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                                                                    EXHIBIT 10.1

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                                  $400,000,000



                         DIAMOND OFFSHORE DRILLING, INC.





                      1 1/2% CONVERTIBLE SENIOR DEBENTURES
                                    DUE 2031




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                               PURCHASE AGREEMENT





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                               PURCHASE AGREEMENT





                                                                   April 6, 2001


MERRILL LYNCH & CO.
Merrill Lynch, Pierce, Fenner & Smith
            Incorporated
North Tower
World Financial Center
New York, New York  10281-1209

Dear Sirs:

      1. Introductory. Diamond Offshore Drilling, Inc., a Delaware corporation
(the "COMPANY"), confirms its agreement with Merrill Lynch & Co., Merrill Lynch,
Pierce, Fenner & Smith Incorporated (the "PURCHASER"), with respect to the issue
and sale by the Company and the purchase by the Purchaser of $400,000,000
aggregate principal amount of the Company's 1 1/2% Convertible Senior Debentures
due 2031 (the "INITIAL SECURITIES") and the grant by the Company to the
Purchaser of the option described in Section 3(b) to purchase all or any part of
an additional $60,000,000 aggregate principal amount of the Company's 1 1/2%
Convertible Senior Debentures due 2031 to cover over-allotments, if any (the
"OPTION SECURITIES"). The Initial Securities, together with the Option
Securities, are collectively referred to herein as the "OFFERED SECURITIES". The
Offered Securities are to be issued under an Indenture dated as of February 4,
1997, as supplemented by a Third Supplemental Indenture to be dated as of the
Closing Date (as defined below) (as so amended and supplemented, the
"INDENTURE"), between the Company and The Chase Manhattan Bank, as trustee (the
"TRUSTEE"). The Offered Securities will be represented by one or more permanent
global Offered Securities in definitive form (the "GLOBAL SECURITIES") deposited
with the Trustee as custodian for The Depository Trust Company ("DTC") and
registered in the name of Cede & Co., as nominee for DTC. Interests in any
Global Securities will be held only in book-entry form through DTC, except in
the limited circumstances described in the Offering Document (as defined below).

      The holders of Offered Securities will be entitled to the benefits of a
Registration Rights Agreement, substantially in the form attached hereto as
Exhibit A with such changes as shall be agreed to by the parties hereto (the
"REGISTRATION RIGHTS AGREEMENT"), pursuant to which the Company will file a
registration statement with the Securities and Exchange Commission (the
"COMMISSION") registering resales of the Offered Securities and the shares of
common stock, par value $.01 per share, of the Company (the "COMMON STOCK")
issuable upon conversion thereof, as referred to in the Registration Rights
Agreement, under the Securities Act of 1933, as amended (the "SECURITIES ACT").

      The Company understands that the Purchaser proposes to make an offering of
the Offered Securities on the terms and in the manner set forth herein and
agrees that the Purchaser

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may resell, subject to the conditions set forth herein, all or a portion of the
Offered Securities to purchasers ("SUBSEQUENT PURCHASERS") at any time after the
date of this Agreement. The Offered Securities are to be offered and sold
through the Purchaser without being registered under the Securities Act, in
reliance upon exemptions therefrom. Pursuant to the terms of the Offered
Securities and the Indenture, investors that acquire Offered Securities may only
resell or otherwise transfer such Offered Securities if such Offered Securities
are hereafter registered under the Securities Act or if an exemption from the
registration requirements of the Securities Act is available (including the
exemption afforded by Rule 144A ("RULE 144A") of the rules and regulations
promulgated under the Securities Act (the "RULE AND REGULATIONS") by the
Commission).

      2. Representations and Warranties of the Company. The Company represents
and warrants to the Purchaser as of the date hereof and as of the Closing Date,
and as of the Date of Delivery (if any) referred to in Section 3(b) hereof, and
agrees with the Purchaser, as follows:

          (a) The Company has prepared and delivered to the Purchaser copies of
a preliminary offering memorandum dated April 5, 2001 (the "PRELIMINARY OFFERING
MEMORANDUM"), and has prepared and will deliver to the Purchaser on the date
hereof or the next succeeding day copies of a final offering memorandum dated
April 6, 2001 (the "FINAL OFFERING MEMORANDUM"), each for use by the Purchaser
in connection with the solicitation of purchases of, or offering of, the Offered
Securities. "OFFERING DOCUMENT" means, with respect to any date or time referred
to in this Agreement, the most recent offering memorandum (whether the
Preliminary Offering Memorandum or the Final Offering Memorandum, or any
amendment or supplement to either such document), including exhibits thereto and
any documents incorporated therein by reference, which has been prepared and
delivered by the Company to the Purchaser in connection with its solicitation of
purchases of, or offering of, the Offered Securities. The Offering Document does
not, and on the Closing Date (as defined herein) (and, if any Option Securities
are purchased, on the Date of Delivery (as defined herein)) will not, include
any untrue statement of a material fact or omit 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. The preceding sentence
does not apply to statements in or omissions from the Offering Document based
upon written information furnished to the Company by the Purchaser specifically
for use in the Offering Document as specified in Section 7(a).

      The Offering Document as delivered from time to time shall incorporate by
reference the most recent Annual Report of the Company on Form 10-K filed with
the Commission and each subsequent report filed with the Commission since the
end of the fiscal year to which such Annual Report relates (collectively, the
"EXCHANGE ACT REPORTS"). Except as disclosed in the Offering Document, the
Exchange Act Reports, when read together with the other information in the
Offering Document, do not, and on the Closing Date (as defined herein) (and, if
any Option Securities are purchased, on the Date of Delivery (as defined
herein)) will not, 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. The Exchange
Act Reports, when they were or hereafter are filed with the Commission, complied
and will at the time of such filing comply in all material respects to the
requirements of the Exchange Act and the rules and regulations of the Commission
thereunder.

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      All references in this Agreement to financial statements and schedules and
other information which is "contained," "included" or "stated" in the Offering
Document (or other references of like import) shall be deemed to mean and
include all such financial statements and schedules and other information which
are incorporated by reference in the Offering Document; and all references in
this Agreement to amendments or supplements to the Offering Document shall be
deemed to mean and include the filing of any document under the Exchange Act
which is incorporated or deemed to be incorporated by reference in the Offering
Document.

          (b) The Company 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 Offering Document and to enter into and perform its
obligations under this Agreement, the Indenture and the Registration Rights
Agreement; and the Company is duly qualified to transact 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 the Company to be so qualified would not have a
material adverse effect on the business, results of operations or financial
condition of the Company and its subsidiaries, taken as a whole (a "MATERIAL
ADVERSE EFFECT").

          (c) Each subsidiary of the Company 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 Offering Document; and
each subsidiary of the Company is duly qualified to transact 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; all of the issued and outstanding
capital stock of each subsidiary of the Company 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; and, except as disclosed in the Offering Document, all
of the capital stock (other than directors' qualifying shares) of each
Subsidiary (as defined in Section 6(d)(ii)) is owned by the Company, directly or
through subsidiaries, free from liens, encumbrances and defects, except where
the failure of the Company to own such capital stock would not have a Material
Adverse Effect.

          (d) The Indenture has been duly authorized; the Offered Securities
have been duly authorized; and when the Offered Securities are delivered and
paid for pursuant to this Agreement on the Closing Date, the Indenture will have
been duly executed and delivered, such Offered Securities will have been duly
executed, authenticated, issued and delivered and the Indenture and such Offered
Securities will conform to the descriptions thereof contained in the Offering
Document and will constitute valid and legally binding obligations of the
Company, enforceable in accordance with their terms, subject to bankruptcy,
insolvency, fraudulent transfer, reorganization, moratorium and similar laws of
general applicability relating to or affecting creditors' rights and to general
equity principles.

          (e) When the Offered Securities are delivered and paid for pursuant to
this Agreement on the Closing Date, such Offered Securities will be convertible
at the rate of



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20.3978 shares (the "UNDERLYING SHARES") of Common Stock per $1,000 principal
amount of such Offered Securities in accordance with the terms of the Indenture;
the Underlying Shares initially issuable upon conversion of such Offered
Securities have been duly authorized and reserved for issuance upon such
conversion and, when issued upon such conversion, will be validly issued, fully
paid and nonassessable. The shares of Common Stock issuable at the Company's
option upon the purchase of Offered Securities at the option of the holder
thereof will have been, prior to the issuance thereof, duly authorized and, if
and when issued in accordance with the terms of the Offered Securities and the
Indenture, will be validly issued, fully paid and nonassessable.

          (f) The authorized, issued and outstanding capital stock and debt of
the Company is as set forth in the Offering Document in the column entitled
"Historical" under the caption "Capitalization" (except for subsequent
repurchases pursuant to the Company's stock repurchase program or subsequent
issuances, if any, pursuant to this Agreement, pursuant to reservations,
agreements, employee benefit plans referred to in the Offering Document or
pursuant to the exercise or redemption of convertible securities or options
referred to in the Offering Document); the outstanding shares of Common Stock
have been duly authorized and validly issued, are fully paid and nonassessable
and conform to the description thereof contained in the Offering Document; and
the stockholders of the Company have no preemptive rights with respect to the
Offered Securities or the Underlying Shares.

          (g) Except as disclosed in the Offering Document, there are no
contracts, agreements or understandings between the Company and any person that
would give rise to a valid claim against the Company or the Purchaser for a
brokerage commission, finder's fee or other like payment.

          (h) Except for the Registration Rights Agreement dated October 16,
1995, between the Company and Loews Corporation ("LOEWS"), as amended (the
"LOEWS REGISTRATION RIGHTS AGREEMENT"), the Registration Rights Agreement dated
June 6, 2000, between the Company and Credit Suisse First Boston Corporation
(the "ZERO DEBENTURES REGISTRATION RIGHTS AGREEMENT") and the Registration
Rights Agreement, there are no contracts, agreements or understandings between
the Company and any person granting such person the right to require the Company
to file a registration statement under the Securities Act with respect to any
securities of the Company owned or to be owned by such person or to require the
Company to include such securities in the securities registered pursuant to the
Shelf Registration Statement (as defined in the Registration Rights Agreement)
or in any securities being registered pursuant to any other registration
statement filed by the Company under the Securities Act.

          (i) The outstanding shares of Common Stock are listed on The New York
Stock Exchange (the "STOCK EXCHANGE").

          (j) No consent, approval, authorization or order of, or filing with,
any governmental agency or body or any court is required for the performance by
the Company of its obligations hereunder or the consummation of the transactions
contemplated by this Agreement and the Registration Rights Agreement, except for
the filing of the Shelf Registration Statement (as defined in the Registration
Rights Agreement) and the order of the Commission declaring the



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Shelf Registration Statement (as defined in the Registration Rights Agreement)
effective and such as may be required under state securities laws.

          (k) The execution, delivery and performance of the Indenture, this
Agreement and the Registration Rights Agreement, the issuance and sale of the
Offered Securities and compliance with the terms and provisions thereof and the
issuance of the Underlying Shares 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 the Company or any of its subsidiaries is a party or by
which the Company or any of its subsidiaries is bound, or to which any of the
property or assets of the Company or any of its subsidiaries is subject (except
for such conflicts, breaches, violations or defaults that, individually or in
the aggregate, would not have a Material Adverse Effect or impair the Company's
ability to perform its obligations hereunder or have any material adverse effect
upon the consummation of the transactions contemplated hereby), nor will such
action result in any violation of the provisions of the charter or bylaws of the
Company 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
the Company or any of its subsidiaries or the property of the Company or any of
its subsidiaries.

          (l) This Agreement has been duly authorized, executed and delivered by
the Company; the Registration Rights Agreement has been duly authorized and, as
of the Closing Date, will have been duly executed and delivered by the Company.

          (m) Except for Permitted Liens, as such term is defined below, the
Company and its subsidiaries have good and marketable title to all offshore
drilling rigs described as being owned by them in the Offering Document, 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 Offering Document, the Company 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 for taxes that are being contested in good
faith and by appropriate proceedings diligently prosecuted and for which
appropriate reserves have been established by the Company as required by
generally accepted accounting principles in the United States; (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.

          (n) The Company 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



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relating to the revocation or modification of any such certificate, authority or
permit that, if determined adversely to the Company or any of its subsidiaries,
would individually or in the aggregate have a Material Adverse Effect.

          (o) No labor dispute with the employees of the Company or any
subsidiary exists or, to the knowledge of the Company, is imminent that might
have a Material Adverse Effect.

          (p) The Company 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 the Company or any of its subsidiaries, would individually or in
the aggregate have a Material Adverse Effect.

          (q) Neither the Company 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; and the Company is not aware of
any pending investigation which might lead to such a claim.

          (r) There are no pending actions, suits or proceedings against or
affecting the Company, any of its subsidiaries or any of their respective
properties except as disclosed in the Offering Document, or as individually or
in the aggregate do not now have and, to the best of the knowledge of the
Company, are not reasonably expected in the future to have a Material Adverse
Effect or would materially and adversely affect the ability of the Company to
perform its obligations under the Indenture, the Offered Securities, this
Agreement or the Registration Rights Agreement, or which are otherwise material
in the context of the sale of the Offered Securities; and no such actions, suits
or proceedings are, to the Company's knowledge, threatened or contemplated.

          (s) The financial statements included or incorporated by reference in
the Offering Document present fairly in all material respects the financial
position of the Company 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 the generally
accepted accounting principles in the United States applied on a consistent
basis.

          (t) Except as disclosed in the Offering Document, since the date of
the latest audited financial statements included or incorporated by reference in
the Offering Document, 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



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operations of the Company and its subsidiaries taken as a whole, and there has
been no dividend or distribution of any kind declared, paid or made by the
Company on any class of its capital stock.

          (u) The Company is not and, after giving effect to the offering and
sale of the Offered Securities and the application of the proceeds thereof as
described in the Offering Document, will not be (i) an "investment company" or a
company "controlled" by an "investment company" within the meaning of in the
Investment Company Act of 1940, as amended (the "INVESTMENT COMPANY ACT") 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 (the "HOLDING COMPANY ACT").

          (v) No securities of the same class (within the meaning of Rule
144A(d)(3) under the Securities Act) as the Offered Securities are listed on any
national securities exchange registered under Section 6 of the Exchange Act or
quoted in a U.S. automated inter-dealer quotation system.

          (w) Assuming the accuracy of the Purchaser's representations and
performance by the Purchaser of its covenants and warranties contained in
Section 4 herein, the offer, sale and delivery of the Offered Securities by the
Company to the Purchaser and the resale of the Offered Securities by the
Purchaser to each Subsequent Purchaser in the manner contemplated by this
Agreement will be exempt from the registration requirements of the Securities
Act, and it is not necessary to qualify an indenture in respect of the Offered
Securities under the Trust Indenture Act of 1939, as amended (the "TRUST
INDENTURE ACT").

          (x) Neither the Company, nor any of its affiliates (as such term is
defined in Rule 501(b) under the Securities Act (each, an "AFFILIATE")), nor any
person acting on its or their behalf (i) has solicited any offer to buy, sold or
offered to sell, or will solicit any offer to buy, sell or offer to sell, any
security which is or would be integrated with the sale of the Offered Securities
in a manner that would require the Offered Securities to be registered under the
Securities Act or (ii) has offered or will offer or sell the Offered Securities
by means of any form of general solicitation or general advertising within the
meaning of Rule 502(c) under the Securities Act. The Company has not entered and
will not enter into any contractual arrangement with respect to the distribution
of the Offered Securities except for this Agreement.

      3. Purchase, Sale and Delivery of Offered Securities. (a) On the basis of
the representations, warranties and agreements herein contained, but subject to
the terms and conditions herein set forth, the Company agrees to sell to the
Purchaser, and the Purchaser agrees to purchase from the Company, at a purchase
price of $977.50 per $1,000 principal amount thereof, $400,000,000 aggregate
principal amount of the Initial Securities.

      (b) In addition, on the basis of the representations, warranties and
agreements herein contained, but subject to the terms and conditions herein set
forth, the Company hereby grants an option to the Purchaser to purchase any or
all of the Option Securities (in multiples of $1,000 principal amount) at the
same price per $1,000 principal amount thereof set forth in Section 3(a) for the
Initial Securities plus accrued interest, if any, from the Closing Date to the
Date of Delivery. The option hereby granted will expire 30 days after the date
hereof and may be

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exercised in whole or in part (but only once) only for the purpose of covering
over-allotments that may be made in connection with the offering and
distribution of the Initial Securities upon notice by the Purchaser to the
Company setting forth the principal amount of Option Securities as to which the
Purchaser is exercising the option and the time and date of payment and delivery
for such Option Securities. Any such time and date of delivery (a "DATE OF
DELIVERY") shall be determined by the Purchaser, 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.

      (c) Payment of the purchase price for, and delivery of the Global
Securities representing, the Initial Securities shall be made at the offices of
Shearman & Sterling, 599 Lexington Avenue, New York, New York 10022, or at such
other place as shall be agreed upon by the Purchaser and the Company, at 9:00
A.M. (New York City time) on April 11, 2001, or such other time not later than
ten business days after such date as shall be agreed upon by the Purchaser and
the Company (such time and date of payment and delivery being herein called the
"CLOSING DATE").

      In addition, in the event that any or all of the Option Securities are
purchased by the Purchaser, payment of the purchase price for, and delivery of
the Global Securities representing, such Option Securities shall be made at the
above-mentioned offices, or at such other place as shall be agreed upon by the
Purchaser and the Company, on the Date of Delivery as specified in the notice
from the Purchaser to the Company.

      Payment of the purchase price for the Initial Securities and, if
applicable, the Option Securities shall be made by the Purchaser to the Company
by wire transfer of immediately available funds to a bank account designated by
the Company, against delivery by the Company to the Purchaser of the Offered
Securities to be purchased by it.

      4. Representations by Purchaser; Resale by Purchaser.

          (a) The Purchaser represents and warrants to the Company that it is an
"accredited investor" within the meaning of Regulation D under the Securities
Act.

          (b) The Purchaser acknowledges that the Offered Securities have not
been registered under the Securities Act and may not be offered or sold within
the United States except pursuant to an exemption from, or in a transaction not
subject to, the registration requirements of the Securities Act. The Purchaser
represents and agrees that it has not offered and sold the Offered Securities
and will not offer and sell the Offered Securities, except to persons whom the
Purchaser reasonably believes to be qualified institutional buyers within the
meaning of Rule 144A under the Securities Act.

          (c) The Purchaser agrees that it and each of its Affiliates has not
entered and will not enter into any contractual arrangement with respect to the
distribution of the Offered Securities except with the prior written consent of
the Company.

          (d) The Purchaser agrees that it and each of its Affiliates will not
offer or sell the Offered Securities by means of any form of general
solicitation or general advertising, within the meaning of Rule 502(c) under the
Securities Act, including, but not limited to (i) any advertisement, article,
notice or other communication published in any newspaper, magazine or



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similar media or broadcast over television or radio or (ii) any seminar or
meeting whose attendees have been invited by any general solicitation or general
advertising.

          (e) The Purchaser agrees to inform, and cause each of its Affiliates
to inform, persons acquiring Offered Securities from the Purchaser or such
Affiliate, as the case may be, that the Offered Securities (A) have not been and
will not be registered under the Securities Act, (B) are being sold by them
without registration under the Securities Act in reliance on Rule 144A or in
accordance with another exemption from registration under the Securities Act, as
the case may be, and (C) may not be offered, sold or otherwise transferred
except (1) to the Company, (2) outside the United States in accordance with
Regulation S under the Securities Act or (3) inside the United States (x) in
accordance with Rule 144A to a person whom the seller reasonably believes is a
qualified institutional buyer that is purchasing for its own account or for the
account of a qualified institutional buyer in a transaction meeting the
requirements of Rule 144A and to whom notice is given that the offer, sale or
transfer is being made in reliance on Rule 144A or (y) pursuant to another
available exemption from registration under the Securities Act.

          (f) The Purchaser acknowledges and agrees that the transfer
restrictions and the other provisions set forth in the Offering Document under
the heading "Transfer Restrictions", including the legends required thereby,
shall apply to the Offered Securities except as otherwise agreed by the Company
and the Purchaser.

      5. Certain Agreements of the Company. The Company agrees with the
Purchaser that:

          (a) The Company will advise the Purchaser promptly of any proposal to
amend or supplement the Offering Document after the Closing Date and will not
effect such amendment or supplementation without the Purchaser's consent, which
will not be reasonably withheld. If, at any time prior to the completion of the
resale of the Offered Securities by the Purchaser any event occurs as a result
of which the Offering Document as then amended or supplemented would include an
untrue statement of a material fact or omit 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, or if it is necessary at any such time to
amend or supplement the Offering Document to comply with any applicable law, the
Company promptly will notify the Purchaser of such event and promptly will
prepare, at its own expense, an amendment or supplement which will correct such
statement or omission or effect such compliance. Neither the Purchaser's consent
to, nor delivery to offerees or investors of, any such amendment or supplement
shall constitute a waiver of any of the conditions set forth in Section 6.

          (b) The Company will furnish to the Purchaser copies of the Offering
Document and all amendments and supplements to such documents, in each case as
soon as available and in such quantities as the Purchaser requests. At any time
when the Company is not subject to Section 13 or 15(d) of the Exchange Act, the
Company will promptly furnish or cause to be furnished to the Purchaser and,
upon request of holders and prospective purchasers of the Offered Securities, to
such holders and purchasers, copies of the information required to be delivered
to holders and prospective purchasers of the Offered Securities pursuant to Rule
144A(d)(4) under the Securities Act (or any successor provision thereto) in
order to permit compliance with Rule 144A in connection with resales by such
holders of the Offered Securities



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in reliance upon Rule 144A. The Company will pay the expenses of printing and
distributing to the Purchaser all such documents.

          (c) The Company will arrange for the qualification of the Offered
Securities for sale and the determination of their eligibility for investment
under the laws of such states in the United States as the Purchaser designates
and will continue such qualifications in effect so long as required for the
resale of the Offered Securities by the Purchaser; provided that the Company
will not be required to qualify as a foreign corporation or to file a general
consent to service of process in any such state.

          (d) During the period of five years hereafter, the Company will
furnish to the Purchaser as soon as practicable after the end of each fiscal
year, a copy of its annual report to stockholders for such year; and the Company
will furnish to the Purchaser as soon as available, a copy of each report and
any definitive proxy statement of the Company filed with the Commission under
the Exchange Act or mailed to stockholders. It is understood and agreed that the
Company may satisfy its obligations under this Section 5(d) by publishing such
reports and proxy statements at the Company's Web site on the World Wide Web or
through such other public medium as the Company may use at that time.

          (e) During the period of two years after the Closing Date, the Company
will, upon request, furnish to the Purchaser and any holder of Offered
Securities a copy of the restrictions on transfer applicable to the Offered
Securities.

          (f) During the period of two years after the Closing Date, the Company
will not, and will not permit any of its affiliates (as defined in Rule 144
under the Securities Act) to, resell any of the Offered Securities that have
been reacquired by any of them.

          (g) The Company will pay all expenses incidental to the performance of
its obligations under this Agreement, the Offered Securities and the Indenture,
including, but not limited to, (i) any filing fees or other expenses (including
fees and disbursements of counsel not to exceed $5,000) in connection with the
qualification pursuant to Section 5(c) of the Offered Securities or Underlying
Shares for sale and any determination for eligibility for investment under the
laws of such jurisdictions as the Purchaser may designate and the printing of
memoranda relating thereto, (ii) any fees charged by investment rating agencies
for the rating of the Offered Securities, (iii) the fees and expenses of the
Trustee and its professional advisers, (iv) all expenses in connection with the
execution, issue, authentication, packaging and initial delivery of the Offered
Securities and, as applicable, the Underlying Shares, the preparation and
printing of this Agreement, the Registration Rights Agreement, the Offered
Securities, the Indenture, the Offering Document and amendments and supplements
thereto, and any other document relating to the issuance, offer, sale and
delivery of the Offered Securities and as applicable the Underlying Shares, (v)
the cost of qualifying the Offered Securities for trading in The Portal Market
("PORTAL") of The Nasdaq Stock Market, Inc. and any expenses incidental thereto,
(vi) the cost of any advertising approved by the Company in connection with the
issue of the Offered Securities, (vii) any travel expenses of the Company's
officers and employees and any other expenses of the Company in connection with
attending or hosting meetings with prospective purchasers of Offered Securities
and for expenses incurred in distributing the Offering Document (including any
amendments and supplements thereto). Except as provided in



                                       11
<PAGE>   12

the preceding sentence, the Purchaser will pay the expenses incident to the
performance of its obligations under this Agreement and will reimburse the
Company (if and to the extent incurred by the Company) for any travel expenses
of the Purchaser's representatives and any other expenses of the Purchaser in
connection with attending or hosting meetings with prospective purchasers of the
Offered Securities.

          (h) The Company agrees that it will not and will cause its Affiliates
not to, directly or indirectly, solicit any offer to buy or make any offer or
sale of securities of the Company of any class if, as a result of the doctrine
of "integration" referred to in Rule 502 under the Securities Act, such offer or
sale would render invalid (for the purpose of (i) the sale of the Offered
Securities by the Company to the Purchaser, (ii) the resale of the Offered
Securities by the Purchaser to Subsequent Purchasers or (iii) the resale of the
Offered Securities by such Subsequent Purchasers to others) the exemption from
the registration requirements of the Securities Act provided by Section 4(2)
thereof or by Rule 144A thereunder or otherwise.

          (i) For a period of 90 days after the date hereof, except for the sale
of the Offered Securities to the Purchaser, the Company will not offer, sell,
pledge, or otherwise dispose of (other than any contract to sell), directly or
indirectly, any shares of Common Stock or any securities convertible into or
exercisable or exchangeable for Common Stock without the prior written consent
of the Purchaser, or publicly disclose the intention to make any such offer,
sale, pledge or disposition, except grants of employee or director stock
options, stock appreciation rights or restricted stock grants pursuant to the
terms of a plan in effect on the date hereof, issuances of Common Stock pursuant
to the exercise of such options or the exercise of any other employee stock
options currently outstanding or upon the conversion of the Offered Securities
or the Company's Zero Coupon Convertible Debentures due 2020.

          (j) The Company will promptly apply for the listing on the Stock
Exchange of the Underlying Shares and will use its reasonable best efforts to
obtain such listing within 15 days of the Closing Date.

      6. Conditions of the Obligation of the Purchaser. The obligation of the
Purchaser to purchase and pay for the Offered Securities will be subject to the
accuracy of the representations and warranties on the part of the Company
herein, to the accuracy of the statements of officers of the Company made
pursuant to the provisions hereof, to the performance by the Company of its
obligations hereunder and to the following additional conditions precedent:

          (a) The Purchaser shall have received a letter, dated the date of this
Agreement, of Deloitte & Touche LLP confirming that they are independent public
accountants within the meaning of the Securities Act and the applicable
published Rules and Regulations thereunder and to the effect that:

            (i) In their opinion the financial statements examined by them and
     included or incorporated by reference in the Offering Document comply as to
     form in all material respects with the applicable accounting requirements
     of the Securities Act and the related published Rules and Regulations;

                                       12
<PAGE>   13

            (ii) they have performed the procedures specified by the American
     Institute of Certified Public Accountants for a review of interim financial
     information as described in Statement of Auditing Standards No. 71, Interim
     Financial Information, on the unaudited financial statements included or
     incorporated by reference in the Offering Document;

            (iii) on the basis of the review referred to in clause (ii) above, a
     reading of the latest available interim financial statements of the
     Company, inquiries of officials of the Company who have responsibility for
     financial and accounting matters and other specified procedures, nothing
     came to their attention that caused them to believe that:

                  (A) the unaudited financial statements included or
            incorporated by reference in the Offering Document do not comply as
            to form in all material respects with the applicable accounting
            requirements of the Securities Act and the related published Rules
            and Regulations or any material modifications should be made to such
            unaudited financial statements for them to be in conformity with
            generally accepted accounting principles;

                  (B) at the date of the latest available balance sheet read by
            such accountants, or at a subsequent specified date not more than
            three business days prior to the date of this Agreement, there was
            any change in the capital stock or any increase in short-term
            indebtedness or long-term debt of the Company and its consolidated
            subsidiaries or, at the date of the latest available balance sheet
            read by such accountants, there was any decrease in consolidated net
            current assets or net assets, as compared with amounts shown on the
            latest balance sheet included or incorporated by reference in the
            Offering Document; or

                  (C) for the period from the closing date of the latest income
            statement included in or incorporated by reference in the Offering
            Document to the closing date of the latest available income
            statement read by such accountants there were any decreases, as
            compared with the corresponding period of the previous year, and
            with the period of corresponding length ended the date of the latest
            income statement included in or incorporated by references in the
            Offering Document, in the contract drilling revenue, net operating
            income or in the total or per share amounts of consolidated income
            before extraordinary items or net income or in the ratio of earnings
            to fixed charges;

            except in all cases set forth in clauses (B) and (C) above for
            changes, increases or decreases which the Offering Document
            discloses have occurred or may occur or which are described in such
            letter; and

            (iv) they have compared specified dollar amounts (or percentages
     derived from such dollar amounts) and other financial information contained
     in the Offering Document (in each case to the extent that such dollar
     amounts, percentages and other financial information are derived from the
     general accounting records of the Company and its subsidiaries subject to
     the internal controls of the Company's accounting system or are derived
     directly from such records by analysis or computation)



                                       13
<PAGE>   14

     with the results obtained from inquiries, a reading of such general
     accounting records and other procedures specified in such letter and have
     found such dollar amounts, percentages and other financial information to
     be in agreement with such results, except as otherwise specified in such
     letter.

      (b) The Purchaser shall have received from Deloitte & Touche LLP a letter,
dated as of the Closing Date, to the effect that the reaffirm the statements
made in the letter furnished pursuant to subsection (a) of this Section, except
that the specified date referred to shall be a date not more than three business
days prior to the Closing Date.

      (c) Subsequent to the execution and delivery of this Agreement, there
shall not have occurred (i) any change, or any development or event involving a
prospective change, in the condition (financial or other), business, properties
or results of operations of the Company or its subsidiaries which, in the
judgment of the Purchaser is material and adverse and makes it impractical or
inadvisable to proceed with completion of the offering or the sale of and
payment for the Offered Securities; (ii) any downgrading in the rating of any
debt securities of the Company by any "nationally recognized statistical rating
organization" (as defined for purposes of Rule 436(g) under the Securities Act),
or any public announcement that any such organization has under surveillance or
review its rating of any debt securities of the Company (other than an
announcement with positive implications of a possible upgrading, and no
implication of a possible downgrading, of such rating); (iii) any material
suspension or material limitation of trading in securities generally on the New
York Stock Exchange or any setting of minimum prices for trading on such
exchange; (iv) or any suspension of trading of any securities of the Company on
any exchange in the over-the-counter market; (v) any banking moratorium declared
by U.S. Federal or New York authorities; or (vi) any outbreak or escalation of
major hostilities in which the United States is involved, any declaration of war
by Congress or any other substantial national or international calamity or
emergency if, in the judgment of the Purchaser, the effect of any such outbreak,
escalation, declaration, calamity or emergency makes it impractical or
inadvisable to proceed with completion of the offering or sale of and payment
for the Offered Securities.

      (d) The Purchaser shall have received an opinion, dated the Closing Date,
of William C. Long, Esq., the General Counsel of the Company, to the effect
that:

            (i) The Company is duly qualified to transact business and is in
     good standing as a foreign corporation in each jurisdiction where the
     character of its activities requires such qualification, except where the
     failure of the Company to be so qualified would not have a material adverse
     effect on the business, results of operations or financial condition of the
     Company and its subsidiaries taken as a whole.

            (ii) All of the issued and outstanding shares of capital stock or
     membership interests, as applicable, of (i) each subsidiary of the Company
     listed on Exhibit A attached hereto (each, a "SUBSIDIARY" and collectively,
     the "SUBSIDIARIES") and, (ii) to such counsel's knowledge, Diamond Offshore
     Limited and Diamond Offshore Drilling (UK) Limited, are owned, directly or
     indirectly, of record and beneficially by the Company, free and clear of
     all liens, claims, limitations on voting rights, options, security
     interests and other encumbrances and have been duly authorized and validly
     issued and



                                       14
<PAGE>   15

     are fully paid and nonassessable, except to the extent that 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, results of operations or financial condition of the
     Company and its subsidiaries, taken as a whole.

            (iii) Each Subsidiary is a corporation or limited liability company,
     as applicable, duly organized, validly existing and in good standing under
     the laws of its jurisdiction of organization. Each Subsidiary is duly
     qualified to transact business and is in good standing as a foreign
     corporation or limited liability company, as applicable, in the states
     listed by such Subsidiary's name on the attached Exhibit A (such states
     being the only states in which each such Subsidiary is required to be
     qualified, except where the failure to be so qualified would not have a
     material adverse effect on the business, results of operations or financial
     condition of the Company and its subsidiaries, taken as a whole).

            (iv) Except as described under the caption "Risk Factors -- The sale
     of shares available for future sale could hurt our common stock price." and
     under the caption "Description of the Debentures -- Registration Rights" in
     the Offering Document and except for the Zero Debentures Registration
     Rights Agreement, there are no contracts, agreements or understandings
     known to such counsel between the Company and any person granting such
     person the right to require the Company to file a registration statement
     under the Securities Act with respect to any securities of the Company
     owned or to be owned by such person or to require the Company to include
     such securities in the securities registered pursuant to the Shelf
     Registration Statement (as defined in the Registration Rights Agreement) or
     in any securities being registered pursuant to any other registration
     statement filed by the Company under the Securities Act.

            (v) The execution, delivery and performance by the Company of the
     Indenture and the Agreement and the issuance and sale of the Offered
     Securities to the Purchaser thereunder and the compliance by the Company
     with all the provisions of the Indenture and this Agreement and the
     consummation of the transactions contemplated thereby and hereby will not
     conflict with, constitute a breach of or default under or violate (i) any
     of the terms, conditions or provisions of the certificate of incorporation
     or by-laws of any of the Subsidiaries, (ii) any of the terms, conditions or
     provisions of any document, agreement or other instrument to which the
     Company or any of the Subsidiaries is a party or by which the Company or
     any of the Subsidiaries is bound or to which any of the properties of the
     Company or any of the Subsidiaries is subject, or (iii) any judgment, writ,
     injunction, decree, order or ruling of any court or governmental authority
     binding on any of the Subsidiaries, except (other than with respect to
     clause (i)) any such conflict, breach, default or violation which would
     not, individually or in the aggregate, have a material adverse effect on
     the business, results of operations or financial condition of the Company
     and its subsidiaries, taken as a whole.

            (vi) To such counsel's knowledge, there are no legal or governmental
     proceedings that are required to be described in the Offering Document that
     are not described therein.



                                       15
<PAGE>   16

            (vii) Except as disclosed in the Offering Document, there is no
     litigation, proceeding or governmental investigation pending or, to such
     counsel's knowledge, overtly threatened against the Company or any of its
     subsidiaries or to which any of the property of the Company or any of its
     subsidiaries is subject which, in such counsel's opinion, if adversely
     determined would, individually or in the aggregate, have a material adverse
     effect on the business, assets, results of operations or financial
     condition of the Company and its subsidiaries, taken as a whole.

            (viii) No consent or approval of any federal governmental agency
     with respect to any federal maritime law matter is required in connection
     with performance by the Company of its obligations under this Agreement or
     the issuance and sale of the Offered Securities or the Underlying Shares.
     Neither the issuance, offer, sale or delivery by the Company of the Offered
     Securities pursuant to this Agreement nor the execution, delivery and
     performance thereof by the Company or consummation of the transactions
     contemplated thereby, including the issuance and delivery of the Underlying
     Shares, will violate any existing federal maritime laws, including, without
     limitation, the Shipping Act, 1916, as amended, and the rules and
     regulations of the Maritime Administration and the United States Coast
     Guard.

     The opinions expressed in such opinion may be limited to the laws of the
State of Texas, the corporate laws of the State of Delaware and the federal laws
of the United States.

          (e) The Purchaser shall have received an opinion, dated the Closing
Date, of Weil, Gotshal & Manges LLP, counsel for the Company, to the effect
that:

            (i) The Company is a corporation 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 Offering Document.

            (ii) The Offered Securities are convertible into Common Stock in
     accordance with the Indenture. The shares of Common Stock issuable upon
     conversion of the Offered Securities have been duly authorized and reserved
     for issuance upon such conversion, and such Common Stock, when issued upon
     such conversion in accordance with the provisions of the Indenture, will be
     validly issued, fully paid and nonassessable. All of the outstanding shares
     of the Common Stock have been duly authorized and validly issued, are fully
     paid and nonassessable, are free of any preemptive rights pursuant to law
     or the Company's Certificate of Incorporation and conform as to legal
     matters in all material respects to the description thereof contained in
     the Offering Document.

            (iii) The Company has the requisite corporate power and authority to
     authorize, issue and sell the Offered Securities as contemplated by this
     Agreement. The Offered Securities to be issued pursuant to this Agreement
     have been duly authorized. The Offered Securities have been duly executed,
     authenticated, issued and delivered and conform in all material respects to
     the description thereof contained in the Offering Document.



                                       16
<PAGE>   17

            (iv) The Company has all requisite corporate power and authority to
     execute and deliver the Indenture, the Registration Rights Agreement and
     this Agreement and to issue, sell and deliver the Offered Securities to the
     Purchaser pursuant to the Indenture and this Agreement. The execution,
     delivery and performance of the Indenture and this Agreement and the
     issuance, sale and delivery of the Offered Securities by the Company to the
     Purchaser thereunder have been duly authorized by all necessary corporate
     action on the part of the Company. This Agreement and the Indenture have
     been duly executed and delivered by the Company. The Indenture (assuming
     the due authorization, execution and delivery thereof by the Trustee), the
     Offered Securities and the Registration Rights Agreement (other than
     Section 6 as to which no opinion need be expressed) constitute legal, valid
     and binding obligations of the Company, enforceable against it in
     accordance with their terms, subject to applicable bankruptcy, insolvency,
     fraudulent conveyance, reorganization, moratorium and similar laws
     affecting creditors' rights and remedies generally, and subject, as to
     enforceability, to general principles of equity, including principles of
     commercial reasonableness, good faith and fair dealing (regardless of
     whether enforcement is sought in a proceeding at law or in equity).

            (v) The execution and delivery by the Company of the Indenture, this
     Agreement and the Registration Rights Agreement and the performance by the
     Company of its obligations thereunder and the issuance and sale of the
     Offered Securities to the Purchaser pursuant to the Indenture and this
     Agreement and the compliance by the Company with the provisions of the
     Indenture, this Agreement and the Registration Rights Agreement and the
     consummation by the Company of the transactions contemplated thereby will
     not conflict with, constitute a default under or violate (i) any of the
     terms, conditions or provisions of the Certificate of Incorporation or
     Amended Bylaws, of the Company, (ii) any New York, Texas, Delaware
     corporate or federal law or regulation (other than federal and state
     securities or blue sky laws or the Shipping Act, 1916, as amended, as to
     which no opinion need be expressed), or (iii) any judgment, writ,
     injunction, decree, order or ruling of any federal or state court or
     governmental authority binding on the Company or any of its properties of
     which we are aware, except in each case other than with respect to clause
     (i), any such conflict, default or violation as would not impair the
     Company's ability to perform its obligations under the Indenture, the
     Offered Securities, this Agreement or the Registration Rights Agreement or
     have any material adverse effect upon the consummation of the transactions
     contemplated by the Indenture, the Offered Securities, this Agreement or
     the Registration Rights Agreement.

            (vi) 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, delivery or performance by the Company of this
     Agreement, the Indenture or the Registration Rights Agreement or the
     consummation by the Company of the transactions contemplated hereby and
     thereby, except for filings and other actions required pursuant to federal
     and state securities or blue sky laws or the order of the Commission
     declaring the Shelf Registration Statement effective, as to which no
     opinion need be expressed, or the Shipping Act, 1916, as amended, as to
     which no opinion need be expressed, and those already obtained and made
     under the Delaware General Corporation Law ("DGCL").



                                       17
<PAGE>   18

            (vii) The Company is not (A) an "investment company" or an entity
     "controlled" by an "investment company" under 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. In rendering the opinion in this paragraph (vii) Weil, Gotshal &
     Manges LLP shall have assumed with the Purchaser's permission that Loews
     (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.

            (viii) The statements in the Offering Document under the caption
     "Description of the Debentures", insofar as they constitute descriptions of
     the Indenture or the Offered Securities or refer to statements of law or
     legal conclusions under the DGCL, constitute fair summaries thereof in all
     material respects. The statements in the Offering Document under the
     caption "Description of Capital Stock", insofar as they constitute
     descriptions of the Common Stock or refer to statements of law or legal
     conclusions under the DGCL, constitute fair summaries thereof in all
     material respects. The discussion under the caption "Certain United States
     Federal Income Tax Considerations" in the Offering Document accurately
     describes in all material respects the U.S. federal income tax aspects of
     the acquisition, ownership and disposition of the Offered Securities and
     the Underlying Shares, and provides a fair summary in all material respects
     of the provisions of the Internal Revenue Code of 1986, as amended,
     summarized therein. The opinions of such counsel under the caption "Certain
     United States Federal Income Tax Considerations" in the Offering Document
     are confirmed.

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

            (x) It is not necessary in connection with (i) the offer, sale and
     delivery of the Offered Securities by the Company to the Purchaser pursuant
     to this Agreement or (ii) the resales of the Offered Securities by the
     Purchaser to Subsequent Purchasers in the manner contemplated hereby to
     register the Offered Securities under the Securities Act or to qualify an
     indenture in respect thereof under the Trust Indenture Act; and

            (xi) Such counsel has participated in conferences with directors,
     officers and other representatives of the Company, representatives of the
     independent public accountants for the Company, representatives of the
     Purchaser and representatives of counsel for the Purchaser, at which
     conferences the contents of the Offering Document 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 the statements contained in the Offering
     Document (except to the extent specified in such counsel's opinion), no
     facts have come to such counsel's attention which lead such counsel to
     believe that the Offering Document or any amendment or supplement thereto
     prior to the Closing Date, at the time the Offering Document was issued, at
     the time any such amended or supplemented Offering Document was issued or
     at the Closing Date, contained or contains an untrue statement of



                                       18
<PAGE>   19

     a material fact or omitted or omits to state a material fact necessary to
     make the statements contained therein, in light of the circumstances under
     which they were made, not misleading (it being understood that such counsel
     need express no view with respect to the financial statements and related
     notes and the other financial, statistical and accounting data included or
     which should be included in the Offering Document).

     Such opinion may be limited to the laws of the States of New York and
Texas, the corporate laws of the State of Delaware and the federal laws of the
United States.

            (f) The Purchaser shall have received from Shearman & Sterling,
counsel for the Purchaser, such opinion or opinions, dated the Closing Date,
with respect to the incorporation of the Company, the validity of the Offered
Securities, the Offering Document, the exemption from registration for the offer
and sale of the Offered Securities by the Company to the Purchaser and the
resales by the Purchaser as contemplated hereby and other related matters as the
Purchaser may require, and the Company shall have furnished to such counsel such
documents as they request for the purpose of enabling them to pass upon such
matters.

            (g) The Purchaser shall have received a certificate, dated the
Closing Date, of the President or any Vice President and a principal financial
or accounting officer of the Company in which such officers, to the best of
their knowledge after reasonable investigation, shall state that the
representations and warranties of the Company in this Agreement are true and
correct, that the Company 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 respective date of the most
recent financial statements included in the Offering Document, 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 the Company and its subsidiaries taken as
a whole, except as set forth in or contemplated by the Offering Document or as
described in such certificate.

            (h) The Purchaser shall have received from Loews an executed copy of
an agreement that Loews, for a period of 90 days after the date hereof, will not
offer, sell, contract to sell, pledge or otherwise dispose of, directly or
indirectly, any shares of Common Stock of the Company or any securities
convertible into or exercisable or exchangeable for such Common Stock without
the prior written consent of the Purchaser, or publicly disclose the intention
to make any such offer, sale, pledge or disposition, except for the exchange of
shares of Common Stock for any of Loews' outstanding 3 1/8% Exchangeable
Subordinated Notes due 2007.

            (i) The Registration Rights Agreement shall have been duly executed
and delivered by the Company and (assuming due execution, delivery and
performance by the Purchaser) be in full force and effect. The Purchaser shall
have received an executed copy of an agreement between Loews and the Company
under which Loews waives any provisions in the Loews Registration Rights
Agreement that are inconsistent with and would impair the Company's ability to
comply with its covenants and agreements in the Registration Rights Agreement.

            (j) In the event that the Purchaser exercises its option provided in
Section 3(b) to purchase all or any portion of the Option Securities, the
representations and warranties of the



                                       19
<PAGE>   20

Company contained herein and the statements of officers of the Company made
pursuant to the provisions hereof shall be true and correct as of the Date of
Delivery and, at the Date of Delivery, the Purchaser shall have received:

            (i) Letter from Deloitte & Touche LLP dated the Date of Delivery,
     substantially in the same form and substance as the letter furnished to the
     Purchaser pursuant to Section 6(b), except that the "specified date" in the
     letter furnished pursuant to this paragraph shall be a date not more than
     three business days prior to the Date of Delivery.

            (ii) The opinions of William C. Long, Esq., the General Counsel of
     the Company, and Weil, Gotshal & Manges LLP, counsel for the Company, each
     dated the Date of Delivery, relating to the Option Securities to be
     purchased on the Date of Delivery and otherwise to substantially the same
     effect as the opinions provided in Sections 6(d) and 6(e).

            (iii) The opinion of Shearman & Sterling, counsel for the Purchaser,
     dated the Date of Delivery, relating to the Option Securities to be
     purchased on the Date of Delivery and otherwise to the same effect as the
     opinion provided in Section 6(f).

            (iv) A certificate, dated the Date of Delivery, of the President or
     any Vice President and a principal financial or accounting officer of the
     Company confirming that the certificate delivered at the Closing Date
     pursuant to Section 6(g) remains true and correct as of the Date of
     Delivery.

         (k) On the Closing Date and at the Date of Delivery, counsel for the
Purchaser shall have been furnished with such documents as they may reasonably
require for the purpose of enabling them to pass upon the issuance and sale of
the Offered Securities as herein contemplated, or in order to evidence the
accuracy of any of the representations or warranties, or the fulfillment of any
of the conditions, herein contained; and all proceedings taken by the Company in
connection with the issuance and sale of the Offered Securities as herein
contemplated shall be reasonably satisfactory in form and substance to the
Purchaser and counsel for the Purchaser.

     7. Indemnification and Contribution. (a) The Company agrees to indemnify
and hold harmless the Purchaser and each person, if any, who controls the
Purchaser within the meaning of Section 15 of the Securities Act or Section 20
of the Exchange Act as follows:

            (i) against any and all loss, liability, claim or damage, as
     incurred, arising out of any untrue statement or alleged untrue statement
     of a material fact contained in the Offering Document, or the omission or
     alleged omission therefrom of a material fact necessary in order to make
     the statements therein, in the light of the circumstances under which they
     were made, not misleading;

            (ii) against any and all loss, liability, claim or damage, as
     incurred, to the extent of the aggregate amount paid in settlement of any
     litigation, or any investigation or proceeding by any governmental agency
     or body, commenced or threatened, or of any claim whatsoever based upon any
     such untrue statement or omission, or any such alleged


                                       20
<PAGE>   21

     untrue statement or omission; provided that any such settlement is effected
     with the written consent of the Company; and

            (iii) against any and all expense whatsoever, as incurred (including
     the fees and disbursements of counsel chosen by the Purchaser), reasonably
     incurred in investigating, preparing or defending against any litigation,
     or any investigation or proceeding by any governmental agency or body,
     commenced or threatened, or any claim whatsoever based upon any such untrue
     statement or omission, or any such alleged untrue statement or omission;

provided, however, that the Company shall not be liable in any such case for or
in respect of any loss, liability, claim, damage or expense to the extent
arising out of or based upon any untrue statement or omission or alleged untrue
statement or omission made in reliance upon and in conformity with written
information furnished to the Company by the Purchaser expressly for use in the
Offering Document, it being understood and agreed that the only such information
consists of the information described in subsection (b) below.

      (b) The Purchaser agrees to indemnify and hold harmless the Company and
each person, if any, who controls the Company within the meaning of Section 15
of the Securities Act or Section 20 of the Exchange Act against any and all
loss, liability, claim, damage and expense described in the indemnity contained
in subsections (a)(i), (ii) and (iii) of this Section, as incurred, but only
with respect to untrue statements or omissions, or alleged untrue statements or
omissions, made in the Offering Document in reliance upon and in conformity with
written information furnished to the Company by the Purchaser expressly for use
in the Offering Document, it being understood and agreed that the following is
the only such information furnished by the Purchaser to the Company for use in
the Offering Document: the first, second and third sentences of the first
paragraph and the second paragraph under the caption "Plan of Distribution -
Debentures Are Not Being Registered," the second sentence of the paragraph under
the caption "Plan of Distribution - New Issue of Debentures" and the first and
second paragraphs under the caption "Plan of Distribution - Price Stabilization
and Short Positions."

      (c) Each indemnified party shall give notice as promptly as reasonably
practicable to each indemnifying party of any action commenced against it in
respect of which indemnity may be sought hereunder, but failure to so notify an
indemnifying party shall not relieve such indemnifying party from any liability
hereunder to the extent it is not materially prejudiced as a result thereof and
in any event shall not relieve it from any liability which it may have otherwise
than on account of this indemnity agreement. In case any such action is brought
against any indemnified party and it notifies the indemnifying party of the
commencement thereof, the indemnifying party will be entitled to participate
therein and, to the extent that it may wish, 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 will not be liable to such
indemnified party under this Section for any legal or other expenses
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, settle,
compromise or consent to the entry of any



                                       21
<PAGE>   22

judgment with respect to any pending or threatened action in respect of which
any indemnified party is or could have been a party and indemnity could have
been sought hereunder by such indemnified party unless such settlement,
compromise or consent (i) includes an unconditional release of such indemnified
party from all liability on any claims that are the subject matter of such
action and (ii) does not include any statement as to, or an admission of, fault,
culpability or a failure to act by or on behalf of an indemnified person.

      (d) If the indemnification provided for in Section 7(a) or (b) is for any
reason unavailable or insufficient to hold harmless an indemnified party in
respect of any losses, liabilities, claims, damages or expenses referred to
therein, then each indemnifying party shall contribute to the aggregate amount
of such losses, liabilities, claims, damages and expenses incurred by such
indemnified party, as incurred, (i) in such proportion as is appropriate to
reflect the relative benefits received by the Company on the one hand and the
Purchaser on the other hand from the offering of the Offered Securities pursuant
to this Agreement or (ii) if the allocation provided by clause (i) is not
permitted by applicable law, in such proportion as is appropriate to reflect not
only the relative benefits referred to in clause (i) above but also the relative
fault of the Company on the one hand and of the Purchaser on the other hand in
connection with the statements or omissions which resulted in such losses,
liabilities, claims, damages or expenses, as well as any other relevant
equitable considerations. The relative benefits received by the Company on the
one hand and the Purchaser on the other hand in connection with the offering of
the Offered Securities pursuant to this Agreement shall be deemed to be in the
same respective proportions as the total net proceeds from the offering of the
Offered Securities pursuant to this Agreement (before deducting expenses)
received by the Company and the total discounts and commissions received by the
Purchaser, bear to the aggregate initial offering price of the Offered
Securities. The relative fault of the Company on the one hand and the Purchaser
on the other hand shall be determined by reference to, among other things,
whether any such untrue or alleged untrue statement of a material fact or
omission or alleged omission to state a material fact relates to information
supplied by the Company or by the Purchaser and the parties' relative intent,
knowledge, access to information and opportunity to correct or prevent such
statement or omission.

      The Company and the Purchaser agree that it would not be just and
equitable if contribution pursuant to this Section 7(d) were determined by pro
rata allocation or by any other method of allocation which does not take account
of the equitable considerations referred to above in this Section 7(d). The
aggregate amount of losses, liabilities, claims, damages and expenses incurred
by an indemnified party and referred to above in this Section 7(d) shall be
deemed to include any legal or other expenses reasonably incurred by such
indemnified party in investigating, preparing or defending against any
litigation, or any investigation or proceeding by any governmental agency or
body, commenced or threatened, or any claim whatsoever based upon any such
untrue or alleged untrue statement or omission or alleged omission.

      Notwithstanding the provisions of this Section 7(d), the Purchaser shall
not be required to contribute any amount in excess of the amount by which the
total price at which the Offered Securities purchased by it were resold exceeds
the amount of any damages which the Purchaser has otherwise been required to pay
by reason of such untrue or alleged untrue statement or omission or alleged
omission.



                                       22
<PAGE>   23

      No person guilty of fraudulent misrepresentation (within the meaning of
Section 11(f) of the Securities Act) shall be entitled to contribution from any
person who was not guilty of such fraudulent misrepresentation.

      For purposes of this Section 7(d), each person, if any, who controls the
Purchaser within the meaning of Section 15 of the Securities Act or Section 20
of the Exchange Act shall have the same rights to contribution as the Purchaser,
and each person, if any, who controls the Company within the meaning of Section
15 of the Securities Act or Section 20 of the Exchange Act shall have the same
rights to contribution as the Company.

      8. Survival of Certain Representations and Obligations. The respective
indemnities, agreements, representations, warranties and other statements of the
Company or its officers and of the Purchaser set forth in or made pursuant to
this Agreement will remain in full force and effect, regardless of any
investigation, or statement as to the results thereof, made by or on behalf of
the Purchaser, the Company or any of their respective representatives, officers
or directors or any controlling person, and will survive delivery of and payment
for the Offered Securities. If for any reason the purchase of the Offered
Securities by the Purchaser is not consummated, the Company shall remain
responsible for the expenses to be paid or reimbursed by it pursuant to Section
5 and the respective obligations of the Company and the Purchaser pursuant to
Section 7 shall remain in effect and if any Offered Securities have been
purchased hereunder the representations and warranties in Sections 2 and 4 and
all obligations under Section 5 shall remain in effect. If the purchase of the
Offered Securities by the Purchaser is not consummated for any reason other than
solely because of the occurrence of any event specified in clause (iii), (iv),
(v) or (vi) of Section 6(b), the Company will reimburse the Purchaser for all
out-of-pocket expenses (including fees and disbursements of counsel) reasonably
incurred by it in connection with the offering of the Offered Securities.

      9. Notices. All communications hereunder will be in writing and, if sent
to the Purchaser will be mailed, delivered or telegraphed and confirmed to the
Purchaser at 4 World Financial Center New York, N.Y 10080, Attention: Raymond
Wong, or, if sent to the Company, will be mailed, delivered or telegraphed and
confirmed to it at 15415 Katy Freeway, Houston, Texas 77094, Attention:
Corporate Secretary.

      10. Successors. This Agreement will inure to the benefit of and be binding
upon the parties hereto and their respective successors and the controlling
persons referred to in Section 7, and no other person will have any right or
obligation hereunder, except that holders of Offered Securities shall be
entitled to enforce the agreements for their benefit contained in the second and
third sentences of Section 5(b) hereof against the Company as if such holders
were parties hereto.

      11. Counterparts. This Agreement may be executed in any number of
counterparts, each of which shall be deemed to be an original, but all such
counterparts shall together constitute one and the same Agreement.

      12. APPLICABLE LAW. THIS AGREEMENT SHALL BE GOVERNED BY, AND CONSTRUED IN
ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK WITHOUT REGARD TO PRINCIPLES
OF CONFLICTS OF LAWS.



                                       23
<PAGE>   24

          The Company hereby submits to the non-exclusive jurisdiction of the
Federal and state courts in the Borough of Manhattan in The City of New York in
any suit or proceeding arising out of or relating to this Agreement or the
transactions contemplated hereby.

                            [SIGNATURE PAGE FOLLOWS]


                                       24
<PAGE>   25




      If the foregoing is in accordance with the Purchaser's understanding of
our agreement, kindly sign and return to the Company one of the counterparts
hereof, whereupon it will become a binding agreement between the Company and the
Purchaser in accordance with its terms.

                                       Very truly yours,

                                       DIAMOND OFFSHORE DRILLING, INC.



                                       By: /s/ William C. Long
                                          --------------------------------------
                                          Name: William C. Long
                                          Title: Vice President, General Counsel
                                                 & Secretary

The foregoing Purchase Agreement is
hereby confirmed and accepted as of the
date first above written.

MERRILL LYNCH & CO.
MERRILL LYNCH, PIERCE, FENNER & SMITH
            INCORPORATED




By: /s/ Joseph C. Gatto, Jr.
   --------------------------------------
           Authorized Signatory