form S-4 issued in
              connection with an acquisition, merger or similar transaction, in
              which event an acquiror of such securities who is, or would by
              virtue of such acquisition be, an affiliate of the issuer, agrees
              to the foregoing lock-up restriction for the remainder of the
              90-day period), except for the Underwritten Securities offered in
              connection with the offering.

                   (ix)  The Company will keep available at all times such
              number of shares of Underlying Securities sufficient to enable
              the Company to satisfy its obligations under the terms of the
              Underwritten Securities.

                   (x)  The Company will use reasonable efforts to cause its 
              ownership of shares of





                                      -17-
<PAGE>   18
              the common stock, par value $.01 per share, of Diamond Offshore
              ("Diamond Offshore Common Stock") not to be less than 50% of the
              issued and outstanding shares of Diamond Offshore Common Stock at
              the Closing Date.

              (b)  Diamond Offshore agrees with the several Underwriters that:

                   (i)  Diamond Offshore shall cooperate with the Company to
              effect compliance with the covenants and agreements set forth in
              Sections (4)(a)(i),(ii) and (iii).

                   (ii)  Until the termination of the offering of the
              Underwritten Securities and the Underlying Securities, Diamond
              Offshore will file all documents required to be filed with the
              Commission pursuant to Sections 13, 14 or 15 of the Exchange Act
              within the time periods required by the Exchange Act and the
              Exchange Act Regulations.

                   (iii)  During the period beginning from the date of the
              Final Prospectus and continuing to and including the date 90 days
              after the date of the Final Prospectus, neither Diamond Offshore
              nor its subsidiaries will offer, sell, contract to sell or
              otherwise dispose of any shares of the Underlying Securities or
              any securities of Diamond Offshore or the Company which are
              substantially similar to the Underwritten Securities or the
              Underlying Securities or which are convertible into or
              exchangeable for the Underlying Securities or securities which
              are substantially similar to the Underwritten Securities or
              shares of the Underlying Securities (the "lock-up restriction")
              without the prior written consent of the Representatives (other
              than (i) pursuant to employee stock option plans existing, or on
              the conversion or exchange of convertible or exchangeable
              securities outstanding, on the date of the Final Prospectus or
              (ii) the issuance of securities registered on Form S-4 issued in
              connection with an acquisition, merger or similar transaction, in
              which event an acquiror of such securities who is, or would by
              virtue of such acquisition be, an affiliate of the issuer, agrees
              to the foregoing lock-up restriction for the remainder of the
              90-day period), except for the Underwritten Securities offered in
              connection with the offering.

                   (iv)  Diamond Offshore hereby covenants with the
              Underwriters that it shall comply with all its obligations under
              the Amended Registration Rights Agreement, including without
              limitation all provisions relating to the timely filing with (and
              the declaration of effectiveness by) the Commission of a shelf
              registration statement in respect of the Underlying Securities.

         5.   Offering by the Underwriters.  It is understood that the several
Underwriters propose to offer the Underwritten Securities for sale to the
public as set forth in the Final Prospectus.





                                      -18-
<PAGE>   19
         6.   Payment of Expenses.  The Company agrees with the Underwriters 
that it will pay or cause the payment on its behalf of all expenses incident to
the performance of its obligations under this Underwriting Agreement, including
(a) the preparation, printing, filing and mailing of the Registration Statement
as originally filed and of each amendment thereto; (b) the printing of this
Underwriting Agreement, any applicable Indentures and any blue sky and legal
investment surveys and any other documents in connection with the offering,
purchase, sale and delivery of the Underwritten Securities; (c) the
preparation, issuance, and delivery to the Underwriters of the certificates for
the Underwritten Securities and any related Underlying Securities, any
certificates for the Underwritten Securities or such Underlying Securities, to
the Underwriters, including any transfer taxes and any stamp or other duties
payable upon the sale, issuance or delivery of the Underwritten Securities to
the Underwriters; (d) the fees and disbursements of the Company's counsel and
accountants; (e) the qualification of the Securities under state securities
laws in accordance with this Underwriting Agreement, including filing fees and
the fee and disbursements of your counsel in connection therewith and in
connection with the preparation of the blue sky and legal investment surveys in
accordance with Section 4(a)(vi); (f) the printing and delivery to you of
copies of the Registration Statement as originally filed and of each amendment
thereto, of the Preliminary Prospectuses, and of the Final Prospectus and any
amendments or supplements thereto; (g) the costs of preparing the Securities;
(h) the fees, if any, of the National Association of Securities Dealers, Inc.
and the New York Stock Exchange; (i) the fees and expenses of the Trustee,
including the fees and disbursements of counsel for the Trustee in connection
with the Indenture; (j) if the Company determines to request rating of the
Underwritten Securities by particular rating agencies, any fees payable in
connection with such rating of the Underwritten Securities by such rating
agencies; and (k) the fees and expenses incurred, if any, in connection with
the listing of the Underwritten Securities.  Diamond Offshore agrees with the
Underwriters that it will pay or cause the payment on its behalf of all
expenses incident to the performance of its obligations under this Underwriting
Agreement.  It is understood that the Company and Diamond Offshore have
separately agreed between themselves as to their respective responsibilities to
pay expenses in the Amended Registration Rights Agreement.  The Underwriters
agree to make a payment to the Company in lieu of reimbursement of expenses
incurred in connection with the offering and sale of the Underwritten
Securities.

         7.  Conditions to the Obligations of the Underwriters.  The
obligations of the Underwriters to purchase the Underwritten Securities shall
be subject to the accuracy of the representations and warranties on the part of
the Company and Diamond Offshore contained herein as of the date hereof, as of
the date of the effectiveness of any amendment to the Registration Statement
filed prior to the Closing Date (including the filing of any document
incorporated by reference therein), as of the date of the filing by Diamond
Offshore of any document under the Exchange Act and the Exchange Act
Regulations, and as of the Closing Date, to the accuracy of the statements of
the Company and Diamond Offshore made in any certificates pursuant to the
provisions hereof, to the performance by each of the Company and Diamond
Offshore of its obligations hereunder and to the following additional
conditions:





                                      -19-
<PAGE>   20
              (a)  The Registration Statement, including any Rule 462(b)
         Registration Statement, has become effective under the Act and no stop
         order suspending the effectiveness of the Registration Statement, as
         amended from time to time, shall have been issued and no proceedings
         for that purpose shall have been instituted or threatened, and any
         request on the part of the Commission for additional information shall
         have been complied with to the reasonable satisfaction of counsel to
         the Underwriters.  A prospectus containing information relating to the
         description of the Underwritten Securities and any related Underlying
         Securities, the specific method of distribution and similar matters
         shall have been filed with the Commission in accordance with Rule
         424(b) (or any required post-effective amendment providing such
         information shall have been filed and declared effective in accordance
         with the requirements of Rule 430A), or, if the Company has elected to
         rely upon Rule 434 of the Act Regulations, a Term Sheet including the
         Rule 434 Information shall have been filed with the Commission in
         accordance with Rule 424(b)(7).

              (b)  The Company shall have furnished to the Representatives the
         opinion of Barry Hirsch, General Counsel for the Company, dated the
         Closing Date, to the effect that:

                   (i)  the Company has been duly incorporated and is validly
              existing as a corporation in good standing under the laws of
              Delaware, with full corporate power and authority to own, lease
              and operate its properties and conduct its business as described
              in the Final Prospectus and to enter into and perform its
              obligations under, or as contemplated under, the Underwriting
              Agreement, and is duly qualified to do business as a foreign
              corporation and is in good standing under the laws of each
              jurisdiction which requires such qualification wherein it owns or
              leases material properties or conducts material business where
              the failure to be in good standing or so qualified would result
              in a Material Adverse Effect;

                   (ii)  each of Lorillard, Inc., CNA Financial Corporation and
              Diamond Offshore (each a "Subsidiary" and together the
              "Subsidiaries") has been duly incorporated and is validly
              existing as a corporation in good standing under the laws of the
              jurisdiction in which it is chartered or organized, with full
              corporate power and authority to own its properties and conduct
              its business as described in the Final Prospectus, and is duly
              qualified to do business as a foreign corporation and is in good
              standing under the laws of each jurisdiction which requires such
              qualification wherein it owns or leases material properties or
              conducts material business where the failure to be in good
              standing or so qualified would have a Material Adverse Effect;

                   (iii)  all the outstanding shares of capital stock of each
              Subsidiary that are owned by the Company have been duly and
              validly authorized and issued and are fully paid and
              nonassessable, and, except as otherwise set forth in the Final
              Prospectus, all





                                      -20-
<PAGE>   21
              outstanding shares of capital stock of the Subsidiaries are owned
              by the Company either directly or through wholly owned
              subsidiaries free and clear of any perfected security interest
              and, to the knowledge of such counsel, after due inquiry, any
              other security interests, claims, liens or encumbrances;

                   (iv)  the Underwritten Securities conform in all material
              respects to the description thereof contained in the Final
              Prospectus;

                   (v)  the Underwritten Securities have been duly authorized
              by the Company for issuance and sale pursuant to the Underwriting
              Agreement.  The Underwritten Securities, when issued and
              authenticated in the manner provided for in the applicable
              Indenture and delivered against payment of the consideration
              therefor specified in the Underwriting Agreement, will constitute
              valid and legally binding obligations of the Company, enforceable
              against the Company in accordance with their terms, except as the
              enforcement thereof may be limited by bankruptcy, insolvency,
              reorganization, moratorium or other similar laws relating to or
              affecting creditors' rights generally or by general equitable
              principles, and except further as enforcement thereof may be
              limited by governmental authority to limit, delay or prohibit the
              making of payments outside the United States.  The Underwritten
              Securities are in the form contemplated by, and each registered
              holder thereof is entitled to the benefits of, the applicable
              Indenture;

                   (vi)  the applicable Indenture has been duly authorized,
              executed and delivered by the Company and (assuming due
              authorization, execution and delivery thereof by the applicable
              Trustee) constitutes a valid and legally binding agreement of the
              Company, enforceable against the Company in accordance with its
              terms, except as the enforcement thereof may be limited by
              bankruptcy, insolvency, reorganization, moratorium or other
              similar laws relating to or affecting creditors' rights generally
              or by general equitable principles;

                   (vii)  the Amended Registration Rights Agreement has been
              duly authorized, executed and delivered by the Company;

                   (viii)  there is no pending or, to the best knowledge of
              such counsel, threatened action, suit or proceeding before any
              court or governmental agency, authority or body or any arbitrator
              involving the Company or any of its subsidiaries, of a character
              required to be disclosed in the Registration Statement which is
              not adequately disclosed in the Final Prospectus, and there is no
              franchise, contract or other document of a character required to
              be described in the Registration Statement or Final Prospectus,
              or to be filed as an exhibit, which is not described or filed as
              required; and the statements included or incorporated in the
              Final Prospectus





                                      -21-
<PAGE>   22
              describing any legal proceedings or material contracts or
              agreements relating to the Company fairly summarize such matters
              in all material respects;

                   (ix)  the Registration Statement and any amendments thereto
              have become effective under the Act; to the best knowledge of
              such counsel, no stop order suspending the effectiveness of the
              Registration Statement, as amended, has been issued, no
              proceedings for that purpose have been instituted or threatened,
              and the Registration Statement, the Final Prospectus and each
              amendment thereof or supplement thereto as of their respective
              effective or issue dates (other than the financial statements and
              other financial and statistical information contained therein as
              to which such counsel need express no opinion) complied as to
              form in all material respects with the applicable requirements of
              the Act and the Exchange Act and the respective rules thereunder;
              and such counsel has no reason to believe that the Registration
              Statement, or any amendment thereof, at the time it became
              effective and at the date of this Underwriting Agreement,
              contained any untrue statement of a material fact or omitted to
              state any material fact required to be stated therein or
              necessary to make the statements therein not misleading or that
              the Final Prospectus, as amended or supplemented, as of its date
              and as of the date hereof, includes any untrue statement of a
              material fact or omits to state a material fact necessary to make
              the statements therein, in light of the circumstances under which
              they were made, not misleading;

                   (x)  this Underwriting Agreement has been duly authorized,
              executed and delivered by the Company;

                   (xi)  no consent, approval, authorization or order of any
              court or governmental agency or body is required for the
              consummation by the Company of the transactions contemplated
              herein or in the Delayed Delivery Contracts, except such as have
              been obtained under the Act and such as may be required under the
              blue sky laws of any jurisdiction in connection with the purchase
              and distribution of the Underwritten Securities by the
              Underwriters and such other approvals (specified in such opinion)
              as have been obtained;

                   (xii)  neither the issue and sale of the Underwritten
              Securities, nor the consummation of any other of the transactions
              herein contemplated nor the fulfillment of the terms hereof or of
              any Delayed Delivery Contracts will conflict with, result in a
              breach of, or constitute a default under the Restated Certificate
              of Incorporation or By-laws of the Company or the terms of any
              indenture or other agreement or instrument known to such counsel
              and to which the Company is a party or bound, or any order or
              regulation known to such counsel to be applicable to the Company
              of any court, regulatory body, administrative agency,
              governmental body or arbitrator having jurisdiction over the
              Company; and





                                      -22-
<PAGE>   23
                   (xiii)  the Company is not now, and upon the sale of the
              Underwritten Securities to be sold by it hereunder and
              application of the net proceeds from such sale as described in
              the Final Prospectus under "Use of Proceeds" will not be, an
              "investment company" within the meaning of the Investment Company
              Act of 1940, as amended.

              In rendering such opinion, such counsel may rely (A) as to
         matters involving the application of laws of any jurisdiction other
         than the corporate laws of the State of Delaware and the laws of the
         State of New York or the United States, to the extent deemed proper
         and specified in such opinion, upon the opinion of other counsel of
         good standing believed to be reliable and who are satisfactory to
         counsel for the Underwriters and (B) as to matters of fact, to the
         extent deemed proper, on certificates of responsible officers of the
         Company and public officials.

              (c)(I)  The Representatives shall have received an opinion, dated
         such Closing Date, of Weil, Gotshal & Manges LLP, counsel to Diamond
         Offshore, to the effect that:

                   (i)  Diamond Offshore is a corporation duly organized,
              validly existing and in good standing under the laws of the State
              of Delaware, and has all requisite corporate power and authority
              to own, lease and operate its properties and to carry on its
              business as described in the Final Prospectus;

                   (ii)  all of the outstanding shares of Diamond Offshore
              Common Stock (including the Underlying Securities) have been duly
              authorized and validly issued, are fully paid and non-assessable,
              are free of any preemptive rights pursuant to law or Diamond
              Offshore's Restated Certificate of Incorporation and conform as
              to legal matters in all material respects to the description
              thereof contained in the Final Prospectus;

                   (iii)  Diamond Offshore has all requisite corporate power
              and authority to execute and deliver each of the Underwriting
              Agreement and the Amended Registration Rights Agreement and to
              perform its obligations thereunder.  The execution, delivery and
              performance of each of the Underwriting Agreement and the Amended
              Registration Rights Agreement have been duly authorized by all
              necessary corporate action on the part of Diamond Offshore.  Each
              of the Underwriting Agreement and the Amended Registration Rights
              Agreement has been duly executed and delivered by Diamond
              Offshore;

                   (iv)  the execution, delivery and performance by Diamond
              Offshore of each of the Underwriting Agreement and the Amended
              Registration Rights Agreement and the compliance by Diamond
              Offshore with the provisions of each of the Underwriting
              Agreement and the Amended Registration Rights Agreement and the





                                      -23-
<PAGE>   24
              consummation of the transactions contemplated thereby will not
              conflict with, constitute a default under or result in a breach
              or violation of (a) any of the terms, conditions or provisions of
              the Restated Certificate of Incorporation or Amended By-Laws, as
              amended, of Diamond Offshore, (b) any New York, Texas, Delaware
              corporate or federal law or regulation (other than federal and
              state securities or blue sky laws, as to which such counsel need
              express no opinion in this sentence, and the Shipping Act, 1916,
              as amended, as to which such counsel need express no opinion), or
              (c) any judgment, writ, injunction, decree, order or ruling of
              any federal or state court or governmental authority binding on
              Diamond Offshore or any of it properties which remains
              unsatisfied and unperformed on the Closing Date and of which such
              counsel is aware, except in each case other than with respect to
              clause (a), any such conflict, default, breach or violation as
              would not impair Diamond Offshore's ability to perform its
              obligations under the Underwriting Agreement or the Amended
              Registration Rights Agreement or have any material adverse effect
              upon the consummation of the transactions contemplated by the
              Underwriting Agreement or the Amended Registration Rights
              Agreement;

                   (v)  no consent, approval, waiver, license, order or
              authorization or other action by or filing with any New York,
              Texas, Delaware corporate or federal governmental agency, body or
              court is required in connection with the execution and delivery
              by Diamond Offshore of the Underwriting Agreement or the Amended
              Registration Rights Agreement, or for the consummation by Diamond
              Offshore of the transactions contemplated thereby, except for
              filings and other action required pursuant to federal and state
              securities or blue sky laws, as to which such counsel need
              express no opinion, or the Shipping Act, 1916, as amended, as to
              which such counsel need express no opinion, and those already
              obtained and made under the Act or the Delaware General
              Corporation Law ("DGCL");

                   (vi)  Diamond Offshore is not (A) an "investment company" or
              an entity "controlled" by an "investment company" under the
              Investment Company Act, as amended, and the rules and regulations
              promulgated by the Commission thereunder (the "Investment Company
              Act") or (B) a "holding company" or a "subsidiary company" or an
              "affiliate" of a holding company within the meaning of the Public
              Utility Holding Company Act of 1935, as amended, and the rules
              and regulations promulgated by the Commission thereunder (the
              "Holding Company Act") (in rendering such opinion, such counsel
              may assume that the Company (x) is not and is not controlled by
              an "investment company" under the Investment Company Act and (y)
              is not a "holding company" or a "subsidiary company" or an
              "affiliate" of a holding company under the Holding Company Act);

                   (vii)  the statements in the Final Prospectus under the
              caption "Description of Diamond Offshore Capital Stock", insofar
              as they constitute descriptions of





                                      -24-
<PAGE>   25
              Diamond Offshore Common Stock or refer to statements of laws or
              legal conclusions under the DGCL, constitute fair summaries
              thereof in all material respects. The statements in the Final
              Prospectus under the caption "The Company and Relationship with
              Diamond Offshore", insofar as they constitute descriptions of the
              Amended Registration Rights Agreement, constitute fair summaries
              thereof in all material respects;

              In addition, such counsel shall state that such counsel has
         participated in conferences with officers and other representatives of
         the Company and Diamond Offshore, independent public accountants for
         Diamond Offshore, representatives of the Underwriters and
         representatives of counsel for the Underwriters, at which conferences
         the contents of the Registration Statement and the Final Prospectus
         and related matters were discussed, and, although such counsel has not
         independently verified and is not passing upon and assumes no
         responsibility for the accuracy, completeness or fairness of such
         statements contained in the Registration Statement or the Final
         Prospectus, such counsel shall advise you, on the basis of the
         foregoing that no facts have come to such counsel's attention which
         lead such counsel to believe that the Final Prospectus, as of the date
         of the Underwriting Agreement or as of such Closing Date contained or
         contains an untrue statement of a material fact or omitted to state
         any material fact necessary in order to make the statements therein,
         in the light of the circumstances under which they were made, not
         misleading (it being understood that such counsel need only express
         such views in respect of information relating to Diamond Offshore that
         is included in the Final Prospectus and need express no opinion as to
         the financial statements and related notes or the other financial,
         statistical and accounting data stated or omitted in the Final
         Prospectus);

         (c)(II)  The Representatives shall have received an opinion, dated
     such Closing Date, of the Vice President and General Counsel of Diamond
     Offshore, to the effect that:

              (i)  Diamond Offshore is duly qualified to transact business as a
         foreign corporation in good standing in all jurisdictions other than
         the State of Delaware in which its ownership or lease of property or
         the conduct of its business requires such qualification, except those
         jurisdictions where the failure to be so qualified would not have a
         material adverse effect on the business, operations or financial
         condition of Diamond Offshore and its subsidiaries taken as a whole;

              (ii) all of the issued and outstanding shares of capital stock of
         each subsidiary of Diamond Offshore listed on Schedule III hereto
         (each, a "DO Subsidiary" and collectively the "DO Subsidiaries") are
         owned, directly or indirectly, of record and beneficially by Diamond
         Offshore, free and clear of all liens, claims, limitations on voting
         rights, options, security interests and other encumbrances and have
         been duly authorized, validly issued, and are fully paid and
         nonassessable, except to the extent that





                                      -25-
<PAGE>   26
         any such liens, claims, limitations, options, security interests and
         other encumbrances, individually or in the aggregate, would not have a
         material adverse effect on the business, operations or financial
         condition of Diamond Offshore and its subsidiaries, taken as a whole;

              (iii) each DO Subsidiary is a corporation, duly organized,
         validly existing and in good standing under the laws of its
         jurisdiction of incorporation.  Each DO Subsidiary is duly qualified
         to transact business and is in good standing as a foreign corporation
         in each state listed by such DO Subsidiary's name on Schedule III
         hereto, such states being the only states in which each DO Subsidiary
         is required to be qualified, except where the failure to be so
         qualified would not have a material adverse effect on the business,
         operations or financial condition of Diamond Offshore and its
         subsidiaries, taken as a whole;

              (iv) no consent or approval of any federal governmental agency
         with respect to any federal maritime law matter is required in
         connection with performance by Diamond Offshore of its obligations
         under the Underwriting Agreement or the Amended Registration Rights
         Agreement; and the execution, delivery, and performance by Diamond
         Offshore and the consummation of the transactions contemplated thereby
         will not violate any existing federal maritime laws, including,
         without limitation, the Shipping Act, 1916, as amended, and the rules
         and regulations of the Maritime Administration (MarAd) and the United
         States Coast Guard; and

              (v)  there is no pending or, to the best knowledge of such
         counsel, threatened action, suit or proceeding before any court or
         governmental agency, authority or body or any arbitrator involving
         Diamond Offshore or any DO Subsidiary of a character required to be
         disclosed in the Registration Statement which is not adequately
         disclosed in the Final Prospectus; and the statements included or
         incorporated in the Final Prospectus describing any legal proceedings
         relating to Diamond Offshore fairly summarize such matters in all
         material respects.

         In rendering such opinion, such Vice President and General Counsel may
     rely as to the incorporation of Diamond Offshore, the authorization,
     execution and delivery of the Underwriting Agreement and the Amended
     Registration Rights Agreement and all other matters acceptable to the
     Representatives upon an opinion of counsel satisfactory to the
     Representatives, a copy of which shall be delivered concurrently with the
     opinion of such Vice President and General Counsel.

         The Representatives shall have also received an opinion, dated such
     Closing Date, of Nabarro Nathanson, special English counsel to Diamond
     Offshore, to the effect that each of Diamond Offshore Limited and Diamond
     Offshore (UK) Limited, each of which is a subsidiary of Diamond Offshore
     incorporated under the laws of the United Kingdom, (i) is





                                      -26-
<PAGE>   27
     duly incorporated and validly exists under the laws of England and Wales
     and (ii) has all requisite corporate power and authority to own, operate
     and lease its properties and to carry on its business as now carried on.

         (d)  The Representatives shall have received from each of Mayer, Brown
     & Platt, Andrews & Kurth L.L.P., and Sullivan & Cromwell, counsel for the
     Underwriters, such opinions, dated the Closing Date, with respect to the
     incorporation of the Company and of Diamond Offshore, the validity of the
     Indenture, the Securities and the Underlying Securities, the Registration
     Statement, the Final Prospectus and other related matters as the
     Representatives may reasonably require, and the Company and Diamond
     Offshore shall have furnished to such counsel such documents as they
     request for the purpose of enabling them to pass upon such matters.

         (e)  The Company shall have furnished to the Representatives a
     certificate of a Co-Chairman of the Board, the President or a Vice
     President, and the principal financial or accounting officer of the
     Company, dated the Closing Date, to the effect that the signers of such
     certificate have carefully examined the Registration Statement, the Final
     Prospectus and this Underwriting Agreement and that:

              (i)  the representations and warranties of the Company in this
         Underwriting Agreement are true and correct in all material respects
         on and as of the Closing Date with the same effect as if made on the
         Closing Date and the Company has complied with all the agreements and
         satisfied all the conditions on its part to be performed or satisfied
         at or prior to the Closing Date;

              (ii)  no stop order suspending the effectiveness of the
         Registration Statement, as amended, has been issued and no proceedings
         for that purpose have been instituted or, to the Company's knowledge,
         threatened; and

              (iii)  since the date of the most recent financial statements
         included in the Company's quarterly report on Form 10-Q for the
         quarter ended June 30, 1997, there has been no Material Adverse
         Effect, except as set forth in the Final Prospectus.

         (f)  Diamond Offshore shall have furnished to the Representatives a
     certificate, dated the Closing Date, of the President, any Senior Vice
     President, the Treasurer or any Vice President and a principal financial
     or accounting officer of Diamond Offshore in which such officers, to the
     best of their knowledge after reasonable investigation, shall state that
     the representations and warranties of Diamond Offshore in this
     Underwriting Agreement are true and correct, that Diamond Offshore has
     complied with all agreements and satisfied all conditions on its part to
     be performed or satisfied hereunder at or prior to such Closing Date, and
     that, subsequent to the date of the most recent financial statements in
     the Exchange Act Reports, there has been no material adverse change, nor
     any development or event





                                      -27-
<PAGE>   28
     involving a prospective material adverse change, in the condition
     (financial or other), business, properties or results of operations of
     Diamond Offshore and its subsidiaries taken as a whole except as set forth
     in or contemplated by the Final Prospectus or as described in such
     certificate.

         (g)   At the Closing Date, the Company's independent accountants shall
     have furnished to the Representatives a letter or letters (which may refer
     to letters previously delivered to the Representatives), dated as of the
     Closing Date, in form and substance satisfactory to the Representatives,
     confirming that they are independent accountants within the meaning of the
     Act and the Exchange Act and the respective applicable published rules and
     regulations thereunder, that the response to Item 10 of the Registration
     Statement is correct insofar as it relates to them and stating in effect
     that:

              (i)  in their opinion the audited financial statements and
         financial statement schedules included or incorporated in the
         Registration Statement and the Final Prospectus and reported on by
         them comply in form in all material respects with the applicable
         accounting requirements of the Act and the Exchange Act and the
         related published rules and regulations;

              (ii)  on the basis of a reading of the amounts included or
         incorporated in the Registration Statement and the Final Prospectus in
         response to Item 301 of Regulation S-K and of the latest unaudited
         financial statements made available by the Company and its
         subsidiaries; carrying out certain specified procedures (but not an
         examination in accordance with generally accepted auditing standards)
         which would not necessarily reveal matters of significance with
         respect to the comments set forth in such letter; a reading of the
         minutes of the meetings of the stockholders, directors and committees
         of the Company and the Subsidiaries; and inquiries of certain
         officials of the Company who have responsibility for financial and
         accounting matters of the Company and its subsidiaries as to
         transactions and events subsequent to the date of the most recent
         audited financial statements incorporated in the Registration
         Statement and the Final Prospectus, nothing came to their attention
         which caused them to believe that:

                   (1)  the amounts in the unaudited Selected Consolidated
              Financial Data and Capitalization, if any, included in the
              Registration Statement and the Final Prospectus and the amounts
              included or incorporated in the Registration Statement and the
              Final Prospectus in response to Item 301 of Regulation S-K, do
              not agree with the corresponding amounts in the audited financial
              statements from which such amounts were derived;

                   (2)  any unaudited financial statements included or
              incorporated in the Registration Statement and the Final
              Prospectus do not comply as to form in all material respects with
              applicable accounting requirements and with the published





                                      -28-
<PAGE>   29
              rules and regulations of the Commission with respect to financial
              statements included or incorporated in quarterly reports on Form
              10-Q under the Exchange Act; and said unaudited financial
              statements are not stated (except as permitted by Form 10-Q) in
              conformity with GAAP applied on a basis substantially consistent
              with that of the audited financial statements included or
              incorporated in the Registration Statement and the Final
              Prospectus; or

                   (3)  with respect to the period subsequent to the date of
              the most recent financial statements included or incorporated in
              the Registration Statement and the Final Prospectus, there were
              any changes, at a specified date not more than five business days
              prior to the date of the letter, in the long-term debt of the
              Company and its subsidiaries or capital stock of the Company or
              decreases in the stockholders' equity of the Company and its
              subsidiaries as compared with the amounts shown on the most
              recent consolidated balance sheet included or incorporated in the
              Registration Statement and the Final Prospectus, or for the
              period from the date of the most recent financial statements
              included or incorporated in the Registration Statement and the
              Final Prospectus to such specified date there were any decreases,
              as compared with the corresponding period in the preceding year,
              in total revenues, or in total or per share amounts of income
              before income taxes or of net income, of the Company and its
              subsidiaries, except in all instances for changes or decreases
              set forth in such letter, in which case the letter shall be
              accompanied by an explanation by the Company as to the
              significance thereof unless said explanation is not deemed
              necessary by the Representatives; and

              (iii)  they have performed certain other specified procedures  as
         a result of which they determined that certain information of an
         accounting, financial or statistical nature (which is limited to
         accounting, financial or statistical information derived from the
         general accounting records of the Company) set forth in the
         Registration Statement and the Final Prospectus and in Exhibit 12 to
         the Registration Statement, including the information included or
         incorporated in Items 1, 6, and 7 of the Company's annual report on
         Form 10-K, incorporated in the Registration Statement and the Final
         Prospectus, or in "Management's Discussion and Analysis of Financial
         Condition and Results of Operations" included or incorporated in the
         Company's quarterly reports on Form 10-Q or in any Form 8-K,
         incorporated in the Registration Statement and the Final Prospectus,
         agrees with the accounting records of the Company and its
         subsidiaries, excluding any questions of legal interpretation.

         References to the Registration Statement and the Final Prospectus in
         this paragraph (g) are to such documents as amended and supplemented
         at the date of the letter.

         (h)  At the Closing Date, Diamond Offshore's independent accountants
     shall have furnished to the Representatives a letter or letters (which may
     refer to letters previously





                                      -29-
<PAGE>   30
     delivered to the Representatives), dated as of the Closing Date, with
     respect to such matters and in such form as the Representatives reasonably
     request.

         In addition, except as provided in Schedule I hereto, at the  time
     this Underwriting Agreement is executed, each of the Company's and Diamond
     Offshore's independent public accountants shall have furnished to the
     Representatives a letter or letters, dated the date of this Underwriting
     Agreement, in form and substance satisfactory to the Representatives, to
     the effect set forth above in paragraphs (g) and (h) of this Section 7.

         (i)  Since the respective dates as of which information is given in
     the Final Prospectus as amended prior to the date of this Underwriting
     Agreement there shall not have been any change in the capital stock or
     long-term debt of the Company or Diamond Offshore or any of their
     respective subsidiaries or any change, or any development involving a
     prospective change, in or affecting the general affairs, management,
     financial position, stockholders' equity or results of operations of the
     Company, Diamond Offshore and their respective subsidiaries, otherwise
     than as set forth or contemplated in the Final Prospectus as amended prior
     to the date of this Underwriting Agreement, the effect of which is in the
     judgment of the Representatives so material and adverse as to make it
     impracticable or inadvisable to proceed with the public offering or the
     delivery of the Underwritten Securities on the terms and in the manner
     contemplated in the Final Prospectus as first amended or supplemented
     relating to the Underwritten Securities;

         (j)  On or after the date of this Underwriting Agreement, no
     downgrading shall have occurred in the rating accorded the Company's or
     Diamond Offshore's debt securities or preferred stock by any "nationally
     recognized statistical rating organization", as that term is defined by
     the Commission for purposes of Rule 436(g)(2) under the Act;

         (k)  On or after the date of this Underwriting Agreement there shall
     not have occurred any of the following: (i) a suspension or material
     limitation in trading in securities generally on the New York Stock
     Exchange; (ii) a suspension or material limitation in trading in the
     Company's or Diamond Offshore's securities on the New York Stock Exchange;
     (iii) a general moratorium on commercial banking activities declared by
     either Federal or New York State authorities; or (iv) the outbreak or
     escalation of hostilities involving the United States or the declaration
     by the United States of a national emergency or war, if the effect of any
     such event specified in this clause (iv) in the judgment of the
     Representatives makes it impracticable or inadvisable to proceed with the
     public offering or the delivery of the Underwritten Securities on the
     terms and in the manner contemplated in the Final Prospectus as first
     amended or supplemented relating to the Underwritten Securities;

         (l)  the Underwritten Securities shall have been  approved for
     listing, subject only to official notice of issuance, on the New York
     Stock Exchange;





                                      -30-
<PAGE>   31
         (m)  the Amended Registration Rights Agreement shall have been duly
     executed and delivered by each of the Company and Diamond Offshore;

         (n)  In the event that the Underwriters are granted an over-allotment
     option by the Company and the Underwriters exercise their option to
     purchase all or any portion of the Option Underwritten Securities, the
     representations and warranties of the Company and of Diamond Offshore
     contained herein and the statements in any certificates furnished by the
     Company or Diamond Offshore hereunder shall be true and correct as of each
     Closing Date, and, at the relevant Closing Date, the Representatives shall
     have received:

              (i)  A certificate, dated such Closing Date, of a Co-Chairman of
         the Board, the President or a Vice President of the Company and the
         principal financial officer or accounting officer of the Company,
         confirming that the certificate delivered at the Closing Date pursuant
         to Section 7(e) hereof remains true and correct as of such Closing
         Date.

              (ii)  A certificate, dated such Closing Date, of the President,
         any Senior Vice President, the Treasurer or any Vice President and a
         principal financial or accounting officer of Diamond Offshore,
         confirming that the certificate delivered at the Closing Date pursuant
         to Section 7(f) hereof remains true and correct as of such Closing
         Date.

              (iii)  The opinion of the General Counsel for the Company, dated
         the Closing Date, relating to the Option Underwritten Securities and
         otherwise to the same effect as the opinion required by Section 7(b)
         hereof.

              (iv)  The opinion of Weil, Gotshal & Manges LLP, dated the
         Closing Date, relating to the Option Underwritten Securities and
         otherwise to the same effect as the opinion required by Section
         7(c)(I) hereof.

              (v)  The opinion of the Vice President and General Counsel of
         Diamond Offshore, dated the Closing Date, relating to the Option
         Underwritten Securities and otherwise to the same effect as the
         opinion required by Section 7(c)(II) hereof.

              (vi)  The opinions of the counsel for the Underwriters, dated the
         Closing Date, relating to the Option Underwritten Securities and
         otherwise to the same effect as the opinions required by Section 7(d)
         hereof.

              (vii)  A letter from the Company's independent accountants, in
         form and substance satisfactory to the Representatives and dated such
         Closing Date, substantially in the same form and substance as the
         letter furnished to the Representatives pursuant to Section 7(g)





                                      -31-
<PAGE>   32
         hereof, except that the "specified date" on the letter furnished
         pursuant to this paragraph shall be a date not more than three
         business days prior to such Closing Date.

              (viii)  A letter from Diamond Offshore's independent accountants,
         in form and substance satisfactory to the Representatives and dated
         such Closing Date, substantially in the same form and substance as the
         letter furnished to the Representatives pursuant to Section 7(h)
         hereof, except that the "specified date" on the letter furnished
         pursuant to this paragraph shall be a date not more than three
         business days prior to such Closing Date.

         (o)  Prior to the Closing Date, each of the Company and Diamond
     Offshore shall have furnished to the Representatives such further
     information, certificates and documents as the Representatives may
     reasonably request.

         (p)  The Company shall have accepted Delayed Delivery Contracts in
     any case where sales of Contract Securities arranged by the Underwriters
     have been approved by the Company.

     If any of the conditions specified in this Section 7 shall not have been
fulfilled in all material respects when and as provided in this Underwriting
Agreement, or if any of the opinions and certificates mentioned above or
elsewhere in this Underwriting Agreement shall not be in all material respects
reasonably satisfactory in form and substance to the Representatives and their
counsel, this Underwriting Agreement and all obligations of the Underwriters
hereunder may be canceled at, or at any time prior to, the Closing Date by the
Representatives.  Notice of such cancellation shall be given to the Company in
writing or by telephone or telecopy confirmed in writing.

     8.  Reimbursement of Underwriters' Expenses.  If the sale of the
Underwritten Securities provided for herein is not consummated because any
condition to the obligations of the Underwriters set forth in Section 7 hereof
is not satisfied, or because of any refusal, inability or failure on the part
of the Company to perform any agreement herein or comply with any provision
hereof other than by reason of a default by any of the Underwriters, or because
of the termination of this Underwriting Agreement under Section 11, the Company
will reimburse the Underwriters severally upon demand for all out-of-pocket
expenses (including reasonable fees and disbursements of counsel) that shall
have been incurred by them in connection with the proposed purchase and sale of
the Underwritten Securities; such obligation of the Company to reimburse the
Underwriters shall serve as the exclusive remedy of the Underwriters with
respect to the Company.

     9.  Indemnification.   (a)  The Company will indemnify and hold harmless
each Underwriter against any losses, claims, damages or liabilities, joint or
several, to which such Underwriter may become subject, under the Act or
otherwise, insofar as such losses, claims, damages or





                                      -32-
<PAGE>   33
liabilities (or actions in respect thereof) arise out of or are based upon an
untrue statement or alleged untrue statement of a material fact contained in
any Preliminary Prospectus, any preliminary prospectus supplement, the
Registration Statement, the Final Prospectus as amended or supplemented and any
other prospectus relating to the Securities, or any amendment or supplement
thereto, or arise out of or are based upon the omission or alleged omission to
state therein a material fact required to be stated therein or necessary to
make the statements therein not misleading, and will reimburse each Underwriter
for any legal or other expenses reasonably incurred by such Underwriter in
connection with investigating or defending any such action or claim as such
expenses are incurred; provided, however, that the Company shall not be liable
in any such case to the extent that any such loss, claim, damage or liability
arises out of or is based upon an untrue statement or alleged untrue statement
or omission or alleged omission made in any Preliminary Prospectus, any
preliminary prospectus supplement, the Registration Statement, the Final
Prospectus as amended or supplemented and any other prospectus relating to the
Securities, or any such amendment or supplement in reliance upon and in
conformity with written information furnished to the Company by any Underwriter
of Underwritten Securities through the Representatives expressly for use in the
Final Prospectus as amended or supplemented relating to such Securities.

     (b)  Diamond Offshore will indemnify and hold harmless each Underwriter
against any losses, claims, damages or liabilities, joint or several, to which
such Underwriter may become subject, under the Act or otherwise, insofar as
such losses, claims, damages or liabilities (or actions in respect thereof)
arise out of or are based upon an untrue statement or alleged untrue statement
of a material fact contained in any Preliminary Prospectus, any preliminary
prospectus supplement, the Registration Statement, the Final Prospectus as
amended or supplemented and any other prospectus relating to the Securities, or
any amendment or supplement thereto, or arise out of or are based upon the
omission or alleged omission to state therein a material fact required to be
stated therein or necessary to make the statements therein not misleading, in
each case to the extent, but only to the extent, that such untrue statement or
alleged untrue statement or omission or alleged omission was made (i) in any
Exchange Act Report that has been included in any current report on Form 8-K
filed by the Company and (ii) under the headings "Diamond Offshore", "Price
Range of Diamond Offshore Common Stock and Dividend Policy" and "Description of
Diamond Offshore Capital Stock" in any Preliminary Prospectus, any preliminary
prospectus supplement, the Registration Statement, the Final Prospectus as
amended or supplemented and any other prospectus relating to the Securities, or
any such amendment or supplement; and will reimburse each Underwriter for any
legal or other expenses reasonably incurred by such Underwriter in connection
with investigating or defending any such action or claim as such expenses are
incurred.

     (c)  Each Underwriter will indemnify and hold harmless the Company against
any losses, claims, damages or liabilities to which the Company may become
subject, under the Act or otherwise, insofar as such losses, claims, damages or
liabilities (or actions in respect thereof) arise out of or are based upon an
untrue statement or alleged untrue statement of a material fact





                                      -33-
<PAGE>   34
contained in any Preliminary Prospectus, any preliminary prospectus supplement,
the Registration Statement, the Final Prospectus as amended or supplemented and
any other prospectus relating to the Securities, or any amendment or supplement
thereto, or arise out of or are based upon the omission or alleged omission to
state therein a material fact required to be stated therein or necessary to
make the statements therein not misleading, in each case to the extent, but
only to the extent, that such untrue statement or alleged untrue statement or
omission or alleged omission was made in any Preliminary Prospectus, any
preliminary prospectus supplement, the Registration Statement, the Final
Prospectus as amended or supplemented and any other prospectus relating to the
Securities, or any such amendment or supplement in reliance upon and in
conformity with written information furnished to the Company by such
Underwriter through the Representatives expressly for use therein; and will
reimburse the Company for any legal or other expenses reasonably incurred by
the Company in connection with investigating or defending any such action or
claim as such expenses are incurred.

     (d)  Promptly after receipt by an indemnified party under subsection (a),
(b) or (c) above of notice of the commencement of any action, such indemnified
party shall, if a claim in respect thereof is to be made against the
indemnifying party under such subsection, notify the indemnifying party in
writing of the commencement thereof; but the omission so to notify the
indemnifying party shall not relieve it from any liability which it may have to
any indemnified party otherwise than under such subsection, except to the
extent a defense or counterclaim has been foreclosed.  In case any such action
shall be brought against any indemnified party and it shall notify the
indemnifying party of the commencement thereof, the indemnifying party shall be
entitled to participate therein and, to the extent that it determines, jointly
with any other indemnifying party similarly notified, to assume the defense
thereof, with counsel satisfactory to such indemnified party (who shall not,
except with the consent of the indemnified party, be counsel to the
indemnifying party), and, after notice from the indemnifying party to such
indemnified party of its election so to assume the defense thereof, the
indemnifying party shall not be liable to such indemnified party under such
subsection for any legal expenses of other counsel or any other expenses, in
each case subsequently incurred by such indemnified party, in connection with
the defense thereof other than reasonable costs of investigation.  No
indemnifying party shall, without the prior written consent of the indemnified
party, effect the settlement or compromise of, or consent to the entry of any
judgment with respect to, any pending or threatened action or claim in respect
of which indemnification or contribution may be sought hereunder (whether or
not the indemnified party is an actual or potential party to such action or
claim) unless such settlement, compromise or judgment (i) includes an
unconditional release of the indemnified party from all liability arising out
of such action or claim and (ii) does not include a statement as to or an
admission of fault, culpability or a failure to act, by or on behalf of any
indemnified party.

     (e)  If the indemnification provided for in this Section 9 is unavailable
to or insufficient to hold harmless an indemnified party under subsection (a),
(b) or (c) above in respect of any losses, claims, damages or liabilities (or
actions in respect thereof) referred to therein, then each





                                      -34-
<PAGE>   35
indemnifying party shall contribute to the amount paid or payable by such
indemnified party as a result of such losses, claims, damages or liabilities
(or actions in respect thereof) in such several proportions as are appropriate
to reflect the relative benefits received by each of the Company and Diamond
Offshore, severally, on the one hand and the Underwriters of the Underwritten
Securities on the other from the offering of the Underwritten Securities to
which such loss, claim, damage or liability (or action in respect thereof)
relates.  If, however, the allocation provided by the immediately preceding
sentence is not permitted by applicable law or if the indemnified party failed
to give the notice required under subsection (d) above and a defense or
counterclaim has been foreclosed, then each indemnifying party shall contribute
to such amount paid or payable by such indemnified party in such proportion as
is appropriate to reflect not only such relative benefits but also the relative
fault of the Company and Diamond Offshore on the one hand and the Underwriters
of the Underwritten Securities on the other in connection with the statements
or omissions which resulted in such losses, claims, damages or liabilities (or
actions in respect thereof), as well as any other relevant equitable
considerations.  The relative benefits received by the Company and Diamond
Offshore, severally, on the one hand and such Underwriters on the other shall
be deemed to be in the same proportion as the total net proceeds from such
offering (before deducting expenses) received by each of the Company and
Diamond Offshore, severally, bear to the total underwriting discounts and
commissions received by such Underwriters.  The relative fault shall be
determined by reference to, among other things, whether the untrue or alleged
untrue statement of a material fact or the omission or alleged omission to
state a material fact relates to information supplied by the Company and
Diamond Offshore on the one hand or such Underwriters on the other and the
parties' relative intent, knowledge, access to information and opportunity to
correct or prevent such statement or omission.  The Company, Diamond Offshore
and the Underwriters agree that it would not be just and equitable if
contribution pursuant to this subsection (e) were determined by pro rata
allocation (even if the Underwriters were treated as one entity for such
purpose) or by any other method of allocation which does not take account of
the equitable considerations referred to above in this subsection (e).  The
amount paid or payable by an indemnified party as a result of the losses,
claims, damages or liabilities (or actions in respect thereof) referred to
above in this subsection (e) shall be deemed to include any legal or other
expenses reasonably incurred by such indemnified party in connection with
investigating or defending any such action or claim.  Notwithstanding the
provisions of this subsection (e), no Underwriter shall be required to
contribute any amount in excess of the amount by which the total price at which
the applicable Underwritten Securities underwritten by it and distributed to
the public were offered to the public exceeds the amount of any damages which
such Underwriter has otherwise been required to pay by reason of such untrue or
alleged untrue statement or omission or alleged omission.  No person guilty of
fraudulent misrepresentation (within the meaning of Section 11(f) of the Act)
shall be entitled to contribution from any person who was not guilty of such
fraudulent misrepresentation.  The obligations of the Underwriters of
Underwritten Securities in this subsection (e) to contribute are several in
proportion to their respective underwriting obligations with respect to such
Securities and not joint.





                                      -35-
<PAGE>   36
     (f)  The obligations of the Company and Diamond Offshore under this
Section 9 shall be in addition to any liability which the Company and Diamond
Offshore may otherwise have and shall extend, upon the same terms and
conditions, to each person, if any, who controls any Underwriter within the
meaning of the Act; and the obligations of the Underwriters under this Section
9 shall be in addition to any liability which the respective Underwriters may
otherwise have and shall extend, upon the same terms and conditions, to each
officer and director of the Company and to each person, if any, who controls
the Company within the meaning of the Act.

     10.  Default by an Underwriter.  If any one or more Underwriters shall
fail to purchase and pay for any of the Underwritten Securities agreed to be
purchased by such Underwriter or Underwriters hereunder and such failure to
purchase shall constitute a default in the performance of its obligations under
this Underwriting Agreement, the remaining Underwriters shall be obligated
severally to take up and pay for (in the respective proportions which the
amount of Underwritten Securities set forth opposite their names in Schedule II
hereto bears to the aggregate amount of Underwritten Securities set forth
opposite the names of all the remaining Underwriters) the Underwritten
Securities which the defaulting Underwriter or Underwriters agreed but failed
to purchase; provided, however, that in the event that the aggregate amount of
Underwritten Securities which the defaulting Underwriter or Underwriters agreed
but failed to purchase shall exceed 10% of the aggregate amount of Underwritten
Securities set forth in Schedule II hereto, the remaining Underwriters shall
have the right to purchase all, but shall not be under any obligation to
purchase any, of the Underwritten Securities, and if such nondefaulting
Underwriters do not purchase all the Underwritten Securities, this Underwriting
Agreement will terminate without liability to any nondefaulting Underwriter or
the Company. In the event of a default by any Underwriter as set forth in this
Section 10, the Closing Date shall be postponed for such period, not exceeding
seven days, as the Representatives shall determine in order that the required
changes in the Registration Statement and the Final Prospectus or in any other
documents or arrangements may be effected.  Nothing contained in this
Underwriting Agreement shall relieve any defaulting Underwriter of its
liability, if any, to the Company and any nondefaulting Underwriter for damages
occasioned by its default hereunder.

     11.  Termination and Liabilities.  (a)  This Underwriting Agreement shall
be subject to termination in the absolute discretion of the Representatives, by
notice given to the Company prior to delivery of and payment for the
Underwritten Securities, if after the date of this Underwriting Agreement and
prior to such time there has occurred a development or event of the kind
specified in Section 7(i), 7(j) or 7(k).

     (b)  If this Underwriting Agreement is terminated pursuant to this Section
11, such termination shall be without liability of any party to any other party
except as provided in Sections 6 and 8 hereof, and provided further that
Sections 1A, 1B, 9 and 12 hereof shall survive such termination and remain in
full force and effect.

     12.  Representations and Indemnities to Survive.  The respective
agreements,





                                      -36-
<PAGE>   37
representations, warranties, indemnities and other statements of the Company or
its officers and of the Underwriters set forth in or made pursuant to this
Underwriting Agreement will remain in full force and effect, regardless of any
investigation made by or on behalf of any Underwriter or the Company or any of
the officers, directors or controlling persons referred to in Section 9 hereof,
and will survive delivery of and payment for the Underwritten Securities.

     13.  Notices.  All communications hereunder will be in writing and
effective only on receipt, and, if sent to the Representatives, will be mailed,
delivered, sent by or telegraphed and confirmed to them, at the address
specified in Schedule I hereto; or, if sent to the Company, will be mailed,
delivered or confirmed telecopy at 667 Madison Avenue, New York, New York
10021, attention of the Corporate Secretary; or, if sent to Diamond Offshore,
will be mailed, delivered or confirmed telecopy at 15415 Katy Freeway, Houston,
Texas 77094, attention of the Corporate Secretary.

     14.  Successors.  This Underwriting Agreement will inure to the benefit of
and be binding upon the parties hereto and their respective successors and the
officers and directors and controlling persons referred to in Section 8 hereof,
and no other person will have any right or obligation hereunder.

     15.  Applicable Law.  This Underwriting Agreement will be governed by and
construed in accordance with the laws of the State of New York.

     16.  Counterparts.  This Underwriting Agreement may be signed in various
counterparts which together shall constitute one and the same instrument.





                                      -37-
<PAGE>   38
         If the foregoing is in accordance with your understanding of our
agreement, please sign and return to us the enclosed duplicate hereof,
whereupon this letter and your acceptance shall represent a binding agreement
among the Company, Diamond Offshore and the Underwriter.

                                        Very truly yours,

                                        LOEWS CORPORATION
                                        
                                        
                                        
                                        By: /s/ Peter W. Keegan
                                           ---------------------------------
                                                Its: Chief Financial Officer
                                                    ------------------------
                                                                            
                                        DIAMOND OFFSHORE                    
                                           DRILLING, INC.                   
                                                                            
                                                                            
                                                                            
                                        By: /s/ Robert E. Rose
                                           ---------------------------------
                                                Its: President and CEO
                                                    ------------------------
                                                                            
                                                                            

The foregoing Agreement (including all 
Schedules and Exhibits hereto) is 
hereby confirmed and accepted as of 
the date specified in Schedule I hereto.


      /s/ Goldman, Sachs & Co.
- -----------------------------------------
         (Goldman, Sachs & Co.)

For itself and the other several 
Underwriters, if any, named in 
Schedule II to the foregoing Agreement.





                                      -38-
<PAGE>   39
                                   SCHEDULE I

Underwriting Agreement dated September 16 , 1997

Representatives:          Goldman, Sachs & Co.
                          85 Broad Street
                          New York, New York  10004

The Underwritten Securities shall have the following terms:

Title:   3-1/8% Exchangeable Subordinated Notes due 2007

Rank:      Subordinated Debentures

Aggregate principal amount:       $1,000,000,000 (plus up to $150,000,000 
                                  aggregate principal amount of Option
                                  Underwritten Securities)

Currency of payment:              U.S. Dollar

Interest rate or formula:         3-1/8% per annum

Interest payment dates:           March 15 and September 15

Regular record dates:             March 1 and September 1

Stated maturity date:             September 15, 2007

Redemption:               In whole or in part at option of Company, on or after
September 15, 2002

Exchange provisions:      Exchangeable into shares of the Underlying Securities
                          at any time from and including October 1, 1998 and
                          prior to the close of business on September 15, 2007,
                          unless previously redeemed or repurchased, at an
                          exchange rate of 15.3757 shares per $1,000 principal
                          amount of Underwritten Securities, subject to
                          adjustment and to certain Company rights.

Underlying Securities:    Common stock, par value $.01 per share, of Diamond
Offshore.

Listing requirements:     List the Underwritten Securities and the Underlying
                          Securities on the New York Stock Exchange

<PAGE>   40
Fixed or Variable Price Offering:    Fixed Price Offering

          If Fixed Price Offering, initial public offering price per share: 100%
          of the principal amount, plus accrued interest, if any, from
          September 19, 1997.

Purchase price:         98.00% of principal amount, plus accrued interest, if
                        any, from September 19, 1997.

Form:    Global Security

Closing date and location:          September 19, 1997
                                    Sullivan & Cromwell
                                    125 Broad Street
                                    New York, New York 10004

Delayed Delivery Arrangements:  NONE.

Modification of items to be covered by the letter from the Company's
independent accountants delivered pursuant to Section 5(e) at the time this
Underwriting Agreement is executed:  NONE.





                                      -2-
<PAGE>   41
                                  SCHEDULE II


<TABLE>
<CAPTION>
                                                          Principal Amount of
Underwriters                                          Securities to be Purchased
- ------------                                          --------------------------
<S>                                                         <C>
Goldman, Sachs & Co.  . . . . . . . . . . . . . . . .       $1,000,000,000

   Total  . . . . . . . . . . . . . . . . . . . . . .       $1,000,000,000
                                                            --------------
</TABLE>







                                     -3-

<PAGE>   42
                                  SCHEDULE III

<TABLE>
<CAPTION>
                                                                    State of             States
          Subsidiary                                              Incorporation         Qualified
          ----------                                              -------------         ---------
 <S>      <C>                                                          <C>                 <C>    
  1.      Diamond Offshore Company                                     DE                  TX, LA 
  2.      Diamond Offshore General Company                             DE                  TX     
  3.      Diamond Offshore Guardian Company                            DE                  TX     
  4.      Diamond Offshore Southern Company                            DE                  TX     
  5.      Diamond Offshore Management Company                          DE                  TX, LA 
  6.      Diamond Offshore (USA) Inc.                                  DE                  TX, LA 
  7.      Diamond Offshore Alaska Inc.                                 DE                  TX     
  8.      Diamond Offshore Atlantic Inc.                               DE                  TX     
  9.      Diamond Offshore (Mexico) Company                            DE                  TX     
 10.      Diamond Offshore Drilling Services, Inc.                     DE                  TX, LA 
 11.      Diamond Offshore International Corporation                   DE                  TX     
 12.      Diamond Offshore Enterprises, Inc.                           DE                  TX     
 13.      Cumberland Maritime Corporation                              DE                  TX     
 14.      Diamond Offshore Team Solutions, Inc.                        DE                  TX, LA 
 15.      Diamond Offshore Finance Company                             DE                  TX     
 16.      Diamond Offshore Perforadora, Inc.                           DE                  TX     
 17.      Diamond Offshore Development Company                         DE                  TX     
 18.      Diamond Offshore (Indonesia), Inc.                           DE                  TX     
 19.      Diamond Offshore Drilling (Overseas) Inc.                    DE                  TX     
            (f/k/a Diamond Offshore Champion Inc.)                                                
 20.      Diamond Offshore Exploration (Bermuda) Limited               DE                  TX     
 21.      Arethusa Off-Shore Company                                   DE                  TX, LA 
 22.      Concord Drilling Limited                                     DE                  TX     
 23.      Saratoga Drilling Limited                                    DE                  TX     
 24.      Yorktown Drilling Limited                                    DE                  TX     
 25.      Scotian Drilling Limited                                     DE                  TX     
 26.      Heritage Drilling Limited                                    DE                  TX     
 27.      Sovereign Drilling Limited                                   DE                  TX     
 28.      Miss Kitty Drilling Limited                                  DE                  TX     
 29.      Neptune Drilling Limited                                     DE                  TX     
 30.      Whittington Drilling Limited                                 DE                  TX     
 31.      Yatzy Drilling Limited                                       DE                  TX     
 32.      Winner Drilling Limited                                      DE                  TX     
 33.      Lexington Drilling Limited                                   DE                  TX     
</TABLE>





                                      -4-
<PAGE>   43
                                   EXHIBIT A



              [FORM OF AMENDMENT TO REGISTRATION RIGHTS AGREEMENT]

              [SEE EXHIBIT 4.1 TO THIS CURRENT REPORT ON FORM 8-K]





                                      -5-

<PAGE>   1
                                                                     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.
<PAGE>   2





                 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





                                       2
<PAGE>   3

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





                                       3
<PAGE>   4

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
           ----------------------------





                                       4




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