Document:

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                                                                    EXHIBIT 10.1

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                                  $805,000,000

                         DIAMOND OFFSHORE DRILLING, INC.

                       ZERO COUPON CONVERTIBLE DEBENTURES
                                 DUE JUNE 6, 2020

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                               PURCHASE AGREEMENT

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                               PURCHASE AGREEMENT

                                                                    May 31, 2000

Credit Suisse First Boston Corporation
Eleven Madison Avenue
New York, N.Y. 10010-3629

Dear Sirs:

         1. Introductory. Diamond Offshore Drilling, Inc., a Delaware
corporation (the "COMPANY"), proposes, subject to the terms and conditions
stated herein, to issue and sell to Credit Suisse First Boston Corporation (the
"PURCHASER") and the Purchaser proposes to purchase and accept from the Company
U.S. $805,000,000 aggregate principal amount of its Zero Coupon Convertible
Debentures Due June 6, 2020 (the "OFFERED SECURITIES") to be issued under an
Indenture dated as of February 4, 1997, as supplemented by a Second 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, on a private placement basis pursuant to an exemption under
Section 4(2) of the United States Securities Act of 1933, as amended (the
"SECURITIES ACT"), and hereby agrees with the Purchaser as follows:

         2. Representations and Warranties of the Company. The Company
represents and warrants to, and agrees with, the Purchaser that:

               (a) An offering memorandum relating to the Offered Securities has
been prepared by the Company. Such offering memorandum (the "OFFERING
MEMORANDUM"), as supplemented as of the Closing Date, and any other document
approved in writing by the Company for use in connection with the contemplated
resale of the Offered Securities, are hereinafter collectively referred to as
the "OFFERING DOCUMENT." On the Closing Date, the Offering Document 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 therein, it being understood and agreed that the only such information
is that described as such in Section 7(b) hereof. Except as disclosed in the
Offering Document, on the Closing Date (as defined herein), the Company's Annual
Report on Form 10-K most recently filed with the Securities and Exchange
Commission (the "COMMISSION") and all subsequent reports (collectively, the
"EXCHANGE ACT REPORTS") which have been filed by the Company with the Commission
pursuant to the Securities Exchange Act of 1934 (the "EXCHANGE ACT"), do 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,

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when they were filed with the Commission, conformed in all material respects to
the requirements of the Exchange Act and the rules and regulations of the
Commission thereunder.

               (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 the Company 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 the Company to
be so qualified would not have a material adverse effect on the business,
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 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; 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
the capital stock of each subsidiary owned by the Company, directly or through
subsidiaries, is owned 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 (as
defined below), the Indenture will have been duly executed and delivered, such
Offered Securities will have been duly executed, authenticated, issued and
delivered and will conform to the description thereof contained in the Offering
Document and the Indenture and such Offered Securities 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 each Closing Date, such Offered Securities will be
convertible at the rate of 8.6075 shares (the "UNDERLYING SHARES") of common
stock, par value $.0l per share (the "COMMON STOCK"), of the Company 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 outstanding

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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.

               (f) 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.

               (g) Except for the Registration Rights Agreement dated October
16, 1995, between the Company and Loews Corporation, as amended (the "LOEWS
REGISTRATION RIGHTS AGREEMENT") and the Registration Rights Agreement (as
defined below), 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
Registration Statement or in any securities being registered pursuant to any
other registration statement filed by the Company under the Securities Act.

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

               (i) No consent, approval, authorization, or order of, or filing
with, any governmental agency or body or any court is required for the
consummation of the transactions contemplated by this Agreement and the
Registration Rights Agreement, dated as of the Closing Date, between the Company
and the Purchaser (the "REGISTRATION RIGHTS AGREEMENT") in connection with the
issuance and sale of the Offered Securities by the Company, except for the
filing of the Shelf Registration Statement (as defined in the Registration
Rights Agreement) and the order of the Commission declaring the Shelf
Registration Statement (as defined in the Registration Rights Agreement)
effective and such as may be required under state securities laws.

               (j) 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, 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 except, in each case other than

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with respect to such charter or bylaws, which conflict, breach or default or
violation would not impair the Company's or any of its subsidiaries' ability to
perform the obligations hereunder or have any material adverse effect upon the
consummation of the transactions contemplated hereby; and the Company has full
power and authority to authorize, issue and sell the Offered Securities and the
Underlying Shares as contemplated by this Agreement.

               (k) 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.

               (l) 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 or the
Exchange Act Reports, 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 or the Exchange Act
Reports, 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.

               (m) 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 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.

               (n) 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.

               (o) 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,

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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.

               (p) 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.

               (q) 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 the Exchange Act
Reports, 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, 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.

               (r) 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.

               (s) Except as disclosed in the Offering Document or in the
Exchange Act Reports, 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 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.

               (t) 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"

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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").

         (u) 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.

         (v) 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 and sale of the Offered Securities by the Company to
the Purchaser in the manner contemplated by this Agreement will be exempt from
the registration requirements of the Securities Act by reason of Section 4(2)
thereof; and it is not necessary to qualify an indenture in respect of the
Offered Securities under the United States Trust Indenture Act of 1939, as
amended (the "TRUST INDENTURE ACT").

         (w) Neither the Company, nor any of its affiliates, nor any person
acting on its or their behalf (i) has, within the six-month period prior to the
date hereof, offered or sold the Offered Securities or any security of the same
class or series as the Offered Securities 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. 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 97.75% of issue price of U.S. $499.60 per $1,000 principal amount at
maturity thereof, U.S. $805,000,000 aggregate principal amount at maturity of
the Offered Securities.

     The Company will deliver against payment of the purchase price the Offered
Securities in the form of 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. Payment for the Offered Securities shall be
made by the Purchaser in Federal (same day) funds by wire transfer to an account
at a bank acceptable to the Purchaser drawn to the order of the Company at the
office of Andrews & Kurth L.L.P., Houston, Texas, at 9:00 A.M. (Houston time),
on June 6, 2000, or at such other time not later than seven full business days
thereafter as the Purchaser and the Company determine, such time being herein
referred to as the "CLOSING DATE," against delivery to the Trustee as custodian
for DTC of the Global Securities

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representing all of the Offered Securities. The Global Securities will be made
available for checking at the above office of Andrews & Kurth L.L.P., Houston,
Texas at least 24 hours prior to the Closing Date.

     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 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 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.
The Purchaser agrees, with respect to resales made in reliance on Rule 144A of
any of the Offered Securities, to deliver either with the confirmation of such
resale or otherwise prior to settlement of such resale a notice to the effect
that the resale of such Offered Securities has been made in reliance upon the
exemption from the registration requirements of the Securities Act provided by
Rule 144A.

     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

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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, and the
Company will furnish to the Purchaser on the Closing Date three copies of the
Offering Document signed by a duly authorized officer of the Company, one of
which will include the independent accountants' reports therein manually signed
by such independent accountants. 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 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 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.

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         (g) The Company will pay all expenses incidental to the performance of
its obligations under this Agreement, for 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, for any fees charged by investment
rating agencies for the rating of the Offered Securities, the fees and expenses
of the Trustee and its professional advisers; 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; the
cost of qualifying the Offered Securities for trading in The Portal(SM) Market
("PORTAL") of The Nasdaq Stock Market, Inc. and any expenses incidental thereto,
the cost of any advertising approved by the Company in connection with the issue
of the Offered Securities; for 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 Registered Securities and for
expenses incurred in distributing the Offering Document (including any
amendments and supplements thereto). Except as provided in 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 will not at any time offer, sell, contract to sell,
pledge or otherwise dispose of, directly or indirectly, any securities under
circumstances where such offer, sale, pledge, contract or disposition would
cause the exemption afforded by Section 4(2) of the Securities Act to cease to
be applicable to the offer and sale of the Offered Securities.

         (i) For a period of 90 days after the date hereof, the Company will not
offer, sell, contract to sell, pledge, or otherwise dispose of, 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 Company's 3 3/4%
Convertible Subordinated Notes due 2007.

         (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.

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     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 Closing Date,
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 ("RULES AND REGULATIONS") 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 and in
     the Exchange Act Reports comply as to form in all material respects with
     the applicable accounting requirements of the Securities Act and the
     related published Rules and Regulations;

                 (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 and in the
     Exchange Act Reports;

                 (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 or in the Exchange Act Reports
          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
          and the Exchange Act Reports; or

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                 (C) for the period from the closing date of the latest income
          statement included in or incorporated by reference in the Offering
          Document and Exchange Act Reports 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 and Exchange Act Reports, 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 and
          Exchange Act Reports disclose 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 and the Exchange Act Reports
     (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) 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) 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

                                       12

<PAGE>   13

emergency makes it impractical or inadvisable to proceed with completion of the
offering or sale of and payment for the Offered Securities.

         (c) 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, 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 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, 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, 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 Memorandum, 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 Registration Statement or in any securities being
     registered pursuant to any other registration statement filed by the
     Company under the Securities Act.

                                       13

<PAGE>   14

                 (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 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 default, breach or violation which would not, individually or in the
     aggregate, have a material adverse effect on the business, 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.

                 (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 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.

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

                                       14

<PAGE>   15

                 (i) The Company 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 Offering
     Document and Exchange Act Reports.

                 (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 and upon receipt by the Company of the conversion price
     therefor, will be validly issued, fully paid and non-assessable. 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.

                 (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 4 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

                                       15
<PAGE>   16

     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, 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, breach or violation as would not impair
     the Company's ability to perform its obligations under the Indenture, this
     Agreement or the Registration Rights Agreement or have any material adverse
     effect upon the consummation of the transactions contemplated by the
     Indenture, 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 and delivery by the Company of
     this Agreement or the Registration Rights Agreement or the consummation by
     the Company of the transactions contemplated thereby and hereby, in
     connection with the issuance or sale of the Offered Securities by the
     Company, 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").

                 (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
     Corporation (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 Common 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

                                       16

<PAGE>   17

     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.

                 (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 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, at the time the
     Offering Document was issued or at the Closing Date, contained or contains
     an untrue statement of 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 or that the
     documents incorporated by reference in the Offering Document as filed with
     the Commission prior to the Closing Date as of the dates they were filed
     with the Commission contained an untrue statement of a material fact or
     omitted to state a material fact required to be stated therein or necessary
     to make the statements contained therein 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.

         (e) The Purchaser shall have received from Andrews & Kurth L.L.P.,
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 Memorandum, 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

                                       17

<PAGE>   18

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.

         (f) 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 in the Offering Document and 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 the Company and its subsidiaries taken as
a whole except as set forth in or contemplated by the Offering Document or
Exchange Act Reports or as described in such certificate.

     The Company will furnish the Purchaser with such conformed copies of such
opinions, certificates, letters and documents as the Purchaser reasonably
requests. The Purchaser may in its sole discretion waive on behalf of the
Purchaser compliance with any conditions to the obligations of the Purchaser
hereunder, whether in respect of an Optional Closing Date or otherwise.

         (g) The Purchaser shall have received from Loews Corporation ("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.

         (h) 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.

     7. Indemnification and Contribution. (a) The Company will indemnify and
hold harmless the Purchaser, its partners, directors and officers and each
person, if any, who controls such Purchaser within the meaning of Section 15 of
the Securities Act, against any losses, claims, damages or liabilities, joint or
several, to which the Purchaser may become subject, under the Securities Act or
the Exchange Act or otherwise, insofar as such losses, claims, damages or
liabilities (or actions in respect thereof) arise out of or are based upon any
untrue statement or alleged untrue statement of any material fact contained in
the Offering Document, or any amendment or supplement thereto, or the Exchange
Act Reports, or arise out of or are based upon the omission or alleged omission
to state therein a material fact necessary in order to make the statements
therein, in light of the circumstances under which they were made, not
misleading, and will reimburse the Purchaser

                                       18

<PAGE>   19

for any legal or other expenses reasonably incurred by the Purchaser in
connection with investigating or defending any such loss, claim, damage,
liability or action as such expenses are incurred; provided, however, that the
Company will 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 in or omission or alleged omission from any of such
documents in reliance upon and in conformity with written information furnished
to the Company by the Purchaser specifically for use therein, it being
understood and agreed that the only such information consists of the information
described as such in subsection (b) below.

         (b) The Purchaser will indemnify and hold harmless the Company, its
directors and officers and each person, if any, who controls the Company within
the meaning of Section 15 of the Securities Act, against any losses, claims,
damages or liabilities to which the Company may become subject, under the
Securities Act or the Exchange Act or otherwise, insofar as such losses, claims,
damages or liabilities (or actions in respect thereof) arise out of or are based
upon any untrue statement or alleged untrue statement of any material fact
contained in the Offering Document, or any amendment or supplement thereto, or
arise out of or are based upon the omission or the alleged omission to state
therein a material fact required to be stated or necessary in order to make the
statements therein, in the light of the circumstances under which they were
made, 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 reliance upon and in conformity with written information
furnished to the Company by the Purchaser specifically for use therein, and will
reimburse any legal or other expenses reasonably incurred by the Company in
connection with investigating or defending any such loss, claim, damage,
liability or action as such expenses are incurred, it being understood and
agreed that the only such information furnished by the Purchaser consists of the
following information in the Offering Document furnished on behalf of the
Purchaser: the sixth paragraph below the "Table of Contents" and the second,
third and sixth paragraphs under the caption "Plan of Distribution;" provided
however, that the Purchaser shall not be liable for any losses, claims, damages
or liabilities arising out of or based upon the Company's failure to perform its
obligations under Section 5(a) of this Agreement.

         (c) Promptly after receipt by an indemnified party under this Section
of notice of the commencement of any action, such indemnified party will, if a
claim in respect thereof is to be made against the indemnifying party under
subsection (a) or (b) above, notify the indemnifying party of the commencement
thereof; but the omission so to notify the indemnifying party will not relieve
it from any liability which it may have to any indemnified party otherwise than
under subsection (a) or (b) above, except to the extent a defense or
counterclaim has been foreclosed. 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

                                       19

<PAGE>   20

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, effect any settlement of 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 (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 this Section is unavailable
or insufficient to hold harmless an indemnified party under subsection (a) or
(b) above, then each indemnifying party shall contribute to the amount paid or
payable by such indemnified party as a result of the losses, claims, damages or
liabilities referred to in subsection (a) or (b) above (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 from the offering of the Offered
Securities or (ii) if the allocation provided by clause (i) above 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 the Purchaser on the other in
connection with the statements or omissions which resulted in such losses,
claims, damages or liabilities 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 shall be deemed to be in the same proportion as
the total net proceeds from the offering (before deducting expenses) received by
the Company bear to the total discounts and commissions received by the
Purchaser from the Company under this Agreement. 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 or the Purchaser
and the parties' relative intent, knowledge, access to information and
opportunity to correct or prevent such untrue statement or omission. The amount
paid by an indemnified party as a result of the losses, claims, damages or
liabilities referred to in the first sentence of this subsection (d) shall be
deemed to include any legal or other expenses reasonably incurred by such
indemnified party in connection with investigating or defending any action or
claim which is the subject of this subsection (d). Notwithstanding the
provisions of this subsection (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. 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.

         (e) The obligations of the Company under this Section shall be in
addition to any liability which the Company may otherwise have and shall extend,
upon the same terms and conditions, to each person, if any, who controls the
Purchaser within the meaning of the Securities Act or the Exchange Act; and the
obligations of the Purchaser under this Section shall be in addition to any
liability which the Purchaser may otherwise have and shall extend, upon the same
terms and

                                       20

<PAGE>   21

conditions, to each person, if any, who controls the Company within the meaning
of the Securities Act or the Exchange Act.

     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 Eleven Madison Avenue, New York, N.Y. 10010-3629, Attention:
Investment Banking Department -- Transactions Advisory Group, 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.

     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.

     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.

                                       21
<PAGE>   22

                            [SIGNATURE PAGE FOLLOWS]

                                       22

<PAGE>   23

     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/ LAWRENCE R. DICKERSON
                                                --------------------------------
                                                Lawrence R. Dickerson
                                                President and Chief Operating
                                                Officer

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

CREDIT SUISSE FIRST BOSTON CORPORATION

By: /s/ ROME G. ARNOLD
   ------------------------------
   Rome G. Arnold
   Managing Director

                                       23
<PAGE>   24

                                   SCHEDULE A

<TABLE>
<CAPTION>
                                                        PRINCIPAL AMOUNT
                                                           OF OFFERED
           PURCHASER                                       SECURITIES
           ---------                                    ----------------
<S>                                                       <C>
Credit Suisse First Boston Corporation.............       $805,000,000
                                                          ------------
     Total.........................................       $805,000,000
</TABLE>

                                       24<PAGE>   1
                                                                    EXHIBIT 10.2

                                                                  Execution Copy

                            $805,000,000 AT MATURITY

                         DIAMOND OFFSHORE DRILLING, INC.

               ZERO COUPON CONVERTIBLE DEBENTURES DUE JUNE 6, 2020

                          REGISTRATION RIGHTS AGREEMENT

                                                                    June 6, 2000

Credit Suisse First Boston Corporation
Eleven Madison Avenue
New York, New York 10010-3629

Dear Sirs:

     Diamond Offshore Drilling, Inc., a Delaware corporation (the "Company"),
proposes to issue and sell to Credit Suisse First Boston Corporation (the
"Initial Purchaser"), and the Initial Purchaser proposes to purchase and accept
from the Company, upon the terms set forth in a purchase agreement of even date
herewith (the "Purchase Agreement"), $805,000,000 aggregate principal amount at
maturity of its Zero Coupon Convertible Debentures due June 6, 2020 (the
"Debentures"). The Debentures will be issued pursuant to a Second Supplemental
Indenture, dated as of June 6, 2000, which supplements the Indenture dated
February 4, 1997 (taken together, the "Indenture") by and between the Company
and The Chase Manhattan Bank (the "Trustee"). Under the terms of the Indenture,
the Debentures are convertible, in whole or in part, into shares of Common
Stock, par value $.01 per share (the "Conversion Shares" and, together with the
Debentures, the "Securities"), at the option of the holders thereof at any time
following the date of original issuance thereof at the Conversion Rate (as
defined in the Indenture) set forth in the Debentures, as adjusted from time to
time pursuant to the Indenture. As an inducement to the Initial Purchaser, the
Company agrees with the Initial Purchaser, for the benefit of the holders of the
Debentures (including, without limitation, the Initial Purchaser) and Conversion
Shares (collectively, the "Holders"), as follows:

     1. Resale Shelf Registration. (a) The Company shall, at its cost, use its
reasonable best efforts to file as promptly as practicable (but in no event more
than 90 days after the Closing Date (as defined in the Purchase Agreement)) with
the Securities and Exchange Commission (the "Commission") and thereafter shall
use its reasonable best efforts to cause to be declared effective no later than
180 days after the Closing Date a registration statement (the "Resale Shelf
Registration Statement") on an appropriate form under the Securities Act of
1933, as amended (the "Securities Act") relating to the offer and sale of the
Transfer Restricted Securities (as defined in Section 5 hereof) by the Holders
thereof from time to time in accordance with the methods of distribution set
forth in the Resale Shelf Registration Statement and Rule 415 under the
Securities Act (hereinafter, the "Resale Shelf Registration"); provided,
however, that no Holder (other than the Initial Purchaser) shall be entitled to
have the Securities held by it covered by such Resale Shelf Registration

<PAGE>   2
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Statement unless such Holder agrees in writing to be bound by all the provisions
of this Agreement applicable to such Holder.

          (b) The Company shall use its reasonable best efforts to keep the
Resale Shelf Registration Statement continuously effective in order to permit
the prospectus included therein to be lawfully delivered by the Holders of the
relevant Securities, for a period of two years from the date of its
effectiveness or such shorter period that will terminate when all the Securities
covered by the Resale Shelf Registration Statement (i) have been sold pursuant
thereto or (ii) are no longer Transfer Restricted Securities as defined in
Section 5(d) (in any such case, such period being called the "Shelf Registration
Period"). The Company shall be deemed not to have used its reasonable best
efforts to keep the Resale Shelf Registration Statement effective during the
requisite period if it voluntarily takes any action (other than as contemplated
by Section 2(h)) that would result in Holders of Securities covered thereby not
being able to offer and sell such Securities during that period, unless such
action is required by applicable law.

          (c) Notwithstanding any other provisions of this Agreement to the
contrary, the Company shall cause the Resale Shelf Registration Statement and
the related prospectus and any amendment or supplement thereto, as of the
effective date of the Resale Shelf Registration Statement, amendment or
supplement, (i) to comply in all material respects with the applicable
requirements of the Securities Act and the rules and regulations of the
Commission and (ii) not to contain any untrue statement of a material fact or
omit to state a material fact required to be stated therein or necessary in
order to make the statements therein, in light of the circumstances under which
they were made, not misleading.

          (d) Each Holder agrees that if such Holder wishes to sell such
Holder's Securities pursuant to a Resale Shelf Registration Statement and
related prospectus, it will do so in accordance with this Section 1(d). Each
Holder wishing to sell Securities pursuant to a Resale Shelf Registration
Statement and related prospectus agrees to deliver a Notice and Questionnaire
(the form of which is attached as Annex A to the Offering Memorandum and in
connection with the offering of the Debentures) to the Company prior to any
intended distribution of Securities under the Resale Shelf Registration
Statement. From and after the date the Resale Shelf Registration Statement is
declared effective, the Company shall, as promptly as is practicable after the
date a Notice and Questionnaire is delivered, and in any event within five (5)
Business Days after such date, (i) if required by applicable law, file with the
Commission a post-effective amendment to the Shelf Registration Statement or
prepare and, if required by applicable law, file a supplement to the related
prospectus or a supplement or amendment to any document incorporated therein by
reference or file any other required document so that the Holder delivering such
Notice and Questionnaire is named as a selling securityholder in the Resale
Shelf Registration Statement and the related prospectus in such a manner as to
permit such Holder to deliver such prospectus to purchasers of the Securities in
accordance with applicable law and, if the Company shall file a post-effective
amendment to the Resale Shelf Registration Statement, use all reasonable efforts
to cause such post-effective

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amendment to be declared effective under the Securities Act as promptly as is
practicable, but in any event by the date that is sixty (60) days after the date
such post-effective amendment is required by this clause to be filed; (ii)
provide such Holder copies of any documents filed pursuant to Section 1(d)(i);
and (iii) notify such Holder as promptly as practicable after the effectiveness
under the Securities Act of any post-effective amendment filed pursuant to
Section 1(d)(i); provided, that if such Notice and Questionnaire is delivered
during a period in which the use of the prospectus is suspended pursuant to
Section 2(h), the Company shall so inform the Holder delivering such Notice and
Questionnaire and shall take the actions set forth in clauses (i), (ii) and
(iii) above upon expiration of the suspension period. Notwithstanding anything
contained herein to the contrary, the Company shall be under no obligation to
name any Holder that has not supplied the requisite information required by
Section 1(d) as a selling securityholder in any Registration Statement or
related Prospectus; provided, however, that any Holder that has subsequently
supplied the requisite information required by this Section 1(d) pursuant to the
provisions of this Section (whether or not such Holder has supplied the
requisite information required by this Section 1(d) at the time the Resale Shelf
Registration Statement was declared effective) shall be named as a selling
securityholder in the Resale Shelf Registration Statement or related prospectus
in accordance with the requirements of this Section 1(d).

     2. Registration Procedures. In connection with the Resale Shelf
Registration contemplated by Section 1 hereof, the following provisions apply:

          (a) The Company shall (i) furnish to the Initial Purchaser, prior to
the filing thereof with the Commission, a copy of the Resale Shelf Registration
Statement and each amendment thereof and each supplement, if any, to the
prospectus included therein and, in the event that the Initial Purchaser (with
respect to any portion of an unsold allotment from the original offering) is
participating in the Resale Shelf Registration, the Company shall use its
reasonable best efforts to reflect in each such document, when so filed with the
Commission, such comments as the Initial Purchaser reasonably may propose; and
(ii) include the names of the Holders, who propose to sell Securities pursuant
to the Resale Shelf Registration Statement, as selling securityholders.

          (b) The Company shall give written notice to the Initial Purchaser and
Holders of the Securities (which notice pursuant to clauses (ii)-(v) hereof
shall be accompanied by an instruction to suspend the use of the prospectus
until the requisite changes have been made):

               (i) when the Resale Shelf Registration Statement or any amendment
          thereto has been filed with the Commission and when the Resale Shelf
          Registration Statement or any post-effective amendment thereto has
          become effective;

               (ii) of any request by the Commission for amendments or
          supplements to the Resale Shelf Registration Statement or the
          prospectus included therein or for additional information;

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                                                                  Execution Copy

               (iii) of the issuance by the Commission of any stop order
          suspending the effectiveness of the Resale Shelf Registration
          Statement or the initiation of any proceedings for that purpose;

               (iv) of the receipt by the Company or its legal counsel of any
          notification with respect to the suspension of the qualification of
          the Securities for sale in any jurisdiction or the initiation or
          threatening of any proceeding for such purpose; and

               (v) of the happening of any event (which need not be described
          with any particular degree of specificity) that requires the Company
          to make changes in the prospectus which forms a part of the Resale
          Shelf Registration Statement in order that the prospectus does 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, in light of the circumstances under which they
          were made, not misleading.

          (c) The Company shall make every reasonable effort to obtain the
withdrawal, at the earliest possible time, of any order suspending the
effectiveness of the Resale Shelf Registration Statement.

          (d) The Company shall furnish to each Holder of Securities included
within the coverage of the Resale Shelf Registration, without charge, at least
one copy of the Resale Shelf Registration Statement and any post-effective
amendment thereto, including financial statements and schedules, and, if the
Holder so requests in writing, all exhibits thereto (including those, if any,
incorporated by reference).

          (e) The Company shall, during the Resale Shelf Registration Period,
deliver to each Holder of Securities included within the coverage of the Resale
Shelf Registration, without charge, as many copies of the prospectus (including
each preliminary prospectus) included in the Resale Shelf Registration Statement
and any amendment or supplement thereto as such person may reasonably request.
The Company consents, subject to the provisions of this Agreement, to the use of
the prospectus or any amendment or supplement thereto by each of the selling
Holders of the Securities in connection with the offering and sale of the
Securities covered by the prospectus, or any amendment or supplement thereto,
included in the Resale Shelf Registration Statement in the manner described
therein.

          (f) Prior to any public offering of the Securities, pursuant to any
Resale Shelf Registration Statement, the Company shall register or qualify or
cooperate with the Holders of the Securities included therein and their
respective counsel in connection with the registration or qualification of the
Securities for offer and sale under the securities or "blue sky" laws of such
states of the United States as any Holder of the Securities reasonably requests
in writing and do any and all other acts or things necessary or advisable to
enable the offer and sale in such jurisdictions of the

                                       4
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                                                                  Execution Copy

Securities covered by such Resale Shelf Registration Statement; provided,
however, that the Company shall not be required to (i) qualify generally to do
business in any jurisdiction where it is not then so qualified or (ii) take any
action which would subject it to general service of process or to taxation in
any jurisdiction where it is not then so subject.

          (g) The Company shall cooperate with the Holders of the Securities to
facilitate the timely preparation and delivery of certificates representing the
Securities to be sold pursuant to any Resale Shelf Registration Statement (to
the extent such Securities are certificated) free of any restrictive legends and
in such denominations and registered in such names as the Holders may request a
reasonable period of time prior to sales of the Securities pursuant to such
Resale Shelf Registration Statement.

          (h) Upon the occurrence of any event contemplated by paragraphs (ii)
through (v) of Section 2(b) above during the Shelf Registration Period, the
Company shall promptly prepare and file a post-effective amendment to the Resale
Shelf Registration Statement or a supplement to the related prospectus and any
other required document so that, as thereafter delivered to Holders or
purchasers of Securities, the 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; provided however, that the Company may
delay preparing, filing and distributing any such supplement or amendment (and
continue the suspension of the use of the prospectus) if the Company determines
in good faith that such supplement or amendment would, in the reasonable
judgment of the Company, (i) interfere with or affect the negotiation or
completion of a transaction that is being contemplated by the Company (whether
or not a final decision has been made to undertake such transaction) or (ii)
involve initial or continuing disclosure obligations that are not in the best
interests of the Company's stockholders at such time; provided further, that
neither such delay nor such suspension shall extend for a period of more than 30
days in any three month period or more than 90 days for all such periods in any
twelve month period. If the Company notifies the Initial Purchaser and the
Holders of the Securities in accordance with paragraphs (ii) through (v) of
Section 2(b) above to suspend the use of the prospectus until the requisite
changes to the prospectus have been made, then the Initial Purchaser and the
Holders shall suspend use of such prospectus.

          (i) Not later than the effective date of the Resale Shelf Registration
Statement, the Company will provide CUSIP numbers for the Debentures and the
Conversion Shares registered under the Resale Shelf Registration Statement and
provide the Trustee with a certificate for the Debentures, in a form eligible
for deposit with The Depository Trust Company.

          (j) The Company will comply with all rules and regulations of the
Commission to the extent and so long as they are applicable to the Resale Shelf
Registration and will make generally available to its security holders (or
otherwise provide in accordance with Section 11(a) of the Securities Act) an
earnings statement satisfying the provisions of Section 11(a) of the Securities

                                       5

<PAGE>   6

                                                                  Execution Copy

Act, no later than 45 days after the end of a 12-month period (or 90 days, if
such period is a fiscal year) beginning with the first month of the Company's
first fiscal quarter commencing after the effective date of the Resale Shelf
Registration Statement, which statement shall cover such 12-month period.

          (k) The Company shall cause the Indenture to be qualified under the
Trust Indenture Act of 1939, as amended, in a timely manner and containing such
changes, if any, as shall be necessary for such qualification. In the event that
such qualification would require the appointment of a new trustee under the
Indenture, the Company shall appoint a new trustee thereunder pursuant to the
applicable provisions of the Indenture.

          (l) The Company shall enter into such customary agreements (including,
if requested an underwriting agreement in customary form) and take all such
other action, if any, as any Holder shall reasonably request in order to
facilitate the disposition of the Securities pursuant to any Resale Shelf
Registration.

          (m) The Company shall (i) make reasonably available for inspection by
the Holders, any underwriter participating in any disposition pursuant to the
Resale Shelf Registration Statement and any attorney, accountant or other agent
retained by the Holders or any such underwriter all relevant financial and other
records, pertinent corporate documents and properties of the Company and (ii)
cause the Company's officers, directors, employees, accountants and auditors to
supply all relevant information reasonably requested by the Holders or any such
underwriter, attorney, accountant or agent in connection with the Resale Shelf
Registration Statement, in each case, as shall be reasonably necessary to enable
such persons, to conduct a reasonable investigation within the meaning of
Section 11 of the Securities Act; provided, however, that the foregoing
inspection and information gathering shall be coordinated on behalf of the
Initial Purchaser and the other parties, by one firm of counsel, which firm
shall be Andrews & Kurth L.L.P. until another firm shall be designated as
described in Section 3 hereof; provided further, that (w) no Holder that is a
competitor of the Company shall have any right whatsoever to conduct any
inspection of the Company's records and information; (x) in connection with any
such inspection, any such inspectors shall use their reasonable best efforts to
minimize any disruption to the operation by the Company of its business; (y)
records and information obtained hereunder shall be used by such persons only to
exercise their due diligence responsibility; and (z) records or information
furnished or made available hereunder shall be kept confidential and shall not
be disclosed by any such Holder, underwriter or inspectors unless (A) the
disclosure of such records or information is reasonably necessary to avoid or
correct a misstatement or omission in the Resale Shelf Registration Statement,
(B) the release of such records or information is ordered pursuant to a subpoena
or other order from a court or governmental authority of competent jurisdiction
or (c) such records or information otherwise become generally available to the
public other than through disclosure by such Holder, underwriter or inspector in
breach hereof or by any person in breach of any other confidentiality
arrangement. Each Holder agrees that information obtained by it as a result of
such

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inspections shall be deemed confidential and shall not be used by it as the
basis for any market transactions in the securities of the Company or its
affiliates unless and until such information is made generally available to the
public. Such Holder further agrees that it will, upon learning that disclosure
of such records or information is sought by a court or governmental authority,
give notice to the Company and allow the Company, at the expense of the Company,
to undertake appropriate action to prevent disclosure of the records or
information deemed confidential.

          (n) The Company shall (i) cause its counsel to deliver an opinion and
updates thereof relating to the Securities in customary form addressed to the
Holders and the managing underwriters, if any, thereof and dated, in the case of
the initial opinion, the effective date of such Resale Shelf Registration
Statement (it being agreed that the matters to be covered by such opinion shall
include, without limitation, the due incorporation and good standing of the
Company and its material subsidiaries; the qualification of the Company and its
material subsidiaries to transact business as foreign corporations; the due
authorization, execution and delivery of the relevant agreement of the type
referred to in Section 2(1) hereof; the due authorization, execution,
authentication and issuance, and the validity and enforceability, of the
applicable Securities; the absence of governmental approvals required to be
obtained in connection with the Resale Shelf Registration Statement, the
offering and sale of the applicable Securities or any agreement of the type
referred to in Section 2(n) hereof; the compliance as to form of such Resale
Shelf Registration Statement and any documents incorporated by reference therein
and of the Indenture with the requirements of the Securities Act and the Trust
Indenture Act, respectively; and, as of the date of the opinion and as of the
effective date of the Resale Shelf Registration Statement or most recent
post-effective amendment thereto, as the case may be, a customary statement of
negative assurance regarding the absence from such Resale Shelf Registration
Statement and the prospectus included therein, as then amended or supplemented,
and from any documents incorporated by reference therein of an untrue statement
of a material fact or the omission to state therein a material fact required to
be stated therein or necessary to make the statements therein not misleading (in
the case of any such documents, in the light of the circumstances existing at
the time that such documents were filed with the Commission under the Exchange
Act); (ii) cause its officers to execute and deliver all customary documents and
certificates and updates thereof requested by any underwriters of the applicable
Securities; and (iii) use its reasonable best efforts to cause its independent
public accountants and the independent public accountants, if any with respect
to any other entity for which financial information is provided in the Resale
Shelf Registration Statement to provide to the selling Holders of the applicable
Securities and any underwriter therefor a comfort letter in customary form; and
covering matters of the type customarily covered in comfort letters in
connection with primary underwritten offerings, subject to receipt of
appropriate documentation as contemplated, and only if permitted by Statement
of Auditing Standards No. 72.

          (o) In the event that any broker-dealer registered under the Exchange
Act shall underwrite any Securities or participate as a member of an
underwriting syndicate or selling group or "assist in the distribution" (within
the meaning of the Conduct Rules (the "Rules") of the National

                                       7

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                                                                  Execution Copy

Association of Securities Dealers, Inc. ("NASD")) thereof, whether as a Holder
of such Securities or as an underwriter, a placement or sales agent or a broker
or dealer in respect thereof, or otherwise, the Company will assist such broker-
dealer in complying with the requirements of such Rules, including, without
limitation, by (i) if such Rules, including Rule 2720, shall so require,
engaging a "qualified independent underwriter" (as defined in Rule 2720) to
participate in the preparation of the Resale Shelf Registration Statement
relating to such Securities, to exercise usual standards of due diligence in
respect thereto and, if any portion of the offering contemplated by such Resale
Shelf Registration Statement is an underwritten offering or is made through a
placement or sales agent, to recommend the yield of such Securities, (ii)
indemnifying any such qualified independent underwriter to the extent of the
indemnification of underwriters provided in Section 4 hereof and (iii) providing
such information to such broker-dealer as may be required in order for such
broker-dealer to comply with the requirements of the Rules.

          (p) The Company shall use its reasonable best efforts to take all
other steps necessary to effect the registration of the Securities covered by
the Resale Shelf Registration Statement contemplated hereby.

     3. Registration Expenses. The Company shall bear all fees and expenses (but
not including any underwriting discounts or commissions or transfer taxes, if
any, attributable to the sale of the Securities which discounts, commissions or
taxes shall be paid by Holders of such Securities) incurred in connection with
the performance of its obligations under Sections 1 and 2 hereof whether or not
a Resale Shelf Registration is filed or becomes effective, shall bear or
reimburse the Holders of the Securities covered thereby for the reasonable fees
and disbursements of one firm of counsel, which firm shall be Andrews & Kurth
L.L.P. until another firm shall be designated by the Holders of a majority in
principal amount of the Debentures covered thereby to act as counsel for the
Holders in connection therewith.

     4. Indemnification. (a) The Company agrees to indemnify and hold harmless
each Holder of the Securities and each person, if any, who controls such Holder
within the meaning of the Securities Act or the Exchange Act (each Holder and
such controlling persons are referred to collectively as the "Indemnified
Parties") from and against any losses, claims, damages or liabilities, joint or
several, or any actions in respect thereof (including, but not limited to, any
losses, claims, damages, liabilities or actions relating to purchases and sales
of the Securities) to which each Indemnified Party may become subject under the
Securities Act, the Exchange Act or otherwise, insofar as such losses, claims,
damages, liabilities or actions arise out of or are based upon any untrue
statement or alleged untrue statement of a material fact contained in the Resale
Shelf Registration Statement or prospectus or in any amendment or supplement
thereto or in any preliminary prospectus relating to the Resale Shelf
Registration, 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 in light of the circumstances in which
they were made, not misleading, and shall reimburse, as incurred, the
Indemnified Parties for any legal or other expenses

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                                                                  Execution Copy

reasonably incurred by them in connection with investigating or defending any
such loss, claim, damage, liability or action in respect thereof; provided
however, that (i) the Company shall not be liable in any such case to the extent
that such loss, claim, damage or liability arises out of or is based upon any
untrue statement or alleged untrue statement or omission or alleged omission
made in the Resale Shelf Registration Statement or prospectus or in any
amendment or supplement thereto or in any preliminary prospectus relating to the
Resale Shelf Registration in reliance upon and in conformity with written
information pertaining to a Holder and furnished to the Company by or on behalf
of such Holder specifically for inclusion therein, and (ii) with respect to any
untrue statement or omission or alleged untrue statement or omission made in any
preliminary prospectus relating to the Resale Shelf Registration Statement, the
indemnity agreement contained in this subsection (a) shall not inure to the
benefit of any Holder from whom the person asserting any such losses, claims,
damages or liabilities purchased the Securities concerned, to the extent that a
prospectus relating to such Securities was required to be delivered by such
Holder under the Securities Act in connection with such purchase and any such
loss, claim, damage or liability of such Holder results from the fact that there
was not sent or given to such person, at or prior to the written confirmation of
the sale of such Securities to such person, a copy of the final prospectus if
the Company had previously furnished copies thereof to such Holder, provided,
further, however, that this indemnity agreement will be in addition to any
liability which the Company may otherwise have to such Indemnified Party. The
Company shall also indemnify underwriters, their officers and directors and each
person who controls such underwriters within the meaning of the Securities Act
or the Exchange Act to the same extent as provided above with respect to the
indemnification of the Holders if requested by such Holders.

          (b) Each Holder, severally and not jointly, will indemnify and hold
harmless the Company and each person, if any, who controls the Company within
the meaning of the Securities Act or the Exchange Act from and against any
losses, claims, damages or liabilities or any actions in respect thereof, to
which the Company or any such controlling person may become subject under the
Securities Act, the Exchange Act or otherwise, insofar as such losses, claims,
damages, liabilities or actions arise out of or are based upon any untrue
statement or alleged untrue statement of a material fact contained in the Resale
Shelf Registration Statement or prospectus or in any amendment or supplement
thereto or in any preliminary prospectus relating to the Resale Shelf
Registration, or arise out of or are based upon the omission or alleged omission
to state therein a material fact necessary to make the statements therein in
light of the circumstances in which they were made, not misleading, but in each
case only to the extent that the untrue statement or omission or alleged untrue
statement or omission was made in reliance upon and in conformity with written
information pertaining to such Holder and furnished to the Company by or on
behalf of such Holder specifically for inclusion therein; and, subject to the
limitation set forth immediately preceding this clause, shall reimburse, as
incurred, the Company for any legal or other expenses reasonably incurred by the
Company or any such controlling person in connection with investigating or
defending any loss, claim, damage, liability or action in respect thereof. This
indemnity agreement

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will be in addition to any liability which such Holder may otherwise have to the
Company or any of its controlling persons.

          (c) Promptly after receipt by an indemnified party under this Section
4 of notice of the commencement of any action or proceeding (including a
governmental investigation), such indemnified party will, if a claim in respect
thereof is to be made against the indemnifying party under this Section 4,
notify the indemnifying party of the commencement thereof; but the omission so
to notify the indemnifying party will not, in any event, relieve the
indemnifying party from any obligations to any indemnified party other than the
indemnification obligation provided in subsection (a) or (b) above. In case any
such action is brought against any indemnified party, and it notifies the
indemnifying party of the commencement thereof, the indemnified 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 reasonably satisfactory to such indemnified party (who
shall not, except with the consent of the indemnified party, be counsel to the
indemnified 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 4 for any legal or other expenses, other than reasonable costs of
investigation, subsequently incurred by such indemnified party in connection
with the defense thereof. No indemnifying party shall, without the prior
written consent of the indemnified party, effect any settlement of 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 includes an unconditional release of such
indemnified party from all liability on any claims that are the subject matter
of such action. An indemnifying party will not be liable for any settlement of
any action or claim effected without its written consent; provided, however,
that such consent will not be reasonably withheld.

          (d) If the indemnification provided for in this Section 4 is
unavailable or insufficient to hold harmless an indemnified party under
subsections (a) or (b) above, then each indemnifying party shall contribute to
the amount paid or payable by such indemnified party as a result of the losses,
claims, damages or liabilities (or actions in respect thereof) referred to in
subsection (a) or (b) above (i) in such proportion as is appropriate to reflect
the relative benefits received by the indemnifying party or parties on the one
hand and the indemnified party on the other from the sale of the Securities,
pursuant to the Resale Shelf Registration, or (ii) if the allocation provided by
the foregoing 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 indemnifying party or
parties on the one hand and the indemnified party on the other in connection
with the statements or omissions that resulted in such losses, claims, damages
or liabilities (or actions in respect thereof) as well as any other relevant
equitable considerations. The relative fault of the parties 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 on the one hand or
such Holder or such

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                                                                  Execution Copy

other indemnified party, as the case may be, on the other, and the parties'
relative intent, knowledge, access to information and opportunity to correct or
prevent such statement or omission. The amount paid by an indemnified party as a
result of the losses, claims, damages or liabilities referred to in the first
sentence of this subsection (d) shall be deemed to include any legal or other
expenses reasonably incurred by such indemnified party in connection with
investigating or defending any action or claim which is the subject of this
subsection (d). Notwithstanding any other provision of this Section 4(d), the
Holders shall not be required to contribute any amount in excess of the amount
by which the net proceeds received by such Holders from the sale of the
Securities pursuant to a Resale Shelf Registration Statement exceeds the amount
of damages which such Holders have 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 Securities Act) shall be entitled to contribution from any person
who was not guilty of such fraudulent misrepresentation. For purposes of this
subsection (d), each person, if any, who controls such indemnified party within
the meaning of the Securities Act or the Exchange Act shall have the same rights
to contribution as such indemnified party and each person, if any, who controls
the Company within the meaning of the Securities Act or the Exchange Act shall
have the same rights to contribution as the Company.

                  (e) The agreements contained in this Section 4 shall survive
the sale of the Securities pursuant to the Resale Shelf Registration Statement
and shall remain in full force and effect, regardless of any termination or
cancellation of this Agreement or any investigation made by or on behalf of any
indemnified party.

         5. Additional Interest Under Certain Circumstances. (a) Additional
interest (the "Additional Interest") with respect to the Debentures and
Conversion Shares that are Transfer Restricted Securities shall be assessed as
follows if any of the following events occur (each such event in clauses (i)
through (iii) below a "Registration Default"):

                          (i) If on or prior to the 90th day after the first
         date of original issuance of the Debentures, the Resale Shelf
         Registration Statement has not been filed with the Commission;

                          (ii) If on or prior to the 180th day after the first
         date of original issuance of the Debentures, the Resale Shelf
         Registration Statement has not been declared effective by the
         Commission; or

                          (iii) If after the Resale Shelf Registration Statement
         is declared effective (A) such Resale Shelf Registration Statement
         thereafter ceases to be effective; or (B) such Resale Shelf
         Registration Statement or the related prospectus ceases to be usable
         (except as permitted in Section 5(b)) in connection with resales of
         Transfer Restricted Securities during the periods specified herein
         because either (1) any event occurs as a result of which the

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                       related prospectus forming part of such Resale Shelf
                       Registration Statement 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 (2) it shall be necessary to amend such
                       Resale Shelf Registration Statement or supplement the
                       related prospectus, to comply with the Securities Act or
                       the Exchange Act or the respective rules thereunder.

                       Additional Interest shall accrue on the outstanding
               Debentures and/or the issued and outstanding Conversion Shares
               that are Transfer Restricted Securities over and above the
               interest set forth in the title of the Securities from and
               including the date on which any such Registration Default shall
               occur to but excluding the date on which all such Registration
               Defaults have been cured, at a rate of 0.25% per annum in the
               case of(i) and 0.50% per annum in the case of (ii) or (iii) of
               the sum of (x) the aggregate Applicable Principal Amount of such
               outstanding Debentures and (y) in the case of any issued and
               outstanding Conversion Shares, the aggregate Applicable
               Conversion Price.

                                (b) A Registration Default referred to in
               Section 5(a)(iii)(B) hereof shall be deemed not to have occurred
               and be continuing in relation to the Resale Shelf Registration
               Statement or the related prospectus if such Registration Default
               has occurred solely as a result of (i) the filing of a
               post-effective amendment to such Resale Shelf Registration
               Statement pursuant to Section 1(d) or to incorporate annual
               audited financial information with respect to the Company where
               such post-effective amendment is not yet effective and needs to
               be declared effective to permit Holders to use the related
               prospectus or (ii) imposition of a suspension period pursuant to
               clause (ii) or (v) of Section 2(b) and in the case of clause
               (ii), the Company is proceeding promptly (subject to the
               provisions of Section 2(h)) and in good faith to amend or
               supplement such Resale Shelf Registration Statement and related
               prospectus to describe such events; provided, however, that in
               any case if such Registration Default occurs for a continuous
               period in excess of 30 days, Additional Interest shall be payable
               in accordance with the above paragraph from the day such
               Registration Default occurs until such Registration Default is
               cured.

                                (c) Any amounts of Additional Interest due
               pursuant to clause (i), (ii) or (iii) of Section 5(a) above will
               be payable in cash to the Record Holder on the Damages Payment
               Dates with respect to the Debentures and Conversion Shares. The
               amount of Additional Interest will be determined by multiplying
               the applicable Additional Interest rate by, in the case of the
               Debentures, the Applicable Principal Amount and, in the case of
               the Conversion Shares, the Applicable Conversion Price,
               multiplied by a fraction, the numerator of which is the number of
               days such Additional Interest rate was applicable during such
               period (determined on the basis of a 360-day year comprised of
               twelve 30-day months), and the denominator of which is 360.

                                (d) The parties hereto agree that the Additional
               Interest shall constitute a reasonable estimate of the damages
               that may be incurred by the Holders of Securities (other than the

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Initial Purchaser) for a Registration Default and shall constitute liquidated
damages; the actual damages that the Holders of the Securities might sustain as
a result of a Registration Default would be difficult to ascertain; and the
payment of Additional Interest would be reasonable and just compensation for a
Registration Default.

                  (e) Certain Definitions. For purposes of this Section 5:

         Applicable Conversion Price. The Applicable Conversion Price means the
Applicable Principal Amount divided by the Conversion Rate in effect as of the
next succeeding June 6 or December 6 following such Registration Default in the
case of the first such payment of Additional Interest with respect to a
Registration Default (and thereafter at the next succeeding June 6 or December 6
until the cure of such Registration Default) or, if no Debentures are then
outstanding, the last Conversion Rate that was in effect when the Debentures
were last outstanding.

         Applicable Principal Amount. Applicable Principal Amount with respect
to each $1,000 principal amount at maturity of Debentures means the sum of the
initial issue price of such Debenture ($499.60) plus accrued original issue
discount with respect to such Debenture through the next succeeding June 6 or
December 6 following such Registration Default in the case of the first such
payment of Additional Interest with respect to a Registration Default (and
thereafter at the next succeeding June 6 or December 6 until the cure of such
Registration Default) or, if no Debentures are then outstanding, such sum
calculated as if such Debentures were then outstanding.

         Damages Payment Date. Each June 6 and December 6 in the case of
Debentures and the Conversion Shares.

         Record Holder. With respect to any Damages Payment Date relating to any
Debenture or Conversion Shares as to which any Additional Interest has accrued,
the registered holder of such Debenture or Conversion Shares, as the case may
be, 15 days prior to such Damages Payment Date.

         Transfer Restricted Securities. Each Security until (i) the date on
which such Security has been effectively registered under the Securities Act and
disposed of in accordance with the Resale Shelf Registration Statement or (ii)
the date on which such Security is distributed to the public pursuant to Rule
144 under the Securities Act or is saleable pursuant to Rule 144(k) under the
Securities Act.

         6. Rules 144 and 144A. The Company shall use its reasonable best
efforts to file the reports required to be filed by it under the Securities Act
and the Exchange Act in a timely manner and, if at any time the Company is not
required to file such reports, it will, upon the request of any Holder of
Transfer Restricted Securities, make publicly available such other information
as is necessary to permit sales of their securities pursuant to Rules 144 and
144A. The Company covenants that it will take such further action as any Holder
of Transfer Restricted Securities may

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                                                                  Execution Copy

reasonably request, all to the extent required from time to time to enable such
Holder to sell Transfer Restricted Securities without registration under the
Securities Act within the limitation of the exemptions provided by Rules 144 and
144A (including the requirements of Rule 144A(d)(4)). The Company will provide a
copy of this Agreement to prospective purchasers of Transfer Restricted
Securities identified to the Company by the Initial Purchaser upon request. Upon
the request of any Holder of Transfer Restricted Securities, the Company shall
deliver to such Holder a written statement as to whether it has complied with
such requirements. Notwithstanding the foregoing, nothing in this Section 6
shall be deemed to require the Company to register any of the Debentures
pursuant to the Exchange Act.

         7. Underwritten Registrations. If the Holders of Transfer Restricted
Securities representing at least 25% of the total of the aggregate principal
amount of Debentures originally issued so elect, any one or more offerings of
such Securities pursuant to any Resale Shelf Registration shall be in the form
of an underwritten offering. If any of the Transfer Restricted Securities
covered by any Resale Shelf Registration are to be sold in an underwritten
offering, a nationally recognized investment banker or investment bankers and
manager or managers that will administer the offering ("Managing Underwriters")
will be selected by the Company. No person may participate in any underwritten
registration hereunder unless such person (i) agrees to sell such person's
Transfer Restricted Securities on the basis reasonably provided in any
underwriting arrangements approved by the persons entitled hereunder to approve
such arrangements and (ii) completes and executes all questionnaires, powers of
attorney, indemnities, underwriting agreements and other documents reasonably
required under the terms of such underwriting agreements.

         8. Miscellaneous.

                  (a) Amendments and Waivers. The provisions of this Agreement,
including the provisions of this sentence, may not be amended, modified or
supplemented, and waivers or consents to departures from the provisions hereof
may not be given, unless the Company has obtained the written consent of Holders
of a majority of the then outstanding Conversion Shares constituting Transfer
Restricted Securities (with Holders of Debentures deemed to be the Holders, for
purposes of this Section 8, of the number of outstanding shares of Conversion
Shares into which such Debentures are or would be convertible or exchangeable as
of the date on which such consent is requested). Notwithstanding the foregoing,
a waiver or consent to depart from the provisions hereof with respect to a
matter that relates exclusively to the rights of Holders of Transfer Restricted
Securities whose securities are being sold pursuant to a Resale Shelf
Registration Statement and that does not directly or indirectly affect the
rights of other Holders of Transfer Restricted Securities may be given by
Holders of at least a majority of the Transfer Restricted Securities being sold
by such Holders pursuant to such Resale Shelf Registration Statement; provided,
that the provisions of this sentence may not be amended, modified, or
supplemented except in accordance with the provisions of the immediately
preceding sentence. Each Holder of Transfer Restricted Securities outstanding at
the time of any such amendment, modification, supplement, waiver or consent or
thereafter shall

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<PAGE>   15

                                                                  Execution Copy

be bound by any such amendment, modification, supplement, waiver or consent
effected pursuant to this Section 8, whether or not any notice, writing or
marking indicating such amendment, modification, supplement, waiver or consent
appears on the Transfer Restricted Securities or is delivered to such Holder.
Each Holder may waive compliance with respect to any obligation of the Company
under this Agreement as it may apply or be enforced by such particular Holder.

                  (b) Notices. All notices and other communications provided for
or permitted hereunder shall be made in writing by hand delivery, first-class
mail, facsimile transmission, or air courier which guarantees overnight
delivery:

                  (1)     if to a Ho]der of the Securities, at the most current
address given by such Holder to the Company.

                  (2)     if to the Initial Purchaser:

                          Credit Suisse First Boston Corporation
                          Eleven Madison Avenue
                          New York, NY 10010-3629
                          Fax No.: (212) 325-8278
                          Attention:  Transactions Advisory Group

with a copy to:

                          Andrews & Kurth L.L.P.
                          805 Third Avenue, 7th Floor
                          New York, NY 10022
                          Fax No.: (212) 850-2929
                          Attention:  Allan D. Reiss

                  (3)     if to the Company, at its address as follows:

                          Diamond Offshore Drilling, Inc.
                          15415 Katy Freeway
                          Houston, TX 77094
                          Fax No.: (281) 492-5316

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                                                                  Execution Copy

                          Attention:  Corporate Secretary

with a copy to:

                          Weil Gotshal & Manges LLP
                          700 Louisiana, Suite 1600
                          Houston, TX 77002
                          Fax No.:    (713) 224-9511
                          Attention:  James L. Rice III

         All such notices and communications shall be deemed to have been duly
given: at the time delivered by hand, if personally delivered; three business
days after being deposited in the mail, postage prepaid, if mailed; when receipt
is acknowledged by recipient's facsimile machine operator, if sent by facsimile
transmission; and on the day delivered, if sent by overnight air courier
guaranteeing next day delivery.

                  (c) No Inconsistent Agreements. The Company has not, as of the
date hereof, entered into, nor shall it, on or after the date hereof, enter
into, any agreement with respect to its securities that is inconsistent with the
rights granted to the Holders herein or otherwise conflicts with the provisions
hereof, other than any inconsistencies in any such agreement that have been
waived by the beneficiary thereof.

                  (d) Successors and Assigns. This Agreement shall be binding
upon the Company and its successors and assigns.

                  (e) Counterparts. This Agreement may be executed in any number
of counterparts and by the parties hereto in separate counterparts, each of
which when so executed shall be deemed to be an original and all of which taken
together shall constitute one and the same agreement.

                  (f) Headings. The headings in this Agreement are for
convenience of reference only and shall not limit or otherwise affect the
meaning hereof.

                  (g) Governing 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.

                  (h) Severability. If any one or more of the provisions
contained herein, or the application thereof in any circumstance, is held
invalid, illegal or unenforceable, the validity, legality and enforceability of
any such provision in every other respect and of the remaining provisions
contained herein shall not be affected or impaired thereby.

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                                                                  Execution Copy

                  (i) Securities Held by the Company. Whenever the consent or
approval of Holders of a specified percentage of principal amount of Securities
is required hereunder, Securities held by the Company or its affiliates (other
than subsequent Holders of Securities if such subsequent Holders are deemed to
be affiliates solely by reason of their holdings of such Securities) shall not
be counted in determining whether such consent or approval was given by the
Holders of such required percentage.

                  (j) Remedies. In the event of a breach by the Company of its
obligations under this Agreement, each Holder of Securities, in addition to
being entitled to exercise all rights granted by law, including recovery of
damages, will be entitled to specific performance of its rights under this
Agreement, provided, that the sole damages payable for a Registration Default
shall be Additional Interest as expressly provided in Section 5 hereof. Subject
to the provisions of the preceding sentence, the Company agrees that monetary
damages would not be adequate compensation for any loss incurred by reason of a
breach by it of any of the provisions of this Agreement and hereby further
agrees that, in the event of any action for specific performance in respect of
such breach, it shall waive the defense that a remedy at law would be adequate.

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                                                                  Execution Copy

         If the foregoing is in accordance with your understanding of our
agreement, please sign and return to the Company a counterpart hereof, whereupon
this instrument, along with all counterparts, will become a binding agreement on
the Initial Purchaser and the Company in accordance with its terms.

                                           Very truly yours,

                                           DIAMOND OFFSHORE DRILLING, INC.

                                           By: /s/ LAWRENCE R. DICKERSON
                                              ----------------------------------
                                              Name:  Lawrence R. Dickerson
                                              Title: President & Chief Operating
                                                     Officer

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

CREDIT SUISSE FIRST BOSTON
   CORPORATION

By: CREDIT SUISSE FIRST BOSTON
    CORPORATION

By: /s/ ROME G. ARNOLD
   ---------------------------------------
   Name:  ROME G. ARNOLD
   Title: Managing Director

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