<PAGE>   1
                                                                    EXHIBIT 10.2


                          REGISTRATION RIGHTS AGREEMENT


                  THIS REGISTRATION RIGHTS AGREEMENT (this "Agreement") is made
and entered into as of April 11, 2001 by and between Diamond Offshore Drilling,
Inc., a Delaware corporation (the "Company"), and Merrill Lynch & Co., Merrill
Lynch, Pierce, Fenner & Smith Incorporated (the "Purchaser") pursuant to the
Purchase Agreement, dated as of April 6, 2001 (the "Purchase Agreement"),
between the Company and the Purchaser. In order to induce the Purchaser to enter
into the Purchase Agreement, the Company has agreed to provide the registration
rights set forth in this Agreement. The execution of this Agreement is a
condition to the closing under the Purchase Agreement.

                  The Company agrees with the Purchaser, (i) for the benefit of
the Purchaser and (ii) for the benefit of the beneficial owners (including the
Purchaser) from time to time of the Securities (as defined herein) and the
beneficial owners from time to time of the Underlying Common Stock (as defined
herein) issued upon conversion of the Securities (each of the foregoing a
"Holder" and together the "Holders"), as follows:

                  Section 1. Definitions. Capitalized terms used herein without
definition shall have their respective meanings set forth in the Purchase
Agreement. As used in this Agreement, the following terms shall have the
following meanings:

                  "Affiliate" means, with respect to any specified person, an
"affiliate," as defined in Rule 144, of such person.

                  "Applicable Conversion Price" means, as of any date of
determination, the principal amount of Securities as of such date of
determination divided by the Conversion Rate in effect as of such date of
determination or, if no Securities are then outstanding, the Conversion Rate
that would be in effect were Securities then outstanding.

                  "Business Day" means each Monday, Tuesday, Wednesday, Thursday
and Friday that is not a day on which banking institutions in The City of New
York are authorized or obligated by law or executive order to close.

                  "Common Stock" means any shares of Common Stock, par value
$.01 per share, of the Company and any other shares of common stock as may
constitute "Common Stock" for purposes of the Indenture, including the
Underlying Common Stock.

                  "Conversion Rate" has the meaning assigned to that term in the
Indenture.

                  "Damages Accrual Period" has the meaning specified in Section
2(e) hereof.


<PAGE>   2

                  "Damages Payment Date" means each October 15 and April 15 in
the case of Securities and the Underlying Common Stock.

                  "Deferral Notice" has the meaning specified in Section 3(i)
hereof.

                  "Deferral Period" has the meaning specified in Section 3(i)
hereof.

                  "Effectiveness Deadline Date" has the meaning specified in
Section 2(a) hereof.

                  "Effectiveness Period" means the period of two years from the
date the Shelf Registration Statement is declared effective or such shorter
period terminating upon the earliest to occur of the following: (A) when all the
Securities covered by the Shelf Registration Statement have been sold pursuant
to the Shelf Registration Statement or transferred pursuant to Rule 144, (B)
when all shares of Common Stock issued upon conversion of any such Securities
that had not been sold pursuant to the Shelf Registration Statement or
transferred pursuant to Rule 144 have been sold pursuant to the Shelf
Registration Statement or transferred pursuant to Rule 144 and (C) when all
outstanding Registrable Securities held by persons which are not affiliates of
the Company may be resold without registration under the Securities Act pursuant
to Rule 144(k) under the Securities Act or any successor provision thereto.

                  "Event" has the meaning specified in Section 2(e) hereof.

                  "Event Termination Date" has the meaning specified in Section
2(e) hereof.

                  "Event Date" has the meaning specified in Section 2(e) hereof.

                  "Exchange Act" means the Securities Exchange Act of 1934, as
amended, and the rules and regulations of the SEC promulgated thereunder.

                  "Filing Deadline Date" has the meaning specified in Section
2(a) hereof.

                  "Holder" has the meaning specified in the second paragraph of
this Agreement.

                  "Indenture" means the Indenture dated as of the date hereof
between the Company and the Trustee, pursuant to which the Securities are being
issued.

                  "Initial Shelf Registration Statement" has the meaning
specified in Section 2(a) hereof.

                  "Issue Date" means April 11, 2001.

                  "Liquidated Damages Amount" has the meaning specified in
Section 2(e) hereof.

                  "Losses" has the meaning specified in Section 6 hereof.

                  "Material Event" has the meaning specified in Section 3(i)
hereof.

                  "Notice and Questionnaire" means a duly executed, written
notice delivered to the Company containing the information called for by the
Selling Securityholder Notice and



                                       2
<PAGE>   3

Questionnaire attached as Annex A to the Offering Memorandum of the Company
dated April 6, 2001 relating to the Securities.

                  "Notice Holder" means, on any date, any Holder that has
delivered a Notice and Questionnaire to the Company on or prior to such date.

                  "Prospectus" means the prospectus included in any Registration
Statement (including, without limitation, a prospectus that discloses
information previously omitted from a prospectus filed as part of an effective
registration statement in reliance upon Rule 430A promulgated under the
Securities Act), as amended or supplemented by any amendment or prospectus
supplement, including post-effective amendments, and all materials incorporated
by reference or explicitly deemed to be incorporated by reference in such
Prospectus.

                  "Purchase Agreement" has the meaning specified in the first
paragraph of this Agreement.

                  "Purchaser" means Merrill Lynch & Co., Merrill Lynch, Pierce,
Fenner & Smith Incorporated.

                  "Record Holder" means, with respect to any Damages Payment
Date relating to any Securities or Underlying Common Stock as to which any
Liquidated Damages Amount has accrued, the registered holder of such Securities
or Underlying Common Stock, as the case may be, 14 days prior to the next
succeeding Damages Payment Date or, if all Events giving rise to the Liquidated
Damages Amount payable on such Damages Payment Date have been cured and no such
Event is continuing on such date, as of the date on which the last such Event
was cured.

                  "Registrable Securities" means the Securities and the
Underlying Common Stock, until such securities have been converted or exchanged,
and, at all times subsequent to any such conversion or exchange, any securities
into or for which such securities have been converted or exchanged, and any
security issued with respect thereto upon any stock dividend, split or similar
event until, in the case of any such security, the earliest of (i) its effective
registration under the Securities Act and resale in accordance with the
Registration Statement covering it, (ii) expiration of the holding period that
would be applicable thereto under Rule 144(k) were it not held by an Affiliate
of the Company or (iii) its sale to the public pursuant to Rule 144.

                  "Registration Expenses" has the meaning specified in Section 5
hereof.

                  "Registration Statement" means any registration statement of
the Company that covers any of the Registrable Securities pursuant to the
provisions of this Agreement, including the Prospectus, amendments and
supplements to such registration statement, including post-effective amendments,
all exhibits, and all materials incorporated by reference or explicitly deemed
to be incorporated by reference in such registration statement.

                  "Restricted Securities" has the meaning assigned to that term
in Rule 144.

                  "Rule 144" means Rule 144 under the Securities Act, as such
Rule may be amended from time to time, or any similar rule or regulation
hereafter adopted by the SEC.


                                       3
<PAGE>   4

                  "Rule 144A" means Rule 144A under the Securities Act, as such
Rule may be amended from time to time, or any similar rule or regulation
hereafter adopted by the SEC.

                  "SEC" means the U.S. Securities and Exchange Commission and
any successor agency.

                  "Securities" means the 1 1/2% Convertible Senior Debentures
due 2031 of the Company to be purchased pursuant to the Purchase Agreement.

                  "Securities Act" means the Securities Act of 1933, as amended,
and the rules and regulations promulgated by the SEC thereunder.

                  "Shelf Registration Statement" has the meaning specified in
Section 2(a) hereof.

                  "Subsequent Shelf Registration Statement" has the meaning
specified in Section 2(b) hereof.

                  "TIA" means the Trust Indenture Act of 1939, as amended.

                  "Trustee" means The Chase Manhattan Bank (or any successor
entity), the Trustee under the Indenture.

                  "Underlying Common Stock" means the Common Stock into which
the Securities are convertible or issued upon any such conversion.

                  Section 2. Shelf Registration. (a) The Company shall prepare
and file or cause to be prepared and filed with the SEC, as soon as practicable
but in any event by the date (the "Filing Deadline Date") ninety (90) days after
the Issue Date, a Registration Statement for an offering to be made on a delayed
or continuous basis pursuant to Rule 415 of the Securities Act (a "Shelf
Registration Statement") registering the resale from time to time by Holders
thereof of all of the Registrable Securities (the "Initial Shelf Registration
Statement"). The Initial Shelf Registration Statement shall be on Form S-3 or
another appropriate form permitting registration of such Registrable Securities
for resale by such Holders in accordance with the methods of distribution
elected by the Holders and set forth in the Initial Shelf Registration
Statement, provided that notwithstanding anything herein to the contrary, in no
event will such method(s) of distribution take the form of an underwritten
offering of the Registrable Securities without the prior written agreement of
the Company. The Company shall use reasonable best efforts to cause the Initial
Shelf Registration Statement to be declared effective under the Securities Act
as promptly as is practicable but in any event by the date (the "Effectiveness
Deadline Date") that is one hundred eighty (180) days after the Issue Date, and
to keep the Initial Shelf Registration Statement (or any Subsequent Shelf
Registration Statement) continuously effective under the Securities Act until
the expiration of the Effectiveness Period; provided, however, that no Holder
shall be entitled to have the Registrable Securities held by it covered by such
Shelf Registration Statement unless such Holder shall have provided a Notice and
Questionnaire in accordance with Section 2(d) and is in compliance with Section
4. None of the Company's securityholders (other than the Holders of Registrable
Securities) shall have the right to include any of the Company's securities in
the Shelf Registration Statement.


                                       4
<PAGE>   5

                  (b) If the Initial Shelf Registration Statement or any
Subsequent Shelf Registration Statement ceases to be effective for any reason at
any time during the Effectiveness Period (other than because all Registrable
Securities registered thereunder shall have been resold pursuant thereto or
shall have otherwise ceased to be Registrable Securities), the Company shall use
reasonable best efforts to obtain the prompt withdrawal of any order suspending
the effectiveness thereof, and in any event shall within sixty (60) days of such
cessation of effectiveness amend the Shelf Registration Statement in a manner
reasonably expected to obtain the withdrawal of the order suspending the
effectiveness thereof, or file an additional Shelf Registration Statement
covering all of the securities that as of the date of such filing are
Registrable Securities (a "Subsequent Shelf Registration Statement"). If a
Subsequent Shelf Registration Statement is filed, the Company shall use
reasonable best efforts to cause the Subsequent Shelf Registration Statement to
become effective as promptly as is practicable after such filing or, if filed
during a Deferral Period, after the expiration of such Deferral Period, and to
keep such Registration Statement (or Subsequent Shelf Registration Statement)
continuously effective until the end of the Effectiveness Period.

                  (c) The Company shall supplement and amend the Shelf
Registration Statement if required by the rules, regulations or instructions
applicable to the registration form used by the Company for such Shelf
Registration Statement, if required by the Securities Act or, to the extent to
which the Company does not reasonably object, as reasonably requested by the
Purchaser or by the Trustee on behalf of the registered Holders.

                  (d) Each Holder of Registrable Securities agrees that if such
Holder wishes to sell Registrable Securities pursuant to a Shelf Registration
Statement and related Prospectus, it will do so only in accordance with this
Section 2(d) and Section 3(i). Each Holder of Registrable Securities wishing to
sell Registrable Securities pursuant to a Shelf Registration Statement and
related Prospectus agrees to deliver a Notice and Questionnaire to the Company
at least ten (10) Business Days prior to any intended distribution of
Registrable Securities under the Shelf Registration Statement. From and after
the date the Initial Shelf Registration Statement is declared effective, the
Company shall (i) as promptly as is practicable after the date a Notice and
Questionnaire is delivered, but in any event within ten (10) Business Days after
such date, if required by applicable law, file with the SEC 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 Shelf Registration Statement and the
related Prospectus in such a manner as to permit such Holder to deliver such
Prospectus to purchasers of the Registrable Securities in accordance with
applicable law and, if the Company shall file a post-effective amendment to the
Shelf Registration Statement, use reasonable best efforts to cause such
post-effective amendment to be declared effective under the Securities Act as
promptly as is practicable, but in any event by the date (the "Amendment
Effectiveness Deadline 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 2(d)(i) as
promptly as practicable after the filing of such documents; 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
2(d)(i); provided that if such Notice and Questionnaire is delivered during a
Deferral Period, the Company shall so inform the Holder


                                       5
<PAGE>   6

delivering such Notice and Questionnaire and shall take the actions set forth in
clauses (i), (ii) and (iii) above upon expiration of the Deferral Period in
accordance with Section 3(i) as though such Holder's Notice and Questionnaire
had been delivered on the expiration date of such Deferral Period, provided
further, that if under applicable law the Company has more than one option as to
the type or manner of making any such filing, it will make the required filing
or filings in the manner or of a type that is reasonably expected to result in
the earliest availability of the Prospectus for effecting resales of Registrable
Securities. Notwithstanding anything contained herein to the contrary, the
Company shall be under no obligation to name any Holder that is not a Notice
Holder as a selling securityholder in any Registration Statement or related
Prospectus; provided, however, that any Holder that becomes a Notice Holder
pursuant to the provisions of Section 2(d) of this Agreement (whether or not
such Holder was a Notice Holder at the time the Registration Statement was
declared effective) shall be named as a selling securityholder in the
Registration Statement or related Prospectus in accordance with the requirements
and conditions of this Section 2(d).

                  (e) The parties hereto agree that the Holders of Registrable
Securities will suffer damages, and that it would not be feasible to ascertain
the extent of such damages with precision, if (i) the Initial Shelf Registration
Statement has not been filed on or prior to the Filing Deadline Date, (ii) the
Initial Shelf Registration Statement has not been declared effective under the
Securities Act on or prior to the Effectiveness Deadline Date, (iii) the Company
has failed to perform its obligations set forth in Section 2(d) hereof within
the time period required therein or (iv) the aggregate duration of Deferral
Periods in any period exceeds the number of days permitted in respect of such
period pursuant to Section 3(i) hereof (each of the events of a type described
in any of the foregoing clauses (i) through (iv) are individually referred to
herein as an "Event," and the Filing Deadline Date in the case of clause (i),
the Effectiveness Deadline Date in the case of clause (ii), the date by which
the Company is required to perform its obligations set forth in Section 2(d) in
the case of clause (iii) (including the filing of any post-effective amendment
prior to the Amendment Effectiveness Deadline Date), and the date on which the
aggregate duration of Deferral Periods in any period exceeds the number of days
permitted by Section 3(i) hereof in the case of clause (iv), being referred to
herein as an "Event Date"). Events shall be deemed to continue until the "Event
Termination Date," which shall be the following dates with respect to the
respective types of Events: the date the Initial Shelf Registration Statement is
filed in the case of an Event of the type described in clause (i), the date the
Initial Shelf Registration Statement is declared effective under the Securities
Act in the case of an Event of the type described in clause (ii), the date the
Company performs its obligations set forth in Section 2(d) in the case of an
Event of the type described in clause (iii) (including, without limitation, the
date the relevant post-effective amendment to the Shelf Registration Statement
is declared effective under the Securities Act), and termination of the Deferral
Period that caused the limit on the aggregate duration of Deferral Periods in a
period set forth in Section 3(i) to be exceeded in the case of the commencement
of an Event of the type described in clause (iv).

                  Accordingly, commencing on (and including) any Event Date and
ending on (but excluding) the next date on which there are no Events that have
occurred and are continuing (a "Damages Accrual Period"), the Company agrees to
pay, as liquidated damages and not as a penalty, an amount (the "Liquidated
Damages Amount"), payable on the Damages Payment Dates to Record Holders of then
outstanding Securities that are Registrable Securities and of then

                                       6
<PAGE>   7
outstanding shares of Underlying Common Stock issued upon conversion of
Securities that are Registrable Securities, as the case may be, accruing, for
each portion of such Damages Accrual Period beginning on and including a Damages
Payment Date (or, in respect of the first time that the Liquidated Damages
Amount is to be paid to Holders on a Damages Payment Date as a result of the
occurrence of any particular Event, from the Event Date) and ending on but
excluding the first to occur of (A) the date of the end of the Damages Accrual
Period or (B) the next Damages Payment Date, at a rate per annum equal to
one-quarter of one percent (0.25%) for the first ninety (90) day period from the
Event Date, and thereafter at a rate per annum equal to one-half of one percent
(0.50%) of the aggregate principal amount of such Securities and the aggregate
Applicable Conversion Price of such shares of Underlying Common Stock, as the
case may be, in each case determined as of the Business Day immediately
preceding the next Damages Payment Date; provided that in the case of a Damages
Accrual Period that is in effect solely as a result of an Event of the type
described in clause (iii) of the immediately preceding paragraph, such
Liquidated Damages Amount shall be paid only to the Holders that have delivered
Notice and Questionnaires that caused the Company to incur the obligations set
forth in Section 2(d) the non-performance of which is the basis of such Event;
provided further, that any Liquidated Damages Amount accrued with respect to any
Securities or portion thereof called for redemption on a redemption date or
converted into Underlying Common Stock on a conversion date prior to the Damages
Payment Date, shall, in any such event, be paid instead to the Holder who
submitted such Securities or portion thereof for redemption or conversion on the
applicable redemption date or conversion date, as the case may be, on such date
(or promptly following the conversion date, in the case of conversion).
Notwithstanding the foregoing, no Liquidated Damages Amounts shall accrue as to
any Registrable Security from and after the earlier of (x) the date such
security is no longer a Registrable Security and (y) expiration of the
Effectiveness Period. The rate of accrual of the Liquidated Damages Amount with
respect to any period shall not exceed the rate provided for in this paragraph
notwithstanding the occurrence of multiple concurrent Events. Following the cure
of all Events requiring the payment by the Company of Liquidated Damages Amounts
to the Holders of Registrable Securities pursuant to this Section, the accrual
of Liquidated Damages Amounts will cease (without in any way limiting the effect
of any subsequent Event requiring the payment of Liquidated Damages Amount by
the Company).

                  The Trustee shall be entitled, on behalf of Holders of
Securities or Underlying Common Stock, to seek any available remedy for the
enforcement of this Agreement, including for the payment of any Liquidated
Damages Amount in accordance herewith. Notwithstanding the foregoing, the
parties agree that the sole monetary damages payable for a violation of the
terms of this Agreement with respect to which liquidated damages are expressly
provided shall be such liquidated damages. Nothing shall preclude a Notice
Holder from pursuing or obtaining specific performance or other equitable relief
with respect to this Agreement.

                  All of the Company's obligations set forth in this Section
2(e) that are outstanding with respect to any Registrable Security at the time
such security ceases to be a Registrable Security shall survive until such time
as all such obligations with respect to such security have been satisfied in
full (notwithstanding termination of this Agreement pursuant to Section 8(k)).

                  The parties hereto agree that the liquidated damages provided
for in this Section 2(e) constitute a reasonable estimate of the damages that
may be incurred by Holders of Registrable Securities by reason of the failure of
the Shelf Registration Statement to be filed or



                                       7
<PAGE>   8

declared effective or available for effecting resales of Registrable Securities
in accordance with the provisions hereof.

                  Section 3. Registration Procedures. In connection with the
registration obligations of the Company under Section 2 hereof, the Company
shall:

                  (a) Before filing any Registration Statement or Prospectus or
any amendments or supplements (other than supplements that do nothing more
substantive than name one or more Notice Holders as selling securityholders or
provide other information required by Item 507 of Regulation S-K with respect to
such Notice Holders) thereto with the SEC, furnish to the Purchaser copies of
all such documents proposed to be filed and use reasonable best efforts to
reflect in each such document when so filed with the SEC such comments as the
Purchaser reasonably shall propose within three (3) Business Days of the
delivery of such copies to the Purchaser.

                  (b) Prepare and file with the SEC such amendments and
post-effective amendments to each Registration Statement as may be necessary to
keep such Registration Statement continuously effective for the applicable
period specified in Section 2(a), except as provided in Section 3(i); cause the
related Prospectus to be supplemented by any required Prospectus supplement, and
as so supplemented to be filed pursuant to Rule 424 (or any similar provisions
then in force) under the Securities Act; and use reasonable best efforts to
comply with the provisions of the Securities Act applicable to it with respect
to the disposition of all securities covered by such Registration Statement
during the Effectiveness Period in accordance with the intended methods of
disposition by the sellers thereof set forth in such Registration Statement as
so amended or such Prospectus as so supplemented.

                  (c) As promptly as practicable give notice to the Notice
Holders and the Purchaser (i) when any Prospectus, Prospectus supplement,
Registration Statement or post-effective amendment to a Registration Statement
has been filed with the SEC and, with respect to a Registration Statement or any
post-effective amendment, when the same has been declared effective (provided,
however, that the Company shall not be required by this clause (i) to notify (A)
the Purchaser of the filing of a Prospectus supplement that does nothing more
substantive than name one or more Notice Holders as selling securityholders or
provide other information required by Item 507 of Regulation S-K with respect to
such Notice Holders or (B) any Notice Holder of the filing of a Prospectus
supplement that does nothing more substantive than name one or more other Notice
Holders as selling securityholders or provide other information required by Item
507 of Regulation S-K with respect to such Notice Holders), (ii) of any request,
following the effectiveness of the Initial Shelf Registration Statement under
the Securities Act, by the SEC or any other federal or state governmental
authority for amendments or supplements to any Registration Statement or related
Prospectus or for additional information, (iii) of the issuance by the SEC or
any other federal or state governmental authority of any stop order suspending
the effectiveness of any Registration Statement or the initiation or threatening
of any proceedings for that purpose, (iv) of the receipt by the Company of any
notification with respect to the suspension of the qualification or exemption
from qualification of any of the Registrable Securities for sale in any
jurisdiction or the initiation or threatening of any proceeding for such
purpose, (v) of the occurrence of (but not the nature of or details concerning)
a Material Event (provided, however, that no notice by the Company shall be
required pursuant to this clause (v)


                                       8
<PAGE>   9

in the event that the Company either promptly files a Prospectus supplement to
update the Prospectus or a Form 8-K or other appropriate Exchange Act report
that is incorporated by reference into the Registration Statement, which, in
either case, contains the requisite information with respect to such Material
Event that results in such Registration Statement no longer containing any
untrue statement of material fact or omitting to state a material fact necessary
to make the statements contained therein not misleading) and (vi) of the
determination by the Company that a post-effective amendment to a Registration
Statement will be filed with the SEC, which notice may, at the discretion of the
Company (or as required pursuant to Section 3(i)), state that it constitutes a
Deferral Notice, in which event the provisions of Section 3(i) shall apply.

                  (d) Use reasonable best efforts to obtain the withdrawal of
any order suspending the effectiveness of a Registration Statement or the
lifting of any suspension of the qualification (or exemption from qualification)
of any of the Registrable Securities for sale in any jurisdiction in which they
have been qualified for sale, in either case at the earliest possible moment.

                  (e) If reasonably requested by the Purchaser or any Notice
Holder, promptly as reasonably practicable, but in any event within ten (10)
Business Days of such request, incorporate in a Prospectus supplement or
post-effective amendment to a Registration Statement such information as the
Purchaser or such Notice Holder shall, on the basis of a written opinion of
nationally-recognized counsel experienced in such matters, determine to be
required to be included therein by applicable law and make any required filings
of such Prospectus supplement or such post-effective amendment; provided that
the Company shall not be required to take any actions under this Section 3(e)
that are not, in the reasonable opinion of counsel for the Company, in
compliance with applicable law.

                  (f) As promptly as reasonably practicable furnish to each
Notice Holder and the Purchaser, upon their request and without charge, at least
one (1) conformed copy of the Registration Statement and any amendment thereto,
including financial statements but excluding schedules, all documents
incorporated or deemed to be incorporated therein by reference and all exhibits
(unless requested in writing to the Company by such Notice Holder or the
Purchaser, as the case may be).

                  (g) During the Effectiveness Period, deliver to each Notice
Holder in connection with any sale of Registrable Securities pursuant to a
Registration Statement, without charge, as many copies of the Prospectus or
Prospectuses relating to such Registrable Securities (including each preliminary
prospectus) and any amendment or supplement thereto as such Notice Holder may
reasonably request; and the Company hereby consents (except during such periods
that a Deferral Notice is outstanding and has not been revoked) to the use of
such Prospectus or each amendment or supplement thereto by each Notice Holder in
connection with any offering and sale of the Registrable Securities covered by
such Prospectus or any amendment or supplement thereto in the manner set forth
therein.

                  (h) Prior to any public offering of the Registrable Securities
pursuant to the Shelf Registration Statement, use reasonable best efforts to
register or qualify or cooperate with the Notice Holders in connection with the
registration or qualification (or exemption from such


                                       9
<PAGE>   10

registration or qualification) of such Registrable Securities for offer and sale
under the securities or Blue Sky laws of such jurisdictions within the United
States as any Notice Holder reasonably requests in writing (which request may be
included in the Notice and Questionnaire); prior to any public offering of the
Registrable Securities pursuant to the Shelf Registration Statement, use
reasonable best efforts to keep each such registration or qualification (or
exemption therefrom) effective during the Effectiveness Period in connection
with such Notice Holder's offer and sale of Registrable Securities pursuant to
such registration or qualification (or exemption therefrom) and do any and all
other acts or things necessary or advisable to enable the disposition in such
jurisdictions of such Registrable Securities in the manner set forth in the
relevant Registration Statement and the related Prospectus; provided that the
Company will not be required to (i) qualify as a foreign corporation or as a
dealer in securities in any jurisdiction where it would not otherwise be
required to qualify but for this Agreement or (ii) take any action that would
subject it to general service of process or to taxation in any such jurisdiction
where it is not then so subject.

                  (i) Upon (A) the issuance by the SEC of a stop order
suspending the effectiveness of the Shelf Registration Statement or the
initiation of proceedings with respect to the Shelf Registration Statement under
Section 8(d) or 8(e) of the Securities Act, (B) the occurrence of any event or
the existence of any fact (a "Material Event") as a result of which any
Registration Statement shall contain any untrue statement of a material fact or
omit to state any material fact required to be stated therein or necessary to
make the statements therein not misleading, or any Prospectus shall contain any
untrue statement of a material fact or omit to state any material fact required
to be stated therein or necessary to make the statements therein, in the light
of the circumstances under which they were made, not misleading, or (C) the
occurrence or existence of any pending corporate development that, in the
discretion of the Company, makes it appropriate to suspend the availability of
the Shelf Registration Statement and the related Prospectus, (i) in the case of
clause (B) above, subject to the next sentence, as promptly as practicable,
prepare and file a post-effective amendment to such Registration Statement or a
supplement to the related Prospectus or any document incorporated therein by
reference or file any other required document that would be incorporated by
reference into such Registration Statement and Prospectus so that such
Registration Statement does not contain any untrue statement of a material fact
or omit to state any material fact required to be stated therein or necessary to
make the statements therein not misleading, and such Prospectus does not contain
any untrue statement of a material fact or omit to state any material fact
required to be stated therein or necessary to make the statements therein, in
the light of the circumstances under which they were made, not misleading, as
thereafter delivered to the purchasers of the Registrable Securities being sold
thereunder, and, in the case of a post-effective amendment to a Registration
Statement, subject to the next sentence, use reasonable best efforts to cause it
to be declared effective as promptly as is reasonably practicable, and (ii) give
notice to the Notice Holders that the availability of the Shelf Registration
Statement is suspended (a "Deferral Notice") and, upon receipt of any Deferral
Notice, each Notice Holder agrees to immediately suspend the use of any
Prospectus and not to sell any Registrable Securities pursuant to the
Registration Statement until such Notice Holder's receipt of copies of the
supplemented or amended Prospectus provided for in clause (i) above, or until it
is advised in writing by the Company that the Prospectus may be used, and has
received copies of any additional or supplemental filings that are incorporated
or deemed incorporated by reference in such Prospectus. The Company will use
reasonable best efforts to ensure that the use of the Prospectus may be resumed
(x) in the case of clause (A)


                                       10
<PAGE>   11

above, as promptly as is reasonably practicable, (y) in the case of clause (B)
above, as soon as, in the sole judgment of the Company, public disclosure of
such Material Event would not be prejudicial to or contrary to the interests of
the Company or, if necessary to avoid unreasonable burden or expense, as soon as
reasonably practicable thereafter and (z) in the case of clause (C) above, as
soon as, in the sole discretion of the Company, such suspension is no longer
appropriate. The period during which the availability of the Registration
Statement and any Prospectus is suspended (the "Deferral Period") shall, without
the Company incurring any obligation to pay liquidated damages pursuant to
Section 2(e), not exceed thirty (30) days in any three (3) month period and
ninety (90) days in any twelve (12) month period.

                  (j) If reasonably requested in writing in connection with a
disposition of Registrable Securities pursuant to a Registration Statement, make
reasonably available for inspection during normal business hours by a
representative for the Notice Holders of such Registrable Securities and any
broker-dealers, attorneys and accountants retained by such Notice Holders, all
relevant financial and other records, pertinent corporate documents and
properties of the Company and its subsidiaries, and cause the appropriate
executive officers, directors and designated employees of the Company and its
subsidiaries to make reasonably available for inspection during normal business
hours all relevant information reasonably requested by such representative for
the Notice Holders or any such broker-dealers, attorneys or accountants in
connection with such disposition, in each case as is reasonably necessary to
enable such Notice Holders or any such broker-dealers, attorneys or accountants
to conduct a reasonable investigation within the meaning of Section 11 of the
Securities Act; provided, however, that such persons shall first agree in
writing with the Company that any information that is reasonably and in good
faith designated by the Company in writing as confidential at the time of
delivery of such information shall be kept confidential by such persons and
shall be used solely for the purposes of exercising rights under this Agreement,
unless (i) disclosure of such information is required by court or administrative
order, (ii) disclosure of such information is required by law (including any
disclosure requirements pursuant to federal securities laws in connection with
the filing of any Registration Statement or the use of any Prospectus referred
to in this Agreement), (iii) such information becomes generally available to the
public other than as a result of a disclosure or failure to safeguard by any
such person or (iv) such information becomes available to any such person from a
source other than the Company and such source is not bound by a confidentiality
agreement; provided further, that (x) 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 and (y) in connection with any such inspection
under this Section 3(j), any such inspectors shall use their reasonable best
efforts to minimize any disruption to the operation by the Company of its
business; and provided further, that the foregoing inspection and information
gathering shall, to the greatest extent possible, be coordinated on behalf of
all the Notice Holders and the other parties entitled thereto by the counsel
referred to in Section 5.

                  (k) Comply with all applicable rules and regulations of the
SEC and make generally available to its securityholders earning statements
(which need not be audited) satisfying the provisions of Section 11(a) of the
Securities Act and Rule 158 thereunder (or any similar rule promulgated under
the Securities Act) no later than forty-five (45) days after the end of any
twelve (12) month period (or ninety (90) days after the end of any twelve (12)
month period if such period is a fiscal year) commencing on the first day of the
first fiscal quarter of the

                                       11
<PAGE>   12

Company commencing after the effective date of a Registration Statement, which
statements shall cover said twelve (12) month periods.

                  (l) Cooperate with each Notice Holder to facilitate the timely
preparation and delivery of certificates representing Registrable Securities
sold pursuant to a Registration Statement (to the extent such Registrable
Securities are certificated), and cause such Registrable Securities to be in
such denominations as are permitted by the Indenture and registered in such
names as such Notice Holder may request in writing at least three (3) Business
Days prior to any sale of such Registrable Securities.

                  (m) Provide a CUSIP number for all Registrable Securities
covered by each Registration Statement not later than the effective date of such
Registration Statement and provide the Trustee for the Securities and the
transfer agent for the Securities with printed certificates for the Registrable
Securities that are in a form eligible for deposit with The Depository Trust
Company.

                  (n) Use reasonable best efforts to provide such information as
is required for any filings required to be made with the National Association of
Securities Dealers, Inc.

                  (o) Upon (i) the filing of the Initial Shelf Registration
Statement and (ii) the effectiveness of the Initial Shelf Registration
Statement, announce the same, in each case by release to Reuters Economic
Services and Bloomberg Business News.

                  (p) Enter into such customary agreements and take all such
other reasonable necessary actions in connection therewith (including those
reasonably requested by the Holders of a majority of the Registrable Securities
being sold) in order to expedite or facilitate disposition of such Registrable
Securities.

                  (q) Cause the Indenture to be qualified under the TIA not
later than the effective date of any Registration Statement; and in connection
therewith, cooperate with the Trustee to effect such changes to the Indenture as
may be required for the Indenture to be so qualified in accordance with the
terms of the TIA and execute, and use reasonable best efforts to cause the
Trustee to execute, all documents as may be required to effect such changes, and
all other forms and documents required to be filed with the SEC to enable the
Indenture to be so qualified in a timely manner.

                  Section 4. Holder's Obligations. Each Holder agrees, by
acquisition of the Registrable Securities, to be bound by and to comply in all
respects with its obligations as a Holder under this Agreement and that no
Holder of Registrable Securities shall be entitled to any notice or other rights
hereunder or to sell any of such Registrable Securities pursuant to a
Registration Statement or to receive a Prospectus relating thereto, unless such
Holder has furnished the Company with a Notice and Questionnaire as required
pursuant to Section 2(d) hereof (including all information required to be
included in such Notice and Questionnaire) and the information set forth in the
next sentence. Each Notice Holder agrees promptly to furnish to the Company all
information required to be disclosed in order to make the information previously
furnished to the Company by such Notice Holder not misleading and any other
information regarding such Notice Holder and the distribution of such
Registrable Securities as


                                       12
<PAGE>   13

may be required to be disclosed in the Registration Statement under applicable
law or pursuant to SEC comments or as the Company may reasonably request.

                  Section 5. 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 and taxes shall be paid by Holders of such Securities)
incurred in connection with the performance by the Company of its obligations
under Sections 2 and 3 of this Agreement whether or not any of the Registration
Statements are declared effective. Such fees and expenses shall include, without
limitation, (i) all registration and filing fees (including, without limitation,
fees and expenses (x) with respect to filings required to be made with the
National Association of Securities Dealers, Inc. and (y) of compliance with
federal and state securities or Blue Sky laws (including, without limitation,
reasonable fees and disbursements of the counsel specified in the next sentence
in connection with Blue Sky qualifications of the Registrable Securities under
the laws of such jurisdictions as the Notice Holders of a majority of the
Registrable Securities being sold pursuant to a Registration Statement may
designate)), (ii) printing expenses (including, without limitation, expenses of
printing certificates for Registrable Securities in a form eligible for deposit
with The Depository Trust Company), (iii) duplication expenses relating to
copies of any Registration Statement or Prospectus delivered to any Holders
hereunder, (iv) fees and disbursements of counsel for the Company in connection
with the Shelf Registration Statement, and (v) reasonable fees and disbursements
of the Trustee and its counsel and of the registrar and transfer agent for the
Common Stock. In addition, the Company shall bear or reimburse the Notice
Holders for the reasonable fees and disbursements of one firm of legal counsel
for the Holders, which shall initially be Shearman & Sterling, but which may,
upon the written consent of the Purchaser (which shall not be unreasonably
withheld), be another nationally recognized law firm experienced in securities
law matters designated by the Company. In addition, the Company shall pay the
internal expenses of the Company (including, without limitation, all salaries
and expenses of officers and employees performing legal or accounting duties),
the expense of any annual audit, the fees and expenses incurred in connection
with the listing of the Registrable Securities on any securities exchange on
which similar securities of the Company are then listed and the fees and
expenses of any person, including special experts, retained by the Company.

                  Section 6. Indemnification; Contribution. (a) The Company
agrees to indemnify and hold harmless the Purchaser and each Holder of
Registrable Securities and each person, if any, who controls the Purchaser or
any Holder of Registrable Securities within the meaning of either Section 15 of
the Securities Act or Section 20 of the Exchange Act, as follows:

                  (i) against any and all loss, liability, claim or damage, as
         incurred, arising out of or based upon any untrue statement or alleged
         untrue statement of a material fact contained in the Registration
         Statement (or any amendment thereto), or the omission or alleged
         omission therefrom of a material fact necessary in order to make the
         statements therein, in light of the circumstances under which they were
         made, not misleading or arising out of any untrue statement or alleged
         untrue statement of a material fact included in any preliminary
         prospectus or the Prospectus (or any amendment or supplement thereto),
         or the omission or alleged omission therefrom of a material fact
         necessary in order to make the statements therein, in the light of the
         circumstances under which they were made, not misleading;



                                       13
<PAGE>   14

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

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

provided, however, that the Company shall not be liable in any such case for or
in respect of any loss, liability, claim, damage or expense to the extent
arising out of or based upon any untrue statement or omission or alleged untrue
statement or omission made in reliance upon and in conformity with written
information furnished to the Company by or on behalf of Purchaser or such Holder
of Registrable Securities and each person, if any, who controls the Purchaser or
any such Holder of Registrable Securities expressly for use in the Registration
Statement (or any amendment thereto), or any preliminary prospectus or the
Prospectus (or any amendment or supplement thereto); provided further, that the
Company shall not be liable in any such case for or in respect of any loss,
liability, claim, damage or expense (1) arising from an offer or sale of
Registrable Securities occurring during a Deferral Period, if Notice Holder
received a Deferral Notice, or (2) if the Holder fails to deliver at or prior to
written confirmation of sale, the most recent Prospectus, as amended or
supplemented, and such Prospectus, as amended or supplemented, would have
corrected such untrue statement or omission or alleged untrue statement or
omission of a material fact.

                  (b) In connection with any Registration Statement in which a
Holder, including, without limitation, the Purchaser, of Registrable Securities
is participating, by furnishing information relating to such Holder of
Registrable Securities to the Company in writing expressly for use in such
Registration Statement, any preliminary prospectus, the Prospectus or any
amendments or supplements thereto, such Holder agrees, severally and not
jointly, to indemnify and hold harmless the Purchaser and each person, if any,
who controls the Purchaser within the meaning of either Section 15 of the
Securities Act or Section 20 of the Exchange Act and the Company, its directors,
each of its officers who signed such Registration Statement, and each person, if
any, who controls the Company within the meaning of either such Section, against
any and all loss, liability, claim, damage and expense described in the
indemnity contained in subsections (a)(i), (ii) and (iii) of this Section, as
incurred, but only with respect to untrue statements or omissions, or alleged
untrue statements or omissions, made in the Registration Statement (or any
amendment thereto), or any preliminary prospectus or the Prospectus (or any
amendment or supplement thereto) in reliance upon and in conformity with written
information furnished to the Company by or on behalf of such Holder of
Registrable Securities and each person, if any, who controls any such Holder of
Registrable Securities expressly for use in the Registration Statement (or any
amendment thereto) or such preliminary prospectus or the Prospectus (or any
amendment or supplement thereto).


                                       14
<PAGE>   15

                  The Purchaser agrees to indemnify and hold harmless the
Company, its directors, each of its officers who signed the Registration
Statement, the Holders of Registrable Securities, and each person, if any, who
controls the Company or any Holder of Registrable Securities within the meaning
of either Section 15 of the Securities Act or Section 20 of the Exchange Act
against any and all loss, liability, claim, damage and expense described in the
indemnity contained in subsections (a)(i), (ii) and (iii) of this Section, as
incurred, but only with respect to untrue statements or omissions, or alleged
untrue statements or omissions, made in the Registration Statement (or any
amendment thereto), or any preliminary prospectus or the Prospectus (or any
amendment or supplement thereto) in reliance upon and in conformity with written
information furnished to the Company by or on behalf of the Purchaser expressly
for use in the Registration Statement (or any amendment thereto) or such
preliminary prospectus or the Prospectus (or any amendment or supplement
thereto).

                  (c) Each indemnified party shall give notice as promptly as
reasonably practicable to each indemnifying party of any action commenced
against it in respect of which indemnity may be sought hereunder, but failure to
so notify an indemnifying party shall not relieve such indemnifying party from
any liability hereunder to the extent it is not materially prejudiced as a
result thereof and in any event shall not relieve it from any liability which it
may have otherwise than on account of this indemnity agreement. In case any such
action is brought against any indemnified party and it notifies the indemnifying
party of the commencement thereof, the indemnifying party will be entitled to
participate therein and, to the extent that it may wish, jointly with any other
indemnifying party similarly notified, to assume the defense thereof, with
counsel satisfactory to such indemnified party (who shall not, except with the
consent of the indemnified party, be counsel to the indemnifying party), and
after notice from the indemnifying party to such indemnified party of its
election so to assume the defense thereof, the indemnifying party will not be
liable to such indemnified party under this Section for any legal or other
expenses subsequently incurred by such indemnified party in connection with the
defense thereof other than reasonable costs of investigation. No indemnifying
party shall, without the prior written consent of the indemnified party, settle,
compromise or consent to the entry of any judgment with respect to any pending
or threatened action in respect of which any indemnified party is or could have
been a party and indemnity could have been sought hereunder by such indemnified
party unless such settlement, compromise or consent (i) includes an
unconditional release of such indemnified party from all liability on any claims
that are the subject matter of such action and (ii) does not include any
statement as to, or an admission of, fault, culpability or a failure to act by
or on behalf of an indemnified person.

                  (d) If the indemnification provided for in this Section 6 is
for any reason unavailable to or insufficient to hold harmless an indemnified
party in respect of any losses, liabilities, claims, damages or expenses
referred to therein, then each indemnifying party shall contribute to the
aggregate amount of such losses, liabilities, claims, damages and expenses
incurred by such indemnified party, as incurred, in such proportion as is
appropriate to reflect the relative fault of the indemnifying party or parties
on the one hand and of the indemnified party on the other hand in connection
with the statements or omissions which resulted in such losses, liabilities,
claims, damages or expenses, as well as any other relevant equitable
considerations.

                  The relative fault of the Company on the one hand and the
Holders of the Registrable Securities or the Purchaser on the other hand shall
be determined by reference to,


                                       15
<PAGE>   16

among other things, whether any such untrue or alleged untrue statement of a
material fact or omission or alleged omission to state a material fact relates
to information supplied by the Company on the one hand or by the Holder of the
Registrable Securities or the Purchaser or such other indemnified party, on the
other hand, and the parties' relative intent, knowledge, access to information
and opportunity to correct or prevent such statement or omission.

                  The parties hereto agree that it would not be just and
equitable if contribution pursuant to this Section 6(d) were determined by pro
rata allocation or by any other method of allocation which does not take account
of the equitable considerations referred to above in this Section 6(d). The
aggregate amount of losses, liabilities, claims, damages, and expenses incurred
by an indemnified party and referred to above in this Section 6(d) shall be
deemed to include any legal or other expenses reasonably incurred by such
indemnified party in investigating, preparing or defending against any
litigation, or any investigation or proceeding by any governmental agency or
body, commenced or threatened, or any claim whatsoever based upon any such
untrue or alleged untrue statement or omission or alleged omission.

                  Notwithstanding the provisions of this Section 6, neither the
Holder of any Registrable Securities nor the Purchaser shall be required to
indemnify or contribute any amount in excess of the amount by which the total
price at which the Registrable Securities sold by such Holder of Registrable
Securities or purchased by the Purchaser, as the case may be, and distributed to
the public were offered to the public exceeds the amount of any damages that
such Holder of Registrable Securities or 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.

                  For purposes of this Section 6(d), each person, if any, who
controls the Purchaser or any Holder of Registrable Securities within the
meaning of Section 15 of the Securities Act or Section 20 of the Exchange Act
shall have the same rights to contribution as the Purchaser or such Holder, and
each person, if any, who controls the Company within the meaning of Section 15
of the Securities Act or Section 20 of the Exchange Act shall have the same
rights to contribution as the Company.


                  Section 7. Information Requirements. (a) The Company covenants
that, if at any time before the end of the Effectiveness Period the Company is
not subject to the reporting requirements of the Exchange Act, it will cooperate
with any Holder of Registrable Securities and take such further reasonable
action as any Holder of Registrable Securities may reasonably request in writing
(including, without limitation, making such reasonable representations as any
such Holder may reasonably request), all to the extent required from time to
time to enable such Holder to sell Registrable Securities without registration
under the Securities Act within the limitation of the exemptions provided by
Rule 144 and Rule 144A under the Securities Act and customarily taken in
connection with sales pursuant to such exemptions. Upon the written request of
any Holder of Registrable Securities, the Company shall deliver to such Holder a

                                       16
<PAGE>   17

written statement as to whether it has complied with such filing requirements,
unless such a statement has been included in the Company's most recent report
required to be filed and filed pursuant to Section 13 or Section 15(d) of
Exchange Act. Notwithstanding the foregoing, nothing in this Section 7 shall be
deemed to require the Company to register any of its securities (other than the
Common Stock) under any section of the Exchange Act.

                  Section 8. Miscellaneous.

                  (a) No Conflicting Agreements. The Company is not, as of the
date hereof, a party to, nor shall it, on or after the date of this Agreement,
enter into, any agreement with respect to its securities that conflicts with the
rights granted to the Holders of Registrable Securities in this Agreement, other
than any conflicting rights in any such agreement that have been waived by the
beneficiary thereof. The Company represents and warrants that the rights granted
to the Holders of Registrable Securities hereunder do not in any way conflict
with the rights granted to the holders of the Company's securities under any
other agreements, other than any conflicts in any such agreement that have been
waived by the beneficiary thereof.

                  (b) 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 Underlying Common Stock constituting
Registrable Securities (with Holders of Securities deemed to be the Holders, for
purposes of this Section, of the number of outstanding shares of Underlying
Common Stock into which such Securities 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
Registrable Securities whose securities are being sold pursuant to a
Registration Statement and that does not directly or indirectly affect the
rights of other Holders of Registrable Securities may be given by Holders of at
least a majority of the Registrable Securities being sold by such Holders
pursuant to such 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 Registrable
Securities outstanding at the time of any such amendment, modification,
supplement, waiver or consent or thereafter shall be bound by any such
amendment, modification, supplement, waiver or consent effected pursuant to this
Section 8(b), whether or not any notice, writing or marking indicating such
amendment, modification, supplement, waiver or consent appears on the
Registrable 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.

                  (c) Notices. All notices and other communications provided for
or permitted hereunder shall be made in writing by hand delivery, by telecopier,
by courier guaranteeing overnight delivery or by first-class mail, return
receipt requested, and shall be deemed given (i) when made, if made by hand
delivery, (ii) upon confirmation, if made by telecopier, (iii) one (1) Business
Day after being deposited with such courier, if made by overnight courier or
(iv) on the date indicated on the notice of receipt, if made by first-class
mail, to the parties as follows:

                                       17
<PAGE>   18

                  (x) if to a Holder of Registrable Securities, at the most
         current address given by such Holder to the Company in a Notice and
         Questionnaire or any amendment thereto,

                  (y) if to the Company, to:

                  Diamond Offshore Drilling, Inc.
                  15415 Katy Freeway
                  Houston, TX 77094
                  Attention:  Corporate Secretary
                  Telephone:  (281) 492-5300
                  Facsimile:  (281) 647-2223

                  with a copy to:

                  Weil, Gotshal & Manges LLP
                  700 Louisiana, Suite 1600
                  Houston, TX 77002
                  Attention:  Shelton M. Vaughan
                  Telephone:  (713) 546-5000
                  Facsimile:  (713) 224-9511

                  and

                  (z) if to the Purchaser, to:

                  Merrill Lynch & Co., Merrill Lynch, Pierce,
                  Fenner & Smith Incorporated
                  World Financial Center
                  North Tower
                  250 Vesey Street
                  New York, New York  10281
                  Attention: Syndicate Department
                  Facsimile: (212) 738-1069

                  with a copy to:

                  Shearman & Sterling
                  599 Lexington Avenue
                  New York, New York 10022
                  Attention:  Michael J. Schiavone
                  Telephone:  (212) 848-4000
                  Facsimile:  (212) 848-7179

or to such other address as such person may have furnished to the other persons
identified in this Section 8(c) in writing in accordance herewith.

                  (d) Approval of Holders. Whenever the consent or approval of
Holders of a specified percentage of Registrable Securities is required
hereunder, the Registrable Securities


                                       18
<PAGE>   19

held by the Company or its affiliates (as such term is defined in Rule 405 under
the Securities Act) (other than the Purchaser or subsequent Holders of
Registrable Securities if such subsequent Holders are deemed to be such
affiliates solely by reason of their holdings of such Registrable Securities)
shall not be counted in determining whether such consent or approval was given
by the Holders of such required percentage.

                  (e) Successors and Assigns. This Agreement shall inure to the
benefit of and be binding upon the successors, assigns and transferees of each
of the parties, including, without limitation and without the need for an
express assignment, subsequent Holders; provided that nothing herein shall be
deemed to permit any assignment, transfer or other disposition of Registrable
Securities in violation of the terms of the Purchase Agreement or the Indenture.
If any transferee of any Holder shall acquire Securities or Registrable
Securities, in any manner, whether by operation of law or otherwise, such
Securities or Registrable Securities shall be held subject to all of the terms
of this Agreement, and by taking and holding such Securities or Registrable
Securities, such person shall be conclusively deemed to have agreed to be bound
by and to perform all of the terms and provisions of this Agreement and such
person shall be entitled to receive the benefits hereof. The Purchaser (in its
capacity as Purchaser) shall have no liability or obligation to the Company with
respect to any failure by any other Holder to comply with, or any breach by any
other Holder of, any of the obligations of such other Holder under this
Agreement.

                  (f) 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 original and all of which taken
together shall constitute one and the same agreement.

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

                  (h) Governing Law. THIS AGREEMENT SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE LAW OF THE STATE OF NEW YORK, WITHOUT REGARD TO
CONFLICTS OF LAWS PRINCIPLES THEREOF.

                  (i) Severability. If any term, provision, covenant or
restriction of this Agreement is held to be invalid, illegal, void or
unenforceable, the remainder of the terms, provisions, covenants and
restrictions set forth herein shall remain in full force and effect and shall in
no way be affected, impaired or invalidated thereby, and the parties hereto
shall use their best efforts to find and employ an alternative means to achieve
the same or substantially the same result as that contemplated by such term,
provision, covenant or restriction, it being intended that all of the rights and
privileges of the parties shall be enforceable to the fullest extent permitted
by law.

                  (j) Entire Agreement. This Agreement is intended by the
parties as a final expression of their agreement and is intended to be a
complete and exclusive statement of the agreement and understanding of the
parties hereto in respect of the subject matter contained herein and the
registration rights granted by the Company with respect to the Registrable
Securities. Except as provided in the Purchase Agreement, there are no
restrictions, promises,


                                       19
<PAGE>   20

warranties or undertakings, other than those set forth or referred to herein,
with respect to the registration rights granted by the Company with respect to
the Registrable Securities. This Agreement supersedes all prior agreements and
undertakings among the parties with respect to such registration rights.

                  (k) Termination. This Agreement and the obligations of the
parties hereunder shall terminate upon the expiration of the Effectiveness
Period, except for any liabilities or obligations under Sections 4, 5 or 6
hereof and the obligations to make payments of and provide for liquidated
damages under Section 2(e) hereof to the extent such damages accrue prior to the
end of the Effectiveness Period, each of which shall remain in effect in
accordance with its terms.

                [Remainder of this page intentionally left blank]


                                       20
<PAGE>   21


                  IN WITNESS WHEREOF, the parties have executed this
Registration Rights Agreement as of the date first written above.


DIAMOND OFFSHORE DRILLING, INC.


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


Confirmed and accepted as of the date
first above written:

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


By: /s/ Richard K. Gordon
   -------------------------------
   Name:  Richard K. Gordon
   Title: Vice Chairman