R&B FALCON CORP
S-4, 1998-09-16
DRILLING OIL & GAS WELLS
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<PAGE>   1
 
   AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON SEPTEMBER 15, 1998
 
                                                     REGISTRATION NO. 333-
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
 
                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549
                             ---------------------
 
                                    FORM S-4
            REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933
                             ---------------------
 
                             R&B FALCON CORPORATION
             (Exact name of Registrant as specified in its charter)
 
<TABLE>
<S>                                <C>                                <C>
           DELAWARE                             1381                            76-0544217
(State or Other Jurisdiction of     (Primary Standard Industrial             (I.R.S. Employer
         Incorporation               Classification Code Number)            Identification No.)
       or Organization)
</TABLE>
 
                                901 THREADNEEDLE
                              HOUSTON, TEXAS 77079
                                 (281) 496-5000
  (Address, including zip code, and telephone number, including area code, of
                   Registrant's principal executive offices)
 
                                LEIGHTON E. MOSS
                             R&B FALCON CORPORATION
                                901 THREADNEEDLE
                              HOUSTON, TEXAS 77079
                                 (281) 496-5000
 (Name, address, including zip code, and telephone number, including area code,
                             of agent for service)
 
                                   Copies to:
 
<TABLE>
<S>                                                  <C>
               WILLIAM MARK YOUNG                                    CAROLYN CAMPBELL
      GARDERE WYNNE SEWELL & RIGGS, L.L.P.                        GRIGGS & HARRISON, P.C.
               THREE ALLEN CENTER                                      1301 MCKINNEY
           333 CLAY AVENUE, SUITE 800                                   SUITE 3200
            HOUSTON, TEXAS 77002-4086                            HOUSTON, TEXAS 77010-3033
</TABLE>
 
    Approximate date of commencement of proposed sale of the securities to the
public: As soon as practicable after the effective date of this registration
statement and upon consummation of the merger described herein.
 
    If the securities being registered on this Form are being offered in
connection with the formation of a holding company and there is compliance with
General Instruction G, check the following box.  [ ]
 
    If this form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, check the following box and
list the Securities Act registration statement number of the earlier effective
registration statement for the same offering.  [ ]
- ------------------
 
    If this form is a post-effective amendment filed pursuant to Rule 462(d)
under the Securities Act, check the following box and list the Securities Act
registration statement number of the earlier effective registration statement
for the offering.  [ ]
- ------------------
 
                        CALCULATION OF REGISTRATION FEE
 
<TABLE>
<CAPTION>
- ------------------------------------------------------------------------------------------------------------------------------
- ------------------------------------------------------------------------------------------------------------------------------
                                                                      PROPOSED             PROPOSED
                                                                      MAXIMUM              MAXIMUM
         TITLE OF EACH CLASS OF                AMOUNT TO BE        OFFERING PRICE         AGGREGATE            AMOUNT OF
     SECURITIES TO BE REGISTERED(1)           REGISTERED(2)         PER SHARE(3)      OFFERING PRICE(3)     REGISTRATION FEE
- ------------------------------------------------------------------------------------------------------------------------------
<S>                                        <C>                  <C>                  <C>                  <C>
Common Stock, $0.01 par value............       28,212,564         Not Applicable        $350,167,709           $103,300
- ------------------------------------------------------------------------------------------------------------------------------
- ------------------------------------------------------------------------------------------------------------------------------
</TABLE>
 
(1) Also includes associated Rights to purchase shares of the Registrant's
    Series A Junior Participating Preferred Stock, which Rights (a) are not
    currently separable from the shares of Common Stock and (b) are not
    currently exercisable. See "The Merger -- General Description of the
    Merger."
(2) Consists of (i) 27,103,654 shares of Common Stock issuable upon the
    conversion, pursuant to the Merger, of currently outstanding shares of
    common stock, par value $0.01 per share ("Cliffs Drilling Common Stock") of
    Cliffs Drilling Company, a Delaware corporation ("Cliffs Drilling"), (ii) up
    to 1,056,550 shares of Common Stock issuable upon the exercise of Cliffs
    Drilling options that are outstanding and unexercised at the Effective Time
    and that, pursuant to the Merger, will be assumed by the Registrant and
    converted into options to purchase shares of Common Stock, (iii) 6,460
    shares of Common Stock issuable in satisfaction of deferred stock
    obligations of Cliffs Drilling that, pursuant to the Merger, will be assumed
    by the Registrant, and (iv) up to 45,900 shares of Common Stock issuable
    upon the conversion, pursuant to the Merger, of shares of Cliffs Drilling
    Common Stock currently held in treasury by Cliffs Drilling which are
    anticipated to be issued and outstanding on or before the Effective Time in
    satisfaction of matching obligations under the Cliffs Drilling Savings Plan.
(3) Estimated solely for the purpose of calculating the registration fee
    pursuant to Rule 457(f)(1) and Rule 457(c), based on the product of (a)
    $21.10 (the average of the high and low prices of Cliffs Drilling Common
    Stock on September 11, 1998 as reported by the New York Stock Exchange)
    times (b) 16,595,626 (being the sum of 15,943,326 issued and outstanding
    shares of Cliffs Drilling Common Stock, as of September 11, 1998, 621,500
    shares of Cliffs Drilling Common Stock reserved for issuance upon the
    exercise of outstanding options as of September 11, 1998, 3,800 shares of
    Cliffs Drilling Common Stock issuable in satisfaction of deferred stock
    obligations, and up to 27,000 shares of Cliffs Drilling Common Stock
    currently held in treasury by Cliffs Drilling which are anticipated to be
    issued and outstanding as of the Effective Time).
 
     THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT SHALL
FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS REGISTRATION
STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH SECTION 8(a) OF
THE SECURITIES ACT OF 1933 OR UNTIL THE REGISTRATION STATEMENT SHALL BECOME
EFFECTIVE ON SUCH DATE AS THE COMMISSION, ACTING PURSUANT TO SAID SECTION 8(a),
MAY DETERMINE.
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
<PAGE>   2
 
                                      LOGO
 
               , 1998
 
Dear Stockholders:
 
     A special meeting of stockholders (the "Special Meeting") of Cliffs
Drilling Company, a Delaware corporation ("Cliffs Drilling"), will be held on
                    , 1998 at 10:00 a.m., Houston time, at the Doubletree Hotel
at Allen Center, 400 Dallas Street at Bagby, Houston, Texas, to consider and
vote upon a proposal to approve and adopt the Agreement and Plan of Merger dated
as of August 21, 1998 (the "Merger Agreement") by and among Cliffs Drilling, R&B
Falcon Corporation, a Delaware corporation ("R&B Falcon"), and RBF Cliffs
Acquisition Corp., a wholly owned Delaware subsidiary of R&B Falcon ("Sub").
Pursuant to the terms of the Merger Agreement, Sub will merge with and into
Cliffs Drilling (the "Merger") with Cliffs Drilling continuing as the surviving
corporation and a wholly owned subsidiary of R&B Falcon. In the Merger, each
outstanding share of Cliffs Drilling common stock, par value $0.01 per share
("Cliffs Drilling Common Stock"), shall be converted into the right to receive
1.7 shares of R&B Falcon common stock, par value $0.01 per share. The attached
Proxy Statement/Prospectus explains the terms of the proposed Merger and
provides other information concerning both Cliffs Drilling and R&B Falcon. We
urge you to read these materials fully and carefully.
 
     In connection with its approval of the Merger on August 20, 1998, Cliffs
Drilling's Board of Directors received and took into account the written opinion
of Jefferies & Company, Inc. ("Jefferies"), an investment banking firm retained
by Cliffs Drilling, that, based on the assumptions stated in such opinion, the
Merger consideration to be received by the holders of Cliffs Drilling Common
Stock pursuant to the Merger Agreement is fair, from a financial point of view,
to such holders. Jefferies' opinion is included in the attached Proxy
Statement/Prospectus.
 
     For the Merger to become effective, among other conditions described in the
attached Proxy Statement/Prospectus and the Merger Agreement, the holders of at
least a majority of the outstanding shares of Cliffs Drilling Common Stock must
vote in favor of the Merger. THE BOARD OF DIRECTORS OF CLIFFS DRILLING BELIEVES
THAT THE PROPOSED MERGER IS IN THE BEST INTERESTS OF CLIFFS DRILLING AND THE
STOCKHOLDERS OF CLIFFS DRILLING AND UNANIMOUSLY RECOMMENDS THAT YOU VOTE FOR
APPROVAL OF THE MERGER.
 
     You are cordially invited to attend the Special Meeting. Your vote is
important regardless of how many shares you own. Please take a few minutes to
review the attached Proxy Statement/Prospectus, and to sign, date and mail your
proxy in the envelope provided. FAILURE TO VOTE BY PROXY OR IN PERSON AT THE
SPECIAL MEETING IS THE EQUIVALENT OF A VOTE AGAINST THE MERGER. Thank you for
your prompt response and cooperation.
 
                                            Very truly yours,
 
                                            Douglas E. Swanson
                                            President and Chief Executive
                                            Officer
<PAGE>   3
 
                            CLIFFS DRILLING COMPANY
                          1200 SMITH STREET, SUITE 300
                              HOUSTON, TEXAS 77002
 
                 NOTICE OF SPECIAL MEETING OF THE STOCKHOLDERS
 
To our Stockholders:
 
     Notice is hereby given that a Special Meeting of Stockholders (the "Special
Meeting") of Cliffs Drilling Company ("Cliffs Drilling") will be held on
                    , 1998 at 10:00 a.m., Houston time, at the Doubletree Hotel
at Allen Center, 400 Dallas Street at Bagby, Houston, Texas, to consider and
vote upon a proposal to approve and adopt the Agreement and Plan of Merger dated
as of August 21, 1998 (the "Merger Agreement") by and among Cliffs Drilling, R&B
Falcon Corporation, a Delaware corporation ("R&B Falcon"), and RBF Cliffs
Acquisition Corp., a wholly owned Delaware subsidiary of R&B Falcon ("Sub"),
whereby Sub will merge with and into Cliffs Drilling (the "Merger") with Cliffs
Drilling continuing as the surviving corporation and a wholly owned subsidiary
of R&B Falcon. In the Merger, each outstanding share of Cliffs Drilling common
stock, par value $0.01 per share ("Cliffs Drilling Common Stock"), shall be
converted into the right to receive 1.7 shares of R&B Falcon common stock, par
value $0.01 per share.
 
     Only holders of record of Cliffs Drilling Common Stock at the close of
business on October 16, 1998 are entitled to notice of and to vote at the
Special Meeting or any adjournment or postponement thereof.
 
     Stockholders are cordially invited and urged to attend the Special Meeting
in person. Those who will not attend and who wish their shares to be voted are
requested to sign, date and mail promptly the enclosed proxy in the postage
prepaid return envelope which is also enclosed. The specific details of the
Merger are fully described in the accompanying Proxy Statement/Prospectus and in
the Merger Agreement, a copy of which is attached to the Proxy
Statement/Prospectus as Appendix A.
 
                                            By Order of the Board of Directors
 
                                            Cindy B. Taylor
                                            Secretary
 
Houston, Texas
               , 1998
 
     WHETHER OR NOT YOU PLAN TO BE PRESENT AT THE SPECIAL MEETING, YOU ARE URGED
TO SIGN, DATE AND MAIL PROMPTLY THE ENCLOSED PROXY. STOCKHOLDERS WHO HAVE GIVEN
A PROXY MAY REVOKE THE PROXY AT ANY TIME BEFORE ITS EXERCISE AT THE SPECIAL
MEETING, AND STOCKHOLDERS WHO ARE PRESENT AT THE SPECIAL MEETING MAY WITHDRAW
THEIR PROXY AND VOTE IN PERSON.
<PAGE>   4
 
                            CLIFFS DRILLING COMPANY
                                PROXY STATEMENT
         SPECIAL MEETING OF STOCKHOLDERS TO BE HELD             , 1998
                             ---------------------
 
                             R&B FALCON CORPORATION
                        (COMMON STOCK, $0.01 PAR VALUE)
 
                                   PROSPECTUS
                             ---------------------
 
     This Proxy Statement/Prospectus is being furnished to stockholders of
Cliffs Drilling Company, a Delaware corporation ("Cliffs Drilling"), in
connection with the solicitation of proxies by its Board of Directors for use at
a Special Meeting of Stockholders (the "Special Meeting") to be held on
            , 1998 at 10:00 a.m., Houston time, at the Doubletree Hotel at Allen
Center, 400 Dallas Street at Bagby, Houston, Texas 77002 and any adjournment or
postponement thereof.
 
     At the Special Meeting, stockholders of Cliffs Drilling will be asked to
consider and vote upon a proposal to approve and adopt a Merger Agreement dated
as of August 21, 1998 (the "Merger Agreement") among R&B Falcon Corporation, a
Delaware corporation ("R&B Falcon"), RBF Cliffs Acquisition Corp., a Delaware
corporation and a direct wholly owned subsidiary of R&B Falcon ("Sub"), and
Cliffs Drilling. The Merger Agreement provides for the merger of Sub with and
into Cliffs Drilling (the "Merger"), as a result of which Cliffs Drilling would
become a direct wholly owned subsidiary of R&B Falcon, and each outstanding
share of common stock, par value $0.01 per share, of Cliffs Drilling ("Cliffs
Drilling Common Stock") would be converted into the right to receive 1.7 shares
of common stock, par value $0.01 per share, of R&B Falcon ("R&B Falcon Common
Stock"). Each share of R&B Falcon Common Stock will be issued together with the
associated preferred stock purchase rights under the Rights Agreement (the "R&B
Falcon Rights Plan"), dated as of December 23, 1997 with American Stock Transfer
& Trust Company, as rights agent (the "R&B Falcon Rights"). See "The Merger." A
copy of the Merger Agreement is attached as Appendix A to this Proxy
Statement/Prospectus. Under Delaware law, holders of Cliffs Drilling Common
Stock will not have any dissenter's rights of appraisal in connection with the
Merger.
 
     R&B Falcon has filed a registration statement on Form S-4 pursuant to the
Securities Act of 1933, as amended (the "Securities Act"), covering shares of
R&B Falcon Common Stock to be issued in exchange for shares of Cliffs Drilling
Common Stock pursuant to the Merger Agreement. Based on the market price of the
R&B Falcon Common Stock as of the close of business on September 11, 1998, the
value of the consideration to be paid to the holders of the Cliffs Drilling
Common Stock in the Merger would be $22.31 per share of Cliffs Drilling Common
Stock for an aggregate total consideration pursuant to the Merger Agreement of
approximately $370.3 million.
 
     This Proxy Statement/Prospectus and the accompanying form of proxy are
first being mailed to stockholders of Cliffs Drilling on or about             ,
1998.
 
     R&B Falcon Common Stock and Cliffs Drilling Common Stock are listed on the
New York Stock Exchange, Inc. (the "NYSE") under the trading symbols "FLC" and
"CDG," respectively. On September 11, 1998, the closing price of R&B Falcon
Common Stock as reported on the NYSE was $13.13, and the closing price of Cliffs
Drilling Common Stock as reported on the NYSE was $21.63.
                             ---------------------
 
     SEE "RISK FACTORS" BEGINNING ON PAGE 12 FOR A DISCUSSION OF CERTAIN FACTORS
WHICH SHOULD BE CONSIDERED IN EVALUATING THE SECURITIES OFFERED HEREBY.
                             ---------------------
THE SHARES OF R&B FALCON COMMON STOCK TO BE ISSUED IN CONNECTION WITH THE MERGER
HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE SECURITIES AND EXCHANGE COMMISSION
     OR ANY STATE SECURITIES COMMISSION NOR HAS THE SECURITIES AND EXCHANGE
   COMMISSION OR ANY STATE SECURITIES COMMISSION PASSED UPON THE ACCURACY OR
ADEQUACY OF THIS PROXY STATEMENT/ PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY
                             IS A CRIMINAL OFFENSE.
 
       THE DATE OF THIS PROXY STATEMENT/PROSPECTUS IS             , 1998.
<PAGE>   5
 
                               TABLE OF CONTENTS
 
<TABLE>
<S>                                                            <C>
AVAILABLE INFORMATION.......................................        iii
INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE.............        iii
FORWARD-LOOKING STATEMENTS..................................          v
SUMMARY.....................................................          1
  The Companies.............................................          1
  Date, Place and Purpose of the Cliffs Drilling Special
     Meeting................................................          1
  The Merger................................................          2
  Market Price and Dividend Information.....................          6
  R&B Falcon Selected Historical Financial Data.............          8
  Cliffs Drilling Selected Historical Financial Data........          9
  R&B Falcon and Cliffs Drilling Summary Selected Unaudited
     Pro Forma Combined Financial Data......................         10
  Comparative Per Share Data................................         11
RISK FACTORS................................................         12
THE CLIFFS DRILLING SPECIAL MEETING.........................         16
  General...................................................         16
  Matter to be Considered...................................         16
  Record Date; Shares Entitled to Vote; Quorum..............         16
  Votes Required; Voting and Revocation of Proxies; Effect
     of Abstentions and Non-Votes...........................         16
  Solicitation of Proxies...................................         17
THE MERGER..................................................         17
  General Description of the Merger.........................         17
  Background of the Merger..................................         18
  Recommendation of Cliffs Drilling's Board of Directors;
     Reasons for the Merger.................................         20
  Opinion of Cliffs Drilling's Financial Advisor............         22
  Accounting Treatment of the Merger........................         25
  Certain Federal Income Tax Consequences...................         25
  Regulatory Approvals......................................         27
  Resales of R&B Falcon Common Stock........................         27
  NYSE Listing of Common Stock..............................         27
  No Appraisal Rights.......................................         27
  Interests of Certain Persons in the Merger................         27
  Recent Development........................................         30
THE MERGER AGREEMENT........................................         31
  The Merger................................................         31
  Conversion of Securities..................................         31
  Representations and Warranties............................         32
  Certain Covenants.........................................         32
  No Solicitation...........................................         34
  Additional Agreements.....................................         35
  Employee Matters..........................................         35
  Indemnification...........................................         36
  Conditions to the Merger..................................         37
  Termination...............................................         38
  Expenses and Termination Fees.............................         39
  Amendment and Waiver......................................         40
UNAUDITED PRO FORMA CONDENSED COMBINED FINANCIAL
  STATEMENTS................................................         41
</TABLE>
 
                                        i
<PAGE>   6
 
<TABLE>
<S>                                                                   <C>
COMPARISON OF STOCKHOLDER RIGHTS......................................        46
  Authorized Capital Stock............................................        46
  Rights Plans........................................................        46
  Board of Directors..................................................        46
  Monetary Liability of Directors.....................................        46
  Voting Rights.......................................................        47
  Foreign Ownership Limitation........................................        47
  Removal of Directors and Filling Vacancies on the 
    Board of Directors................................................        47
  Stockholder Action Without a Meeting................................        47
  Special Meetings of Stockholders....................................        47
  Charter and Bylaw Amendments........................................        47
BENEFICIAL OWNERSHIP OF CLIFFS DRILLING COMMON STOCK..................        48
STOCKHOLDER PROPOSALS.................................................        49
INDEPENDENT PUBLIC ACCOUNTANTS........................................        49
LEGAL MATTERS.........................................................        49
EXPERTS...............................................................        49
</TABLE>
 
APPENDIX A -- Agreement and Plan of Merger
 
APPENDIX B -- Fairness Opinion of Jefferies & Company, Inc.
 
                                       ii
<PAGE>   7
 
                             AVAILABLE INFORMATION
 
     Each of R&B Falcon and Cliffs Drilling is subject to the informational
requirements of the Securities Exchange Act of 1934, as amended (the "Exchange
Act"), and, in accordance therewith, files reports, proxy statements and other
information with the Securities and Exchange Commission (the "Commission"). Such
reports and other information may be inspected and copied at the public
reference facilities that the Commission maintains at Room 1024, Judiciary
Plaza, 450 Fifth Street, N.W., Washington, D.C. 20549, and at the following
Regional Offices of the Commission: Citicorp Center, 500 West Madison Street,
Suite 1400, Chicago, Illinois 60661; and Seven World Trade Center, Suite 1300,
New York, New York 10048. Copies of such material can also be obtained from the
Public Reference Section of the Commission at 450 Fifth Street, N.W.,
Washington, D.C. 20549 at prescribed rates. The Commission maintains a Web site
that contains reports, proxy and information statements and other information
filed electronically by R&B Falcon and Cliffs Drilling with the Commission that
can be accessed over the Internet at http://www.sec.gov. In addition, reports,
proxy statements and other information filed by R&B Falcon and Cliffs Drilling
can be inspected at the offices of The New York Stock Exchange, Inc., 20 Broad
Street, New York, New York 10005.
 
     R&B Falcon has filed with the Commission a registration statement on Form
S-4 (together with all the amendments, supplements and exhibits thereto, the
"Registration Statement") under the Securities Act of 1933, as amended (the
"Securities Act") with respect to the R&B Falcon Common Stock issuable in
connection with the Merger. R&B Falcon has provided the information contained
herein with respect to R&B Falcon and its subsidiaries, and Cliffs Drilling has
provided the information with respect to Cliffs Drilling and its subsidiaries.
This Proxy Statement/Prospectus does not contain all of the information set
forth in the Registration Statement and the exhibits thereto, certain parts of
which are omitted in accordance with the rules and regulations of the
Commission. The Registration Statement and any amendments thereto, including
exhibits filed as a part thereof, are available for inspection and copying as
set forth above. Statements contained in this Proxy Statement/Prospectus or in
any document incorporated in this Proxy Statement/ Prospectus by reference as to
the contents of any contract or other document referred to herein or therein are
not necessarily complete, and in each instance reference is made to the copy of
such contract or other document filed as an exhibit to the Registration
Statement or such other document, each such statement being qualified in all
respects by such reference.
 
                INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE
 
     The following documents, which have been filed previously by R&B Falcon
(Commission File No. 001-13729) with the Commission pursuant to the Exchange
Act, are hereby incorporated herein by reference:
 
          (a) Annual Report on Form 10-K for the fiscal year ended December 31,
     1997;
 
          (b) Quarterly Reports on Form 10-Q for the quarters ended March 31,
     1998 and June 30, 1998;
 
          (c) Current Reports on Form 8-K dated March 23, 1998 and August 10,
     1998; and
 
          (d) Registration Statements on Form 8-A relating to the R&B Falcon
     Common Stock and the R&B Falcon Rights, each as amended to date.
 
     The following documents, which have been filed previously by Cliffs
Drilling (Commission File No. 001-12797) with the Commission pursuant to the
Exchange Act, are hereby incorporated herein by reference:
 
          (a) Annual Report on Form 10-K for the fiscal year ended December 31,
     1997;
 
          (b) Quarterly Reports on Form 10-Q for the quarters ended March 31,
     1998 and June 30, 1998;
 
          (c) Current Report on Form 8-K dated August 20, 1998; and
 
          (d) Registration Statements on Form 8-A relating to the Cliffs
     Drilling Common Stock and the rights (the "Cliffs Drilling Rights") to
     acquire shares of Series A Junior Participating Preferred Stock of
 
                                       iii
<PAGE>   8
 
     Cliffs Drilling pursuant to the Rights Agreement dated as of June 17, 1997
     between Cliffs Drilling and Harris Trust and Savings Bank, as rights agent
     (the "Cliffs Drilling Rights Plan"), each as amended to date.
 
     All documents and reports filed by R&B Falcon or Cliffs Drilling pursuant
to Section 13(a), 13(c), 14 or 15(d) of the Exchange Act after the date of this
Proxy Statement/Prospectus and prior to the date of the Special Meeting shall be
deemed to be incorporated by reference herein and to be a part hereof from the
respective dates of filing of such documents or reports. All information
appearing in this Proxy Statement/ Prospectus or in any document incorporated
herein by reference is not necessarily complete and is qualified in its entirety
by the information and financial statements (including notes thereto) appearing
in the documents incorporated herein by reference and should be read together
with such information and documents.
 
     Any statement contained herein or in a document all or a portion of which
is incorporated or deemed to be incorporated by reference herein shall be deemed
to be modified or superseded for purposes of this Proxy Statement/Prospectus to
the extent that a statement contained herein (or in any subsequently filed
document which also is or is deemed to be incorporated by reference herein)
modifies or supersedes such statement. Any such statement so modified or
superseded shall not be deemed to constitute a part of this Proxy Statement/
Prospectus except as so modified or superseded.
 
     R&B Falcon and Cliffs Drilling hereby undertake to provide, without charge,
to each person, including any beneficial owner of Cliffs Drilling Common Stock,
to whom a copy of this Proxy Statement/Prospectus has been delivered, upon the
written or oral request of any such person and by first class mail or equally
prompt means within one business day of the receipt of such request, a copy of
any and all of the documents indicated above which have been or may be
incorporated herein by reference, other than exhibits to such documents, unless
such exhibits are specifically incorporated herein by reference. Requests for
such documents should be directed to the party indicated below.
 
     NO PERSON IS AUTHORIZED TO GIVE ANY INFORMATION OR TO MAKE ANY
REPRESENTATION NOT CONTAINED IN THIS PROXY STATEMENT/PROSPECTUS, AND, IF GIVEN
OR MADE, SUCH INFORMATION OR REPRESENTATION MUST NOT BE RELIED UPON AS HAVING
BEEN AUTHORIZED. THIS PROXY STATEMENT/PROSPECTUS DOES NOT CONSTITUTE AN OFFER TO
SELL, OR A SOLICITATION OF AN OFFER TO PURCHASE, ANY OF THE SECURITIES OFFERED
BY THIS PROXY STATEMENT/PROSPECTUS, OR THE SOLICITATION OF A PROXY, IN ANY
JURISDICTION IN WHICH, OR TO ANY PERSON TO WHOM, IT IS UNLAWFUL TO MAKE SUCH
OFFER OR SOLICITATION OF AN OFFER OR PROXY SOLICITATION. NEITHER THE DELIVERY OF
THIS PROXY STATEMENT/PROSPECTUS NOR ANY DISTRIBUTION OF THE SECURITIES OFFERED
HEREBY SHALL, UNDER ANY CIRCUMSTANCES, CREATE ANY IMPLICATION THAT THE
INFORMATION CONTAINED HEREIN IS CORRECT AS OF ANY TIME SUBSEQUENT TO THE DATE
HEREOF OR THAT THERE HAS BEEN NO CHANGE IN THE AFFAIRS OF R&B FALCON OR CLIFFS
DRILLING SINCE THE DATE HEREOF.
 
     THIS PROXY STATEMENT/PROSPECTUS INCORPORATES CERTAIN DOCUMENTS REGARDING
R&B FALCON AND CLIFFS DRILLING BY REFERENCE THAT ARE NOT PRESENTED HEREIN OR
DELIVERED HEREWITH. THE DOCUMENTS AND EXHIBITS SPECIFICALLY INCORPORATED BY
REFERENCE WITH RESPECT TO R&B FALCON ARE AVAILABLE TO ANY PERSON, INCLUDING ANY
BENEFICIAL OWNER, UPON REQUEST FROM INVESTOR RELATIONS, R&B FALCON CORPORATION,
901 THREADNEEDLE, HOUSTON, TEXAS 77079, TELEPHONE NUMBER (281) 496-5000. THE
DOCUMENTS AND EXHIBITS SPECIFICALLY INCORPORATED BY REFERENCE WITH RESPECT TO
CLIFFS DRILLING ARE AVAILABLE TO ANY PERSON, INCLUDING ANY BENEFICIAL OWNER,
UPON REQUEST FROM INVESTOR RELATIONS, CLIFFS DRILLING COMPANY, 1200 SMITH
STREET, SUITE 300, HOUSTON, TEXAS 77002, TELEPHONE NUMBER (713) 651-9426. TO
ENSURE TIMELY DELIVERY OF THESE DOCUMENTS, ANY REQUEST SHOULD BE MADE
BY                    , 1998.
 
                                       iv
<PAGE>   9
 
                           FORWARD-LOOKING STATEMENTS
 
     This Proxy Statement/Prospectus includes and incorporates by reference
forward-looking statements within the meaning of the Private Securities
Litigation Reform Act of 1995. Such forward-looking statements relate to, among
other matters, analyses, including opinions from independent financial advisors
to the Board of Directors of Cliffs Drilling as to the fairness, from a
financial point of view, of the Merger to the stockholders of Cliffs Drilling,
which are based on forecasts of future results and estimates of amounts not yet
determinable. Such forward-looking statements also relate to the future
prospects, developments and business strategies for the operations of R&B Falcon
and Cliffs Drilling and the synergies that are possible from the Merger. These
forward-looking statements are identified by their use of terms and phrases such
as "anticipate," "believe," "expect," "plan," "intend," "estimate," "project,"
"will," "could," "may," "predict," and similar terms and phrases and are
contained in sections entitled "Summary," "Risk Factors," "The Merger," and
other sections of this Proxy Statement/Prospectus and in the documents
incorporated herein by reference. These statements involve risks and
uncertainties that may cause actual future activities and results of operations
to be materially different from those suggested or described in this Proxy
Statement/Prospectus. These risks include R&B Falcon's dependence on the oil and
gas industry, its commitment to the deepwater drilling market, the risks of
construction and upgrade projects currently being conducted by R&B Falcon,
competition, operational risks, risks involved in foreign operations, the age of
the rigs in R&B Falcon's fleet, government regulation and environmental matters,
the ability of R&B Falcon to integrate and realize anticipated synergies
relating to the Merger, the ability of R&B Falcon to achieve and execute
internal business plans and the impact of any economic downturns and inflation.
These risks are more specifically described in R&B Falcon's Annual Report on
Form 10-K and Quarterly Reports on Form 10-Q, which are incorporated herein by
reference, and in the section entitled "Risk Factors." Should one or more of
these risks or uncertainties materialize, or should underlying assumptions prove
incorrect, actual results may vary materially from those expected, estimated or
projected.
 
                                        v
<PAGE>   10
 
                                    SUMMARY
 
     The following is a summary of certain information contained elsewhere in
this Proxy Statement/ Prospectus. Reference is made to, and this Summary is
qualified in its entirety by, the more detailed information included elsewhere
or incorporated by reference in this Proxy Statement/Prospectus. Stockholders
are urged to read this Proxy Statement/Prospectus and the Appendices hereto in
their entirety. As used in this Proxy Statement/Prospectus, unless the context
otherwise requires, the term "R&B Falcon" means R&B Falcon Corporation and its
consolidated subsidiaries and the term "Cliffs Drilling" means Cliffs Drilling
Company and its consolidated subsidiaries. Certain capitalized terms used in
this summary are defined elsewhere in this Proxy Statement/Prospectus.
 
                                 THE COMPANIES
 
R&B FALCON CORPORATION
 
     R&B Falcon owns and operates the world's largest fleet of marine drilling
rigs. Through its predecessors, R&B Falcon has provided contract drilling
services to the oil and gas industry since 1956. As a result of mergers that
became effective December 31, 1997, Falcon Drilling Company, Inc. ("Falcon") and
Reading & Bates Corporation ("R&B") became wholly owned subsidiaries of R&B
Falcon Corporation. R&B Falcon's executive offices are headquartered at 901
Threadneedle, Houston, Texas 77079, and its telephone number at that location is
(281) 496-5000.
 
CLIFFS DRILLING COMPANY
 
     Cliffs Drilling is an international contract drilling and engineering
company primarily engaged in daywork drilling, engineering services, and to a
lesser extent, the development and operation of mobile offshore production units
("MOPUs"). Cliffs Drilling's domestic operations are concentrated in the
Texas/Louisiana Gulf Coast region and its foreign operations are concentrated in
Venezuela, Trinidad and the Middle East. Cliffs Drilling currently owns 16
jack-up drilling rigs, 11 land rigs, 3 platform rigs and 4 MOPUs. The principal
executive offices of Cliffs Drilling are located at 1200 Smith Street, Suite
300, Houston, Texas 77002, and its telephone number at that location is (713)
651-9426.
 
         DATE, PLACE AND PURPOSE OF THE CLIFFS DRILLING SPECIAL MEETING
 
TIME, DATE AND PLACE
 
     The Special Meeting of the Stockholders of Cliffs Drilling (the "Special
Meeting") will be held on                     , 1998 at 10:00 a.m., Houston
time, at the Doubletree Hotel at Allen Center, 400 Dallas Street at Bagby,
Houston, Texas 77002. See "The Cliffs Drilling Special Meeting -- General."
 
PURPOSE
 
     The purpose of the Special Meeting is to approve the Merger Agreement (the
"Merger Agreement") dated as of August 21, 1998 among R&B Falcon, Cliffs
Drilling and RBF Cliffs Acquisition Corp., a wholly owned Delaware subsidiary of
R&B Falcon ("Sub"), and the Merger of Sub with and into Cliffs Drilling (the
"Merger"). See "The Cliffs Drilling Special Meeting -- Matter to be Considered."
 
VOTE REQUIRED
 
     Approval of the Merger Agreement and the Merger requires the affirmative
vote by the holders of at least a majority of the outstanding shares of Cliffs
Drilling Common Stock. No approval by the holders of outstanding shares of R&B
Falcon Common Stock is required to approve the Merger Agreement or the Merger.
See "The Cliffs Drilling Special Meeting -- Votes Required; Voting and
Revocation of Proxies; Effect of Abstentions and Non-Votes."
 
                                        1
<PAGE>   11
 
RECORD DATE; SHARES ENTITLED TO VOTE
 
     Only holders of record of Cliffs Drilling Common Stock at the close of
business on October 16, 1998 (the "Record Date") are entitled to notice of and
to vote at the Special Meeting. On that date, there
were                    shares of Cliffs Drilling Common Stock outstanding.
Holders of Cliffs Drilling Common Stock are entitled to one vote for each share
held. See "The Cliffs Drilling Special Meeting -- Record Date; Shares Entitled
to Vote; Quorum."
 
SECURITY OWNERSHIP OF MANAGEMENT
 
     Directors and executive officers of Cliffs Drilling and their affiliates as
of the Record Date beneficially owned approximately 2.8% of the outstanding
shares of Cliffs Drilling Common Stock. See "Beneficial Ownership of Cliffs
Drilling Common Stock."
 
                                   THE MERGER
 
EFFECT OF THE MERGER
 
     In the Merger, Sub will merge with and into Cliffs Drilling. Cliffs
Drilling will be the surviving entity of the Merger (the "Surviving
Corporation") and will become a direct wholly owned subsidiary of R&B Falcon.
See "The Merger -- General Description of the Merger."
 
CONVERSION OF CLIFFS DRILLING COMMON STOCK
 
     In the Merger, each share of Cliffs Drilling Common Stock will be converted
into the right to receive 1.7 shares of R&B Falcon Common Stock. Pursuant to the
Merger Agreement, R&B Falcon will issue an aggregate of up to 28,212,564 shares
of R&B Falcon Common Stock in connection with the consummation of the Merger
(the "Merger Consideration"). Cash will be paid in lieu of fractional shares.
See "The Merger -- General Description of the Merger."
 
REASONS FOR THE MERGER
 
     Cliffs Drilling's Board of Directors (the "Cliffs Drilling Board") believes
that the Merger offers to Cliffs Drilling a number of synergystic opportunities
and strategic benefits, including (i) the ability to reduce dependence on
shallow water markets, (ii) the ability to reduce exposure to business cycles in
the Gulf of Mexico and Venezuela, (iii) greater geographical and equipment
diversification, (iv) greater access to equipment for international expansion,
(v) access to existing infrastructure for expansion of well engineering and
integrated services, (vi) enhanced rig engineering and project management
expertise, and (vii) greater access to capital at a reduced cost. The Cliffs
Drilling Board also believes that the Merger offers to holders of Cliffs
Drilling Common Stock a number of significant benefits, including (i) the
opportunity to receive a premium over the market price immediately prior to
announcement of the Merger for Cliffs Drilling Common Stock, (ii) Merger
Consideration consisting of R&B Falcon Common Stock which, based on historical
information, has traded at a higher earnings multiple, is more widely followed
by the investment community, is less volatile, and provides greater liquidity,
than Cliffs Drilling Common Stock, and (iii) the opportunity to receive R&B
Falcon Common Stock in a transaction that is intended to be non-taxable for
federal income tax purposes. See "The Merger -- Recommendation of Cliffs
Drilling's Board of Directors; Reasons for the Merger" and "-- Certain Federal
Income Tax Consequences."
 
RECOMMENDATION OF THE BOARD OF DIRECTORS OF CLIFFS DRILLING
 
     The Cliffs Drilling Board believes that the terms of the Merger are fair to
and in the best interests of Cliffs Drilling and its stockholders and has
unanimously approved the Merger Agreement and the transactions contemplated
thereby. THE CLIFFS DRILLING BOARD UNANIMOUSLY RECOMMENDS THAT THE CLIFFS
DRILLING STOCKHOLDERS VOTE FOR THE MERGER AGREEMENT AND THE
 
                                        2
<PAGE>   12
 
TRANSACTIONS CONTEMPLATED THEREBY. See "The Merger -- Recommendation of Cliffs
Drilling's Board of Directors; Reasons for the Merger."
 
OPINION OF CLIFFS DRILLING'S FINANCIAL ADVISOR
 
     Jefferies & Company, Inc. ("Jefferies") has delivered its written opinion
dated August 20, 1998 (the "Fairness Opinion") to the Cliffs Drilling Board to
the effect that, as of the date of such opinion and subject to the factors,
assumptions, qualifications and limitations set forth therein, the consideration
to be received by the Cliffs Drilling stockholders in the Merger is fair, from a
financial point of view, to the Cliffs Drilling stockholders. The Fairness
Opinion was provided to the Cliffs Drilling Board for its information only and
does not address the merits of the underlying decision by Cliffs Drilling to
enter into the Merger, nor does it constitute a recommendation as to how any
holder of Cliffs Drilling Common Stock should vote on the Merger. See "The
Merger -- Opinion of Cliffs Drilling's Financial Advisor." For information on
the assumptions made, matters considered and the qualifications and limitations
on the review by Jefferies, see "The Merger -- Opinion of Cliffs Drilling's
Financial Advisor." Stockholders of Cliffs Drilling are urged to read the
Fairness Opinion in its entirety, a copy of which is attached as Appendix B to
this Proxy Statement/ Prospectus.
 
EFFECTIVE TIME OF THE MERGER
 
     Unless otherwise agreed to by the parties, the closing of the Merger (the
"Closing") will occur as soon as practicable after satisfaction or waiver of the
conditions set forth in the Merger Agreement (the "Closing Date"). The Merger
will become effective upon filing of a Certificate of Merger with the Secretary
of State of the State of Delaware or at such other time specified in the
Certificate of Merger as the effective time (the "Effective Time"). See "The
Merger -- General Description of the Merger."
 
MANAGEMENT OF CLIFFS DRILLING AFTER THE MERGER
 
     Paul B. Loyd, Jr., Steven A. Webster, and Douglas E. Swanson shall be the
directors of the Surviving Corporation, and the officers of Cliffs Drilling
immediately prior to the Effective Time shall be the officers of the Surviving
Corporation. Such directors and officers shall hold office in accordance with
the certificate of incorporation and bylaws of the Surviving Corporation until
their respective successors are duly elected or appointed and qualified. Mr.
Loyd is the Chairman of the Board of Directors of R&B Falcon, Mr. Webster is the
President and Chief Executive Officer and a director of R&B Falcon, and Mr.
Swanson is the Chairman of the Board, President and Chief Executive Officer of
Cliffs Drilling. See "The Merger -- General Description of the Merger."
 
BOARD OF DIRECTORS OF R&B FALCON FOLLOWING THE MERGER
 
     As of the Effective Time, R&B Falcon shall appoint Douglas E. Swanson,
Cliffs Drilling's Chairman of the Board, President and Chief Executive Officer,
as a Class I director of R&B Falcon with a term expiring in 2001. See "The
Merger -- Interests of Certain Persons in the Merger" and "The Merger
Agreement -- Additional Agreements."
 
CONDITIONS TO THE MERGER
 
     The obligations of Cliffs Drilling and R&B Falcon to consummate the Merger
are subject to certain conditions, including: (i) the approval of the holders of
at least a majority of the outstanding shares of Cliffs Drilling Common Stock;
(ii) the favorable opinion of counsel to Cliffs Drilling that the Merger will
qualify as a tax-free reorganization; and (iii) other conditions customary for
transactions of this nature. See "The Merger Agreement -- Conditions to the
Merger."
 
NO SOLICITATION
 
     Cliffs Drilling has agreed, on behalf of itself and its affiliates, during
the term of the Merger Agreement that it will not: (i) solicit or encourage
(including by way of furnishing information) any Cliffs Acquisition
                                        3
<PAGE>   13
 
Transaction (as defined in the Merger Agreement); (ii) negotiate, explore or
otherwise engage in discussions with others regarding a possible Cliffs
Acquisition Transaction; or (iii) enter into any agreement or understanding
requiring Cliffs Drilling to abandon the Merger. Notwithstanding the foregoing,
the Cliffs Drilling Board may authorize Cliffs Drilling's participation in a
Cliffs Acquisition Transaction if outside legal counsel renders a written
opinion to the Cliffs Drilling Board that such action is required for the Cliffs
Drilling Board to comply with its fiduciary duties under applicable law, and the
Cliffs Drilling Board may withdraw or modify its recommendation of the Merger in
light of a Cliffs Acquisition Transaction if, among other things, outside legal
counsel renders a written opinion to the Cliffs Drilling Board that such action
is required for the Cliffs Drilling Board to comply with its fiduciary duties
under applicable law and a nationally recognized investment banking firm renders
a written opinion to the Cliffs Drilling Board that the consideration payable to
the Cliffs Drilling stockholders under the proposed Cliffs Acquisition
Transaction is superior, from a financial point of view, to the consideration
payable to them in the Merger. See "The Merger Agreement -- No Solicitation."
 
TERMINATION
 
     The Merger Agreement may be terminated and the transactions contemplated
thereby may be abandoned at any time prior to the Closing Date: (i) by mutual
consent of Cliffs Drilling and R&B Falcon; (ii) by either party if the Merger
shall not have occurred, other than through the failure of any such party to
fulfill its obligations under the Merger Agreement, on or before February 28,
1999; (iii) by either party if the fairness opinion provided to it by its
financial advisors is withdrawn; (iv) by either party if a final, unappealable
order of any court or administrative authority of competent jurisdiction shall
have been issued that restrains, enjoins or otherwise prevents the transactions
contemplated by the Merger Agreement; (v) by either party if the Merger
Agreement shall not have been approved or adopted by the stockholders of Cliffs
Drilling; (vi) by either party if (a) since the date of the Merger Agreement
there has been a material adverse change in the other party, or (b) there is an
inaccuracy or breach of any representation, warranty or covenant of the other
party set forth in the Merger Agreement which breach has not been cured within
thirty (30) days following receipt by the other party of notice of such breach;
or (vii) by R&B Falcon if the Cliffs Drilling Board exercises its limited rights
under the no solicitation section of the Merger Agreement to (A) not convene a
meeting of the stockholders of Cliffs Drilling to approve the Merger or (B)
withdraw or otherwise change its recommendation of the Merger. See "The Merger
Agreement -- Termination."
 
EXPENSES AND TERMINATION FEES
 
     Except as set forth below, R&B Falcon and Cliffs Drilling will each pay
their own costs and expenses in connection with the transactions contemplated by
the Merger.
 
     The Merger Agreement provides that Cliffs Drilling will pay R&B Falcon a
termination fee of $15 million if the Merger Agreement is terminated under
certain circumstances specified in the Merger Agreement (including, without
limitation, the failure of Cliffs Drilling stockholders to approve the Merger),
and that R&B Falcon will pay Cliffs Drilling a termination fee of $15 million if
the Merger Agreement is terminated under certain circumstances specified in the
Merger Agreement. In addition, the Merger Agreement provides that Cliffs
Drilling shall pay R&B Falcon a fee of $30 million (less any termination fee
previously paid by Cliffs Drilling to R&B Falcon) if the Merger Agreement is
terminated and Cliffs Drilling enters into a subsequent acquisition transaction
within twelve months after such termination under certain circumstances
specified in the Merger Agreement. These fees are intended, among other things,
to compensate a party for its costs, including lost opportunity costs, if the
Merger is not consummated as a result of certain actions or inactions by the
other party. These fees may have the effect of increasing the likelihood that
the Merger will be consummated in accordance with the terms of the Merger
Agreement. These fees may also have the effect of discouraging persons who might
now or prior to the consummation of the Merger be interested in acquiring all of
or a significant interest in Cliffs Drilling from considering or proposing such
an acquisition by increasing the costs of any such acquisition. See "The Merger
Agreement -- Expenses and Termination Fee."
 
                                        4
<PAGE>   14
 
INDEMNIFICATION
 
     The Merger Agreement provides that R&B Falcon and the Surviving Corporation
shall, to the extent provided in Cliffs Drilling's organizational documents and
the indemnification agreement with such person as in effect on August 11, 1998,
indemnify the present and former directors, officers, employees and agents of
Cliffs Drilling or any of its subsidiaries with respect to matters occurring at
or prior to the Effective Time (including matters arising out of or pertaining
to the transactions contemplated by the Merger Agreement) and periodically
advance expenses as incurred with respect to the foregoing to the fullest extent
permitted under applicable law. See "The Merger Agreement -- Indemnification."
 
AMENDMENT AND WAIVER
 
     Any provision of the Merger Agreement may be waived at any time by the
party that is, or whose stockholders are, entitled to the benefits thereof. The
Merger Agreement may not be amended or supplemented at any time, except by an
instrument in writing signed on behalf of each party thereto. The waiver by any
party of any condition or of a breach of another provision of the Merger
Agreement shall not operate or be construed as a waiver of any other condition
or subsequent breach. The waiver by any party of any of the conditions precedent
to its obligations under the Merger Agreement shall not preclude it from seeking
redress for breach of the Merger Agreement other than with respect to the
condition so waived. See "The Merger Agreement -- Amendment and Waiver."
 
ACCOUNTING TREATMENT
 
     R&B Falcon intends to account for the Merger under the purchase method of
accounting in accordance with generally accepted accounting principles. See "The
Merger -- Accounting Treatment of the Merger."
 
CERTAIN FEDERAL INCOME TAX CONSEQUENCES
 
     Except with respect to cash to be received by Cliffs Drilling stockholders
in lieu of fractional shares of R&B Falcon Common Stock, it is intended that the
Merger qualify as a tax-free transaction for United States federal income tax
purposes. It is a condition to the Merger that Cliffs Drilling receive an
opinion of counsel, based on customary assumptions and representations, that the
Merger so qualifies. Holders of Cliffs Drilling Common Stock are urged to
consult their tax advisors as to the specific tax consequences to them of the
Merger. See "The Merger -- Certain Federal Income Tax Consequences."
 
REGULATORY MATTERS
 
     Consummation of the Merger is conditioned on the expiration or termination
of the applicable waiting period under the Hart-Scott-Rodino Antitrust
Improvements Act of 1976, as amended (the "HSR Act"), which waiting period
terminated on               , 1998. No material federal or state regulatory
approvals are required in order to consummate the Merger. See "The
Merger -- Regulatory Approvals."
 
NO APPRAISAL RIGHTS
 
     Under the provisions of the Delaware General Corporation Laws (the "DGCL"),
holders of Cliffs Drilling Common Stock will not be entitled to any dissenters'
rights of appraisal with respect to the Merger. See "The Merger -- No Appraisal
Rights."
 
RESTRICTIONS ON RESALE OF SECURITIES ISSUED IN THE MERGER
 
     Shares of R&B Falcon Common Stock issued in the Merger will be freely
transferable, except for shares issued to persons who may be deemed "affiliates"
of Cliffs Drilling. See "The Merger -- Resales of R&B Falcon Common Stock."
 
                                        5
<PAGE>   15
 
INTERESTS OF CERTAIN PERSONS IN THE MERGER
 
     Certain members of Cliffs Drilling's management have interests in the
Merger that are in addition to the interests of Cliffs Drilling stockholders
generally. It is a condition to the Merger that Cliffs Drilling obtain waivers
and releases of its obligations to certain executive officers of Cliffs Drilling
that would otherwise arise upon consummation of the Merger. In conjunction
therewith, these executive officers of Cliffs Drilling will receive in the
aggregate approximately $7.1 million in cash, plus an additional amount of
approximately $1.8 million in tax "gross-up" payments, upon consummation of the
Merger. The Surviving Corporation has agreed to enter into new Employment
Agreements with these executive officers effective as of the consummation of the
Merger. In addition, R&B Falcon has agreed to grant stock options to certain
employees of Cliffs Drilling, including executive officers of Cliffs Drilling,
upon consummation of the Merger. See "The Merger -- Background of the Merger"
and "-- Interests of Certain Persons in the Merger."
 
COMPARISON OF STOCKHOLDER RIGHTS
 
     The rights of holders of Cliffs Drilling are currently governed by the DGCL
and the certificate of incorporation and bylaws of Cliffs Drilling. Upon
consummation of the Merger, holders of Cliffs Drilling Common Stock will become
holders of R&B Falcon Common Stock, and their rights as holders of R&B Falcon
Common Stock will still be governed by the DGCL, but will be governed by the
certificate of incorporation and bylaws of R&B Falcon. There are various
differences between the rights of Cliffs Drilling stockholders and the rights of
R&B Falcon stockholders. Furthermore, the certificate of incorporation of R&B
Falcon contains certain provisions that may have the effect of deterring or
making it more difficult for a third party to acquire control of R&B Falcon. See
"Comparison of Stockholder Rights."
 
                     MARKET PRICE AND DIVIDEND INFORMATION
 
     The following table sets forth the high and low sales prices of Cliffs
Drilling Common Stock and R&B Falcon Common Stock for the calendar quarters
indicated. With respect to Cliffs Drilling Common Stock, the information is as
reported by the NASDAQ Stock Market for periods through April 2, 1997, and as
reported by the NYSE for periods from and after April 3, 1997. The information
with respect to R&B Falcon Common Stock is as reported by the NYSE. R&B Falcon
Common Stock was first traded on January 2, 1998.
 
<TABLE>
<CAPTION>
                                                     CLIFFS DRILLING     R&B FALCON
                                                      COMMON STOCK      COMMON STOCK
                                                     ---------------   ---------------
          FISCAL YEAR ENDED DECEMBER 31,              HIGH     LOW      HIGH     LOW
          ------------------------------             ------   ------   ------   ------
<S>                                                  <C>      <C>      <C>      <C>
1998
First Quarter......................................  $51.81   $32.38   $35.38   $23.13
Second Quarter.....................................   57.31    31.75    34.19    20.50
Third Quarter (through September 11, 1998).........   33.38    13.38    23.19     8.75

1997
First Quarter......................................  $39.75   $20.63       --       --
Second Quarter.....................................   37.13    26.94       --       --
Third Quarter......................................   70.50    36.38       --       --
Fourth Quarter.....................................   82.00    42.00       --       --

1996
First Quarter......................................  $ 7.88   $ 6.88       --       --
Second Quarter.....................................   17.00     7.63       --       --
Third Quarter......................................   18.38    12.88       --       --
Fourth Quarter.....................................   34.63    16.75       --       --
</TABLE>
 
                                        6
<PAGE>   16
 
     The following table sets forth the reported high, low and closing prices
per share of R&B Falcon Common Stock and Cliffs Drilling Common Stock on the
NYSE and the equivalent high, low and closing price per share of Cliffs Drilling
Common Stock (which is calculated by multiplying the high, low and closing price
per share of R&B Falcon Common Stock by 1.7) on August 10, 1998, the last full
day of trading prior to public announcement of the Merger, and on
                    , 1998, the last full day of trading prior to the date of
this Proxy Statement/Prospectus.
 
<TABLE>
<CAPTION>
                                                              HIGH     LOW     CLOSE
                                                             ------   ------   ------
<S>                                                          <C>      <C>      <C>
AUGUST 10, 1998
  R&B Falcon Common Stock..................................  $16.50   $15.25   $15.31
  Cliffs Drilling Common Stock.............................  $20.13   $19.13   $19.38
  Cliffs Drilling Common Stock on an equivalent basis......  $28.05   $25.93   $26.03

          , 1998
  R&B Falcon Common Stock..................................
  Cliffs Drilling Common Stock.............................
  Cliffs Drilling Common Stock on an equivalent basis......
</TABLE>
 
     R&B Falcon has not paid dividends on the R&B Falcon Common Stock and does
not currently intend to pay any cash dividends in the foreseeable future. The
determination of the amount of future cash dividends to be declared and paid on
the R&B Falcon Common Stock, if any, will depend upon R&B Falcon's financial
condition, earnings and cash flow from operations, the level of its capital
expenditures, its future business prospects and other factors that the Board of
Directors of R&B Falcon (the "R&B Falcon Board") deems relevant. In addition,
R&B Falcon's bank credit facility contains covenants that may operate to
restrict the payment of dividends to R&B Falcon's stockholders.
 
     Cliffs Drilling has never paid cash dividends on the Cliffs Drilling Common
Stock, and it is not anticipated that cash dividends will be paid to holders of
the Cliffs Drilling Common Stock in the foreseeable future. Under Cliffs
Drilling's 10.25% Senior Notes due 2003 and revolving credit facility, Cliffs
Drilling is restricted from declaring, making or paying cash dividends on the
Cliffs Drilling Common Stock.
 
     Following the Merger, Cliffs Drilling will be a wholly owned subsidiary of
R&B Falcon, and the Cliffs Drilling Common Stock will be delisted from trading
on the NYSE. Following the Merger, the R&B Falcon Common Stock will continue to
be traded on the NYSE under the symbol "FLC."
 
     STOCKHOLDERS ARE ADVISED TO OBTAIN CURRENT MARKET QUOTATIONS FOR R&B FALCON
COMMON STOCK AND CLIFFS DRILLING COMMON STOCK. No assurance can be given as to
the market price of R&B Falcon Common Stock at or after the Effective Time.
 
                                        7
<PAGE>   17
 
                 R&B FALCON SELECTED HISTORICAL FINANCIAL DATA
 
     The following table sets forth summary consolidated financial data for R&B
Falcon as of and for the six months ended June 30, 1997 and 1998 and as of and
for each of the years in the five-year period ended December 31, 1997, giving
effect to the merger of R&B and Falcon under the "pooling-of-interests" method
of accounting. The summary consolidated financial data as of and for the six
months ended June 30, 1997 and 1998 have been derived from the unaudited
condensed consolidated financial statements of R&B Falcon and include all
adjustments (consisting only of normal recurring adjustments) that management
considers necessary for a fair presentation of the interim periods. Results of
interim periods are not necessarily indicative of results for the full year. The
summary consolidated financial data as of and for the three-year period ended
December 31, 1997 have been derived from R&B Falcon's audited consolidated
financial statements and, with respect to the years ended December 31, 1994 and
1993, the separate audited consolidated financial statements of R&B and Falcon.
The following data should be read in conjunction with the historical
consolidated financial statements of R&B Falcon, the related notes and other
financial data incorporated herein by reference.
 
                             R&B FALCON CORPORATION
                    (IN MILLIONS, EXCEPT PER SHARE AMOUNTS)
 
<TABLE>
<CAPTION>
                                 SIX MONTHS ENDED
                                     JUNE 30,
                                    (UNAUDITED)                  YEARS ENDED DECEMBER 31,
                                -------------------   ----------------------------------------------
                                  1998       1997       1997       1996      1995     1994     1993
                                --------   --------   --------   --------   ------   ------   ------
<S>                             <C>        <C>        <C>        <C>        <C>      <C>      <C>
INCOME STATEMENT DATA
Operating revenues............  $  560.4   $  425.3   $  942.1   $  609.6   $390.3   $307.6   $245.6
Income (loss) from continuing
  operations..................  $  130.2   $  105.4   $  156.0   $  106.4   $ 23.5   $(12.7)  $  8.5
Income (loss) from continuing
  operations per common share:
     Basic....................  $    .79   $    .64   $    .95   $    .70   $  .16   $ (.18)  $  .06
     Diluted..................  $    .78   $    .64   $    .94   $    .67   $  .15   $ (.18)  $  .05

BALANCE SHEET DATA
Total assets..................  $2,531.2   $1,672.6   $1,928.4   $1,455.8   $946.8   $810.9   $722.5
Long-term obligations
  (including current portion)
  and redeemable stocks.......  $1,205.2   $  610.4   $  827.4   $  514.2   $296.7   $288.6   $166.3
Dividends on common stock.....        --         --         --         --       --       --       --
</TABLE>
 
                                        8
<PAGE>   18
 
               CLIFFS DRILLING SELECTED HISTORICAL FINANCIAL DATA
 
     The following selected financial data as of and for each of the five years
in the period ended December 31, 1997 has been derived from the audited
consolidated financial statements of Cliffs Drilling. The selected financial
data as of and for the six months ended June 30, 1997 and 1998 have been derived
from the unaudited consolidated financial statements of Cliffs Drilling and
include all adjustments (consisting only of normal recurring adjustments) that
management considers necessary for a fair presentation of the interim periods.
Results for the interim periods are not necessarily indicative of results for
the full year. The financial data set forth below should be read in conjunction
with the historical consolidated financial statements of Cliffs Drilling, the
related notes and other financial data incorporated herein by reference.
 
                            CLIFFS DRILLING COMPANY
                    (IN MILLIONS, EXCEPT PER SHARE AMOUNTS)
 
<TABLE>
<CAPTION>
                                      SIX MONTHS ENDED
                                          JUNE 30,
                                         (UNAUDITED)               YEARS ENDED DECEMBER 31,
                                      -----------------   ------------------------------------------
                                       1998      1997      1997     1996     1995     1994     1993
                                      -------   -------   ------   ------   ------   ------   ------
<S>                                   <C>       <C>       <C>      <C>      <C>      <C>      <C>
INCOME STATEMENT DATA
Operating revenues..................  $175.0    $121.3    $263.6   $133.1   $ 83.3   $ 83.7   $ 65.5
Income from continuing operations...  $ 28.8    $ 20.6    $ 46.7   $ 14.4   $  5.4   $  6.1   $  3.6
Income from continuing operations
  per common share:
     Basic..........................  $ 1.82    $ 1.36    $ 3.06   $ 1.05   $  .34   $  .40   $  .11
     Diluted........................  $ 1.80    $ 1.34    $ 3.01   $ 1.02   $  .34   $  .40   $  .11
 
BALANCE SHEET DATA
Total assets........................  $532.6    $372.6    $500.2   $339.5   $129.0   $120.2   $133.5
Long-term obligations (including
  current portion) and redeemable
  stocks............................  $203.3    $150.0    $203.6   $150.0   $ 28.8   $ 28.8   $ 41.9
Dividends on common stock...........      --        --        --       --       --       --       --
</TABLE>
 
                                        9
<PAGE>   19
 
  R&B FALCON AND CLIFFS DRILLING SUMMARY SELECTED UNAUDITED PRO FORMA COMBINED
                                 FINANCIAL DATA
 
     The following summary selected unaudited pro forma combined financial data
is presented assuming the Merger will be accounted for under the purchase method
of accounting in accordance with Accounting Principles Board Opinion No. 16. The
income statement data is presented as if the Merger and certain other
acquisition and financing transactions were consummated at the beginning of the
respective periods. The balance sheet data is presented as if the Merger and
certain other acquisition and financing transactions were consummated at the
date of the balance sheet. The summary selected unaudited pro forma combined
financial data does not reflect any anticipated cost savings which may be
realized after consummation of the Merger.
 
     The pro forma data does not purport to represent what R&B Falcon and Cliffs
Drilling's combined results of operations actually would have been if the Merger
had occurred as of the date indicated or will be for any future periods. The
summary selected unaudited pro forma combined financial data should be read in
conjunction with the unaudited pro forma condensed combined financial statements
and the historical financial statements and the notes thereto of R&B Falcon and
Cliffs Drilling contained elsewhere or incorporated herein by reference.
 
               R&B FALCON CORPORATION AND CLIFFS DRILLING COMPANY
          SUMMARY SELECTED UNAUDITED PRO FORMA COMBINED FINANCIAL DATA
                    (IN MILLIONS, EXCEPT PER SHARE AMOUNTS)
 
<TABLE>
<CAPTION>
                                                              SIX MONTHS
                                                                 ENDED       YEAR ENDED
                                                               JUNE 30,     DECEMBER 31,
                                                                 1998           1997
                                                              -----------   ------------
<S>                                                           <C>           <C>
INCOME STATEMENT DATA
Operating revenues..........................................   $  735.4       $1,227.3
Income from continuing operations...........................   $  158.9       $  203.2
Income from continuing operations per common share:
  Basic.....................................................   $    .83       $   1.07
  Diluted...................................................   $    .82       $   1.05
 
BALANCE SHEET DATA AS OF JUNE 30, 1998
Total Assets................................................   $3,279.7
Long-term obligations (including current portion)...........   $1,408.5
</TABLE>
 
                                       10
<PAGE>   20
 
                           COMPARATIVE PER SHARE DATA
 
     The following table presents comparative per share data for R&B Falcon and
Cliffs Drilling on a historical basis. It also includes per share data for R&B
Falcon on a pro forma basis assuming that the Merger had been consummated and
for Cliffs Drilling on an equivalent pro forma basis assuming a conversion ratio
of 1.7. The comparative per share data for the year ended December 31, 1997 has
been derived from the audited consolidated financial statements of each of the
companies. The financial data for the six months ended June 30, 1998 is
unaudited; however, the financial statements reflect all adjustments, consisting
of normal recurring adjustments, which the companies consider necessary for a
fair presentation of the interim periods. The following data should be read in
conjunction with the consolidated financial statements and related notes thereto
incorporated herein by reference.
 
<TABLE>
<CAPTION>
                                                                   AS OF OR FOR THE
                                                              ---------------------------
                                                              SIX MONTHS
                                                                 ENDED
                                                               JUNE 30,       YEAR ENDED
                                                                 1998        DECEMBER 31,
                                                              (UNAUDITED)        1997
                                                              -----------    ------------
<S>                                                           <C>            <C>
R&B FALCON -- HISTORICAL (1)
Book value per share........................................    $ 5.19          $ 4.43
Cash dividends declared per share...........................        --              --
Income per share from continuing operations:
  Basic.....................................................    $  .79          $  .95
  Diluted...................................................    $  .78          $  .94

CLIFFS DRILLING -- HISTORICAL
Book value per share........................................    $15.45          $13.58
Cash dividends declared per share...........................        --              --
Income per share from continuing operations:
  Basic.....................................................    $ 1.82          $ 3.06
  Diluted...................................................    $ 1.80          $ 3.01

R&B FALCON -- PRO FORMA (UNAUDITED)
Book value per share........................................    $ 6.49             N/A
Cash dividends declared per share...........................        --              --
Income per share from continuing operations:
  Basic.....................................................    $  .83          $ 1.07
  Diluted...................................................    $  .82          $ 1.05

CLIFFS DRILLING -- EQUIVALENT PRO FORMA (UNAUDITED) (2)
Book value per share........................................    $11.03             N/A
Cash dividends declared per share...........................        --              --
Income per share from continuing operations:
  Basic.....................................................    $ 1.41          $ 1.82
  Diluted...................................................    $ 1.39          $ 1.79
</TABLE>
 
- ---------------
 
(1) Financial results for periods beginning prior to January 1, 1998 give effect
    to the merger of R&B and Falcon, which was accounted for as a
    "pooling-of-interests." Per share information was calculated on a pro forma
    basis as if such merger had occurred on January 1, 1997.
 
(2) These Equivalent Pro Forma amounts were calculated by multiplying the R&B
    Falcon-Pro Forma per share data by the 1.7 conversion rate. The conversion
    rate represents the number of shares of R&B Falcon Common Stock that a
    holder of Cliffs Drilling Common Stock would receive for each share held.
    The Equivalent Pro Forma amounts should be evaluated in comparison to the
    R&B Falcon Common Stock which, based on historical information, has traded
    at a higher earnings multiple, is more widely followed by the investment
    community, is less volatile, and provides greater liquidity, than Cliffs
    Drilling Common Stock.
 
                                       11
<PAGE>   21
 
                                  RISK FACTORS
 
     In addition to the other information in this Proxy Statement/Prospectus,
the following factors should be considered carefully in evaluating an investment
in the shares of R&B Falcon Common Stock offered by this Proxy
Statement/Prospectus.
 
DEPENDENCE ON OIL AND GAS INDUSTRY
 
     R&B Falcon's operations are materially dependent upon the level of activity
in offshore oil and gas exploration and production. The level of such activity
is affected by both short-term and long-term trends in oil and gas prices. Oil
and gas prices and, therefore, the level of drilling, exploration and production
activity, can be volatile. Worldwide military, political and economic events,
including initiatives by the Organization of Petroleum Exporting Countries, have
contributed to, and are likely to continue to contribute to, price volatility.
R&B Falcon believes that any prolonged reduction in oil and gas prices will
depress the level of exploration and production activity and result in a
corresponding decline in the demand for R&B Falcon's services and, therefore,
have a material adverse effect on R&B Falcon's revenues, cash flows and
profitability. There can be no assurances as to the future level of demand for
R&B Falcon's services or future conditions in the drilling industry. In May
1998, R&B Falcon began to experience a downturn in demand for R&B Falcon's
drilling rigs that R&B Falcon believes is attributable in large part to declines
in oil and gas prices that began in 1997 and have persisted into 1998. Decreased
demand adversely affects R&B Falcon by lowering utilization of R&B Falcon's rigs
and reducing the dayrates R&B Falcon is able to charge for its rigs.
 
COMMITMENT TO DEEPWATER DRILLING MARKET
 
     R&B Falcon has made a significant commitment to the deepwater drilling
market. Its current projects include the construction or major upgrade of seven
drillships and two semisubmersible rigs. R&B Falcon has long-term contracts or
letters of intent for the use of each deepwater rig that is currently undergoing
construction or upgrade. However, the cost of these projects will exceed the
cash flow R&B Falcon will derive from contractual commitments currently in
place. Upon completion of the initial contract term for each such rig, there is
no assurance that R&B Falcon will be able to obtain contracts for the further
use of the rig, or, if a contract can be obtained, that it will be at a dayrate
as high as the initial contract dayrate. In addition, these contracts may be
terminated in certain instances if R&B Falcon fails to perform its obligations
under such contracts.
 
     The deepwater market requires the use of floating rigs utilizing more
sophisticated technologies than those of the bottom-supported rigs that
previously constituted the majority of R&B Falcon's fleet. R&B Falcon and other
drilling contractors have experienced problems with the new generation of subsea
well control systems designed for drilling in deeper waters. If this equipment
fails to function properly, the rig cannot engage in drilling operations. To the
extent these problems are encountered on the systems that will be installed on
R&B Falcon's deepwater rigs under construction, R&B Falcon will experience lost
revenues and in certain cases may be subject to contract termination by the
customer.
 
     R&B Falcon will be required to hire and retain additional personnel capable
of operating effectively in a deepwater environment. Other drilling contractors
are expanding their deepwater fleets, and will compete with R&B Falcon for
qualified personnel to operate its deepwater rigs. As a result, there can be no
assurance that R&B Falcon will be successful in these efforts.
 
RISKS OF CONSTRUCTION AND UPGRADE PROJECTS
 
     R&B Falcon's deepwater rig construction and upgrade projects are subject to
the risks of delay and cost overruns inherent in any large construction project,
including shortages of equipment, unforeseen engineering problems, work
stoppages, weather interference, unanticipated cost increases and shortages of
materials or skilled labor. In particular, there is a current shortage of
certain types of drilling equipment that could delay and increase the cost of
the deepwater projects. Significant cost overruns or delays would adversely
affect R&B Falcon's financial condition and results of operations. Significant
delays could also result in penalties under, or the termination of, most of the
long-term contracts under which R&B Falcon plans to operate these
                                       12
<PAGE>   22
 
deepwater rigs. The scheduled delivery dates for five of R&B Falcon's nine
deepwater rigs currently under construction is later than the required
commencement date under the initial drilling contracts for such rigs. The
customers have certain rights to cancel these contacts if the rigs are not ready
to commence operations on the dates required under the contracts, and R&B Falcon
anticipates that it will be subject to late delivery penalties ranging from
$3,000 to $41,500 per day for several of these deepwater rigs. Based upon the
currently expected delivery date for one of these rigs, the applicable drilling
contract for that unit will be terminated on January 1, 1999, and R&B Falcon is
negotiating with the operators to extend the contract.
 
COMPETITION
 
     The marine drilling market is highly competitive and no one competitor is
dominant. During periods when the supply of rigs exceeds demand, this
competition results in significant downward pressure on the dayrates at which
R&B Falcon may contract its rigs. Because R&B Falcon's cost of operating its
rigs cannot be materially reduced, any reduction in dayrates has a negative
impact on R&B Falcon's results of operations. Even in an environment of
increased drilling activity, construction of new rigs could lead to an
oversupply of rigs and adversely affect dayrates for R&B Falcon's rigs.
 
OPERATIONAL RISKS AND INSURANCE
 
     R&B Falcon's operations are subject to the hazards inherent in the marine
drilling business, including blowouts, craterings, fires, collisions, capsizings
and adverse weather. These hazards could result in (i) substantial damage to the
environment; (ii) personal injury and loss of life; (iii) suspension of drilling
operations; or (iv) damage to property and producing formations. R&B Falcon may
incur substantial liabilities or losses as a result of these hazards. R&B Falcon
maintains insurance protection that it deems prudent, including liability
insurance and insurance against damage to or loss of equipment. In addition, R&B
Falcon generally seeks to obtain indemnity agreements whenever possible from R&B
Falcon's customers, requiring such customers to hold R&B Falcon harmless in the
event of loss of production, reservoir damage, or liability for pollution that
originates below the water surface. There is no assurance that such insurance or
contractual indemnity protection will be sufficient or effective under all
circumstances or against all hazards to which R&B Falcon may be subject.
Further, there is no assurance that R&B Falcon will be able to obtain adequate
insurance coverage at rates it deems reasonable in the future.
 
FOREIGN OPERATIONS
 
     R&B Falcon currently conducts operations worldwide. Operations in foreign
countries generally are subject to various risks associated with doing business
outside the United States, including risk of war, general strikes, civil
disturbances, guerrilla activity, foreign exchange restrictions, currency
fluctuations and devaluations, and foreign governmental activities that may
limit or disrupt markets, restrict payments or the movement of funds or result
in the deprivation of contract rights or expropriation of property. R&B Falcon
may also encounter difficulty in enforcing its contract rights in foreign
countries, particularly against state-owned oil companies. No prediction can be
made as to what foreign governmental regulations may be enacted in the future
that could be applicable to R&B Falcon.
 
     Fluctuations in the value of the currencies in which R&B Falcon conducts
its business relative to the U.S. dollar could cause currency translation losses
with respect to R&B Falcon's foreign operations. R&B Falcon cannot predict the
effect of exchange rate fluctuations upon future operating results.
 
RIG FLEET AGE
 
     The majority of R&B Falcon's rigs were built between 1978 and 1983. With
increasing age, the likelihood increases that a rig will require major repairs
in order to remain operational. These repairs may result in rigs being
unavailable for service from time to time, potentially reducing R&B Falcon's
revenues, and may require increasing amounts of capital.
 
                                       13
<PAGE>   23
 
GOVERNMENT REGULATION AND ENVIRONMENTAL MATTERS
 
     R&B Falcon's operations are subject to federal, state, local and foreign
laws and regulations controlling the discharge of materials into the environment
or otherwise relating to the protection of the environment, the safety of its
personnel and vessels and other matters. Environmental laws and regulations
could impose significant liability on R&B Falcon for damages, clean-up costs and
penalties in the event of the occurrence of oil spills or similar discharges of
pollutants in the course of R&B Falcon's operations, in certain circumstances
without regard to negligence or fault on R&B Falcon's part. Environmental and
other laws and regulations (and any new laws and regulations) may negatively
impact R&B Falcon by increasing R&B Falcon's costs of doing business and
discouraging R&B Falcon's clients from exploring for hydrocarbons, thus reducing
demand for R&B Falcon's services. R&B Falcon does not believe that environmental
regulations have had any material adverse effect on its capital expenditures,
results of operations or competitive position, and does not anticipate that any
material expenditures will be required to enable it to comply with existing laws
and regulations. Most of R&B Falcon's operations require its customers to obtain
governmental permits to conduct such operations, and delays or increased costs
in obtaining such permits could adversely affect R&B Falcon's results of
operations.
 
LIMITATION ON OWNERSHIP BY NON-U.S. CITIZENS
 
     R&B Falcon, as the owner of United States flag vessels engaging in
coastwise and foreign trade, is subject to the Shipping Act, 1916, which limits
the interest in R&B Falcon that may be acquired by non-U.S. citizens without the
consent of the U.S. Secretary of Transportation, acting through the United
States Maritime Administration ("MARAD"). If the foreign ownership limitation is
exceeded without MARAD's consent, MARAD would have the right to exercise various
remedies under the Shipping Act, 1916, including the seizure of vessels, civil
penalties and certain misdemeanor criminal penalties.
 
FIXED EXCHANGE RATIO
 
     Pursuant to the terms of the Merger Agreement, upon consummation of the
Merger, each outstanding share of Cliffs Drilling Common Stock will be converted
into the right to receive 1.7 shares of R&B Falcon Common Stock. The Merger
Agreement does not contain any provisions for adjustment of this conversion
ratio based upon fluctuations in the market price of the R&B Falcon Common Stock
or the Cliffs Drilling Common Stock. Accordingly, the value of the consideration
to be received by the holders of Cliffs Drilling Common Stock upon the
consummation of the Merger is not presently ascertainable and will depend upon
the market price of the R&B Falcon Common Stock at the Effective Time. On August
10, 1998, the last trading day prior to the public announcement of the Merger,
the closing prices of the R&B Falcon Common Stock and Cliffs Drilling Common
Stock on the NYSE were $15.31 and $19.38, respectively, which constituted a
ratio of 1 to 1.27. On September 11, 1998, the closing prices of the R&B Falcon
Common Stock and the Cliffs Drilling Common Stock on the NYSE were $13.13 and
$21.63, respectively, which constituted a ratio of 1 to 1.65. HOLDERS OF CLIFFS
DRILLING COMMON STOCK ARE URGED TO OBTAIN CURRENT MARKET QUOTATIONS PRIOR TO
MAKING ANY DECISIONS WITH RESPECT TO THE MERGER. The Merger Agreement does not
provide R&B Falcon or Cliffs Drilling the right to terminate the agreement based
upon fluctuations in the price of R&B Falcon Common Stock or Cliffs Drilling
Common Stock.
 
ANTI-TAKEOVER PROVISIONS
 
     Certain provisions of the R&B Falcon certificate of incorporation and
bylaws, the R&B Falcon Rights Plan and the DGCL could discourage potential
acquisition proposals and delay or prevent a change in control of R&B Falcon.
The provisions of the R&B Falcon certificate of incorporation and bylaws include
a classified Board of Directors, prohibit stockholder action by written consent,
prohibit R&B Falcon stockholders from calling special meetings of the R&B Falcon
Board and impose certain super-majority voting requirements on R&B Falcon
stockholders. In addition, the R&B Falcon Rights Plan will cause substantial
dilution to a person or group that attempts to acquire 15% or more of the
outstanding shares of the R&B Falcon Common Stock. Moreover, the R&B Falcon
Board, without further stockholder approval, may fix the rights and preferences
of one or more series of a class of preferred stock of R&B Falcon that could
have the effect of delaying, deterring
                                       14
<PAGE>   24
 
or preventing a change in control of R&B Falcon. R&B Falcon also is subject to
Section 203 of the DGCL which, subject to certain exceptions, prohibits a
Delaware corporation from engaging in a broad range of business combinations
with any "interested stockholder" for a period of three years following the date
that such stockholder became an interested stockholder. See "Comparison of
Rights of Stockholders -- Authorized Capital Stock" and "-- Rights Plans."
 
                                       15
<PAGE>   25
 
                      THE CLIFFS DRILLING SPECIAL MEETING
 
GENERAL
 
     This Proxy Statement/Prospectus is being furnished in connection with the
solicitation of proxies by the Cliffs Drilling Board for use at the Special
Meeting of Cliffs Drilling stockholders to be held on                     , 1998
at the time and place set forth in the accompanying notice and at any
adjournments thereof.
 
MATTER TO BE CONSIDERED
 
     At the Special Meeting, the stockholders of Cliffs Drilling will consider
and vote upon a proposal to approve the Merger Agreement and the Merger.
 
     THE CLIFFS DRILLING BOARD HAS UNANIMOUSLY APPROVED THE MERGER AGREEMENT AND
THE MERGER AND RECOMMENDS THAT CLIFFS DRILLING STOCKHOLDERS VOTE FOR APPROVAL OF
THE MERGER AGREEMENT AND THE MERGER. SEE "THE MERGER -- BACKGROUND OF THE
MERGER" AND "-- RECOMMENDATION OF CLIFFS DRILLING'S BOARD OF DIRECTORS; REASONS
FOR THE MERGER."
 
RECORD DATE; SHARES ENTITLED TO VOTE; QUORUM
 
     The Cliffs Drilling Board has fixed the close of business on October 16,
1998 as the Record Date for determining holders entitled to notice of and to
vote at the Special Meeting. As of the Record Date, there were           shares
of Cliffs Drilling Common Stock issued and outstanding, each of which entitles
its holder to one vote. The presence, either in person or by proxy, of the
holders of a majority of the issued and outstanding shares of Cliffs Drilling
Common Stock entitled to vote at the Special Meeting is necessary to constitute
a quorum for the transaction of business at the Special Meeting.
 
VOTES REQUIRED; VOTING AND REVOCATION OF PROXIES; EFFECT OF ABSTENTIONS AND
NON-VOTES
 
     Under the DGCL, the affirmative vote of the holders of at least a majority
of the outstanding shares of Cliffs Drilling Common Stock is required for
approval of the Merger Agreement and the Merger.
 
     All shares of Cliffs Drilling Common Stock represented by properly executed
proxies will, unless such proxies have been previously revoked, be voted in
accordance with the instructions indicated in such proxies. IF NO INSTRUCTIONS
ARE INDICATED, SUCH SHARES OF CLIFFS DRILLING COMMON STOCK WILL BE VOTED FOR
APPROVAL OF THE MERGER AGREEMENT AND THE MERGER. Cliffs Drilling does not know
of any matters other than approval of the Merger Agreement and the Merger that
are to come before the Special Meeting. If any other matter or matters are
properly presented for action at the Special Meeting, the persons named in the
enclosed form of proxy will have the discretion to vote on such matters in
accordance with their best judgment, unless such authorization is withheld. A
stockholder who has given a proxy may revoke it at any time prior to its
exercise by giving written notice of revocation to the Secretary of Cliffs
Drilling, by signing and returning a later dated proxy, or by voting in person
at the Special Meeting. However, mere attendance at the Special Meeting will not
in and of itself have the effect of revoking the proxy.
 
     Votes cast by proxy or in person at the Special Meeting will be tabulated
by the election inspectors appointed for the Special Meeting and will determine
whether or not a quorum is present. The election inspectors will treat
abstentions and broker non-votes on a returned proxy card as shares that are
present and entitled to vote for purposes of determining the presence of a
quorum but as unvoted for purposes of determining the approval of any matter
submitted to the stockholders for a vote. The failure to submit a proxy or to
vote at the Special Meeting will have the same effect as a vote against the
Merger Agreement and the Merger.
 
     THE MATTER TO BE CONSIDERED AT THE SPECIAL MEETING IS OF GREAT IMPORTANCE
TO THE STOCKHOLDERS OF CLIFFS DRILLING. ACCORDINGLY, CLIFFS DRILLING
STOCKHOLDERS ARE URGED TO READ AND CAREFULLY CONSIDER THE
                                       16
<PAGE>   26
 
INFORMATION PRESENTED IN THIS PROXY STATEMENT/PROSPECTUS, AND TO COMPLETE, DATE,
SIGN AND PROMPTLY RETURN THE ENCLOSED PROXY IN THE ENCLOSED POSTAGE-PAID
ENVELOPE.
 
SOLICITATION OF PROXIES
 
     Proxies will be solicited by mail, and may also be solicited personally, by
telephone, facsimile transmission or other means by the directors, officers and
employees of Cliffs Drilling, with no special or extra compensation therefor,
although such officers, directors and employees may be reimbursed for
out-of-pocket expenses incurred in connection with the solicitation. In
addition, Cliffs Drilling will retain Georgeson & Company Inc., New York, New
York, to aid in the solicitation for an estimated cost of $7,500 plus out-of-
pocket expenses. Arrangements will also be made with custodians, nominees and
fiduciaries for the forwarding of soliciting material to the beneficial owners
of Cliffs Drilling Common Stock held of record by such persons, and Cliffs
Drilling may reimburse such custodians, nominees and fiduciaries for reasonable
out-of-pocket expenses that they incur in that regard. Expenses incurred in
connection with the Merger, including those attributable to the solicitation of
proxies, will be paid by the party to the Merger Agreement incurring the
expense.
 
                                   THE MERGER
 
GENERAL DESCRIPTION OF THE MERGER
 
     General. The Merger Agreement provides that the Merger will be consummated
if the required approval of the Cliffs Drilling stockholders is obtained and all
other conditions to the Merger are satisfied or waived. Upon consummation of the
Merger, Sub will be merged with and into Cliffs Drilling, and Cliffs Drilling
will become a wholly owned subsidiary of R&B Falcon. Cliffs Drilling shall
continue as the Surviving Corporation and shall succeed to and assume all of the
rights and obligations of Cliffs Drilling and Sub.
 
     Effective Time. On the Closing Date, or as soon as practicable thereafter,
Cliffs Drilling and Sub will cause a Certificate of Merger to be filed with the
Secretary of State of the State of Delaware. The Merger will become effective
upon the filing of the Certificate of Merger with the Secretary of State of the
State of Delaware or at such other time specified in the Certificate of Merger
as the Effective Time.
 
     Certificate of Incorporation and Bylaws. Pursuant to the Merger Agreement,
the certificate of incorporation and the bylaws of Cliffs Drilling as in effect
immediately prior to the Effective Time shall be the certificate of
incorporation and bylaws of the Surviving Corporation.
 
     Directors and Officers. Paul B. Loyd, Jr., Steven A. Webster, and Douglas
E. Swanson shall be the directors of the Surviving Corporation, and the officers
of Cliffs Drilling immediately prior to the Effective Time shall be the officers
of the Surviving Corporation. Such directors and officers shall hold office in
accordance with the certificate of incorporation and bylaws of the Surviving
Corporation until their respective successors are duly elected or appointed and
qualified.
 
     Conversion of Cliffs Drilling Common Stock and the Stock of Sub in the
Merger. At the Effective Time, each share of Cliffs Drilling Common Stock issued
and outstanding immediately prior to the Effective Time, with certain exceptions
as set forth in the Merger Agreement, will be converted into the right to
receive 1.7 shares of R&B Falcon Common Stock. Each share of R&B Falcon Common
Stock issued in connection with the Merger will have associated therewith one
R&B Falcon Right, and the Cliffs Drilling Rights that are currently associated
with outstanding shares of Cliffs Drilling Common Stock will, pursuant to
operation of the Cliffs Drilling Rights Plan, as amended, cease to exist upon
consummation of the Merger. Each share of Cliffs Drilling Common Stock held in
the treasury of Cliffs Drilling immediately prior to the Effective Time will be
canceled and extinguished at the Effective Time without any conversion thereof
and no payment shall be made with respect thereto. Each share of common stock,
par value $0.01 per share, of Sub issued and outstanding immediately prior to
the Effective Time shall at the Effective Time be converted into one validly
issued, fully paid and nonassessable share of common stock of the Surviving
Corporation. R&B Falcon will
 
                                       17
<PAGE>   27
 
issue an aggregate of up to 28,212,564 shares of R&B Falcon Common Stock in
connection with the consummation of the Merger. Based upon the capitalization of
R&B Falcon and Cliffs Drilling as of                     , 1998, the
stockholders of Cliffs Drilling will own approximately 14% of the outstanding
R&B Falcon Common Stock following consummation of the Merger.
 
     Fractional Shares. No certificates representing fractional shares of R&B
Falcon Common Stock will be issued in connection with the Merger. In lieu of any
such fractional share, each Cliffs Drilling stockholder who would otherwise be
entitled to receive a fractional share of R&B Falcon Common Stock will be paid
an amount in cash equal to the value of such fractional share of R&B Falcon
Common Stock based upon the closing price of one share of R&B Falcon Common
Stock on the NYSE on the last trading day prior to the Effective Time. No
interest shall be paid on such amount.
 
BACKGROUND OF THE MERGER
 
     Cliffs Drilling has grown substantially during the last several years
through a process of selected acquisitions and internal development designed to
take advantage of consolidation in the contract drilling industry. As part of
its growth strategy, Cliffs Drilling has sought to identify business
opportunities that would expand its asset base, increase profitability and
enhance stockholder value. From time to time, but particularly within the most
recent six months, Cliffs Drilling has been approached by other drilling
contractors to consider some form of business combination. In mid-March, because
of strong interest expressed by other drilling contractors and particularly R&B
Falcon, Cliffs Drilling focused its attention on evaluating business combination
opportunities which might satisfy its growth criteria and be beneficial to its
stockholders.
 
     At the request of R&B Falcon's investment banker, Douglas E. Swanson,
Chairman of the Board, President and Chief Executive Officer of Cliffs Drilling,
met with Steven A. Webster, President, Chief Executive Officer and a director of
R&B Falcon, on March 17, 1998, during which meeting Mr. Webster expressed his
interest in the possible acquisition by R&B Falcon of Cliffs Drilling. Within
weeks of this meeting, two other companies engaged in the contract drilling
business made unsolicited contacts with Mr. Swanson regarding a possible
business combination with Cliffs Drilling.
 
     Several discussions were held with one of these companies, and at the
regularly scheduled meeting of the Cliffs Drilling Board on May 13, 1998,
Jefferies, an investment banking firm regularly retained in connection with
previous acquisitions by Cliffs Drilling, presented its analysis of a potential
business combination with this company. The Cliffs Drilling Board concluded that
under certain conditions, Cliffs Drilling would be interested in pursuing a
business combination with this company and requested that a representative of
Jefferies submit to this company the conditions upon which further discussions
would be pursued. Jefferies advised the other company of these conditions and
was subsequently advised that these conditions were not acceptable.
 
     During the next two months, Jefferies was active in analyzing alternatives
regarding a possible business combination with these three contract drilling
companies. During June and early July, Mr. Swanson had several meetings with two
of the companies regarding a potential business combination. No meetings or
discussions were conducted between Cliffs Drilling management and R&B Falcon
from March 17, 1998 until August 4, 1998. At the regularly scheduled meeting of
the Cliffs Drilling Board on July 28, 1998, Jefferies presented its analysis of
the terms of a potential business combination with each of the three contract
drilling companies with which there had been discussions. The Cliffs Drilling
Board formally engaged Jefferies to assist in the evaluation of two potential
transactions involving Cliffs Drilling, one of which was with R&B Falcon, and to
explore whether such transactions would merit further consideration by the
Cliffs Drilling Board. The Cliffs Drilling Board also instructed Jefferies to
reject the third potential transaction, which involved the company previously
considered by the Cliffs Drilling Board on May 13, 1998.
 
     On August 4, 1998, Mr. Swanson again met with Mr. Webster to discuss a
potential business combination between Cliffs Drilling and R&B Falcon. No
specific merger terms were discussed at this meeting. Later that day, Mr.
Swanson and a representative of Jefferies met with the other contract drilling
company to discuss the terms of a potential business combination, including
among others, the implied premium resulting from the proposed exchange ratio,
board representation, breakup fees, employment
                                       18
<PAGE>   28
 
agreements, stock option grants and change of control payments to executive
officers. A change of control payment to Mr. Swanson in the amount of $4.5
million had previously been offered by this company, and at this meeting, Mr.
Swanson and a representative of Jefferies negotiated change of control payments
for the six other executive officers of Cliffs Drilling. Basic agreement was
reached on all principal terms except for the exchange ratio, which Mr. Swanson
indicated, if as then proposed, would likely be unacceptable to the Cliffs
Drilling Board.
 
     From August 4, 1998 through August 7, 1998, representatives of Cliffs
Drilling and R&B Falcon participated in various discussions in which the terms
of the proposed transaction were negotiated. At the same time, discussions
between representatives of Cliffs Drilling and the other company were ongoing.
Mr. Swanson informally advised the members of the Cliffs Drilling Board of the
nature and substance of these negotiations and obtained the advice and opinions
of certain of the directors concerning the terms and conditions of each
proposal. During this period, Cliffs Drilling and R&B Falcon exchanged certain
business and financial information, subject to a confidentiality agreement, for
purposes of analysis in order to confirm their initial interest in the proposed
business combination between the parties.
 
     On August 7, 1998, Jefferies was advised by the other contract drilling
company that it would not increase its proposed exchange ratio. On the same day,
R&B Falcon made a proposal to Jefferies which provided the same or better terms
than those proposed by the other company with respect to, among others, the
implied premium resulting from the proposed exchange ratio, board
representation, breakup fees, employment agreements, stock option grants and
change of control payments to executive officers. Specifically, the implied
premium resulting from the exchange ratio offered by R&B Falcon was
significantly higher than that proposed by the other company, the proposed
breakup fee offered by R&B Falcon was significantly lower than that proposed by
the other company, and the R&B Falcon proposal allowed Cliffs Drilling
representation on the R&B Falcon Board. See "The Merger -- Opinion of Cliffs
Drilling's Financial Advisor." Further, while R&B Falcon agreed to match the
change of control payments to Cliffs Drilling executive officers that had been
offered by the other company, R&B Falcon required as a condition to the Merger
that such payments be made by Cliffs Drilling. See "The Merger -- Interests of
Certain Persons in the Merger."
 
     As a result of these negotiations, on August 7, 1998, Mr. Swanson and Mr.
Webster reached an agreement in principle concerning the terms of the proposed
merger. Representatives of Cliffs Drilling and its legal and financial advisors
and representatives of R&B Falcon and its legal and financial advisors met on
August 8, 1998 to review and analyze certain business and financial information
regarding the two companies in light of the proposed transaction.
 
     On August 10, 1998, Mr. Swanson convened a special meeting of the Cliffs
Drilling Board. At the meeting, Mr. Swanson advised the Cliffs Drilling Board of
his negotiations concerning a potential business combination and sought
authority to enter into a non-binding letter of intent providing for the
acquisition of Cliffs Drilling by R&B Falcon by way of a merger that would
qualify as a tax-free reorganization. Jefferies presented to the Cliffs Drilling
Board its substantive analysis of the benefits of a business combination between
Cliffs Drilling and R&B Falcon, as well as an alternative business combination
between Cliffs Drilling and the other company. The directors discussed and
considered whether a "collar" on the prices of Cliffs Drilling Common Stock
and/or R&B Falcon Common Stock would be beneficial for the stockholders.
However, the Cliffs Drilling Board concluded, based on factors explained by, and
the advice of, Jefferies, that the interests of the stockholders of Cliffs
Drilling would be best served without imposing a collar. At the conclusion of
the special meeting, the Cliffs Drilling Board unanimously approved the
execution of a letter of intent by Cliffs Drilling and the negotiation of a
definitive agreement with R&B Falcon on the terms outlined by Mr. Swanson.
 
     On August 10, 1998, the R&B Falcon Board held a special meeting at which
Mr. Webster advised the R&B Falcon Board of his negotiations concerning a
potential business combination with Cliffs Drilling and sought authority to
enter into a non-binding letter of intent providing for the acquisition of
Cliffs Drilling by R&B Falcon by way of a merger. R&B Falcon's financial
advisors also presented to the R&B Falcon Board their analysis of the potential
benefits of a business combination between Cliffs Drilling and R&B Falcon. At
the conclusion of the special meeting, the R&B Falcon Board approved the
execution of a letter of intent by
 
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<PAGE>   29
 
R&B Falcon and the negotiation of a definitive agreement with Cliffs Drilling on
the terms outlined by Mr. Webster.
 
     On the evening of August 10, 1998, Cliffs Drilling and R&B Falcon executed
a letter of intent and issued a press release concerning the proposed Merger.
Thereafter, each of Cliffs Drilling and R&B Falcon conducted further due
diligence regarding the business and properties of the other, including a review
of financial and tax information, markets, contracts, commitments, employee
benefit plans and contingent liabilities. During this period, the parties also
negotiated the terms of the Merger Agreement.
 
     The Cliffs Drilling Board convened again on August 20, 1998 and considered
further the advantages and disadvantages of the proposed Merger before entering
into the Merger Agreement. All directors were given opportunities for comments,
questions and discussion of alternatives. Jefferies made a detailed presentation
at the special meeting covering the businesses, markets, and operations of
Cliffs Drilling and R&B Falcon, an analysis of potential combination benefits,
an analysis of the transaction value under the proposed acquisition structure,
and a comparative analysis of various public market trading multiples of
companies deemed comparable to Cliffs Drilling, various acquisition multiples of
transactions deemed comparable to the Merger, and the proposed acquisition
multiples for Cliffs Drilling. Further, Jefferies presented to the Cliffs
Drilling Board a pro forma financial and business review of Cliffs Drilling and
R&B Falcon on a combined basis. Jefferies delivered its verbal opinion (which
was confirmed in writing) to the Cliffs Drilling Board that the proposed Merger
was fair, from a financial point of view, to the holders of Cliffs Drilling
Common Stock. Representatives of Griggs & Harrison, P.C. summarized certain
terms of the Merger Agreement and the fiduciary duties of the Cliffs Drilling
Board in connection therewith. Subsequently, the members of the Cliffs Drilling
Board, excluding Mr. Swanson, met in executive session with representatives of
Jefferies and with representatives of Griggs & Harrison, P.C. to review the
transaction and consider the interests of management with respect to the
transaction. Mr. Swanson returned to the meeting, and after full discussion, the
Cliffs Drilling Board approved the Merger Agreement and the transactions
contemplated thereby (with Mr. Swanson abstaining as to matters pertaining to
him individually) and unanimously recommended approval of the Merger and the
Merger Agreement by the holders of Cliffs Drilling Common Stock.
 
     The R&B Falcon Board convened again on August 21, 1998 and considered
further the advantages and disadvantages of the proposed Merger. The directors
were informed of and considered the results of the additional due diligence that
had been conducted and the material terms of the Merger Agreement. R&B Falcon's
financial advisors made a presentation to the R&B Falcon Board regarding the
proposed Merger and delivered their opinion that the proposed Merger was fair,
from a financial point of view, to the stockholders of R&B Falcon. After full
discussion, the R&B Falcon Board approved the Merger Agreement and the
transactions contemplated thereby.
 
     The Merger Agreement was signed and publicly announced on the afternoon of
August 21, 1998.
 
RECOMMENDATION OF CLIFFS DRILLING'S BOARD OF DIRECTORS; REASONS FOR THE MERGER
 
     The Cliffs Drilling Board believes that the terms of the Merger Agreement
and the transactions contemplated thereby are fair to and in the best interests
of Cliffs Drilling and its stockholders. The Cliffs Drilling Board believes that
the Merger meets its strategic growth objectives to expand its asset base,
increase profitability and enhance stockholder value. The Cliffs Drilling Board
further believes that the Merger will create a larger, more diversified drilling
company that will be able to compete more effectively in the areas in which it
operates. Accordingly, the Cliffs Drilling Board has unanimously approved the
Merger Agreement and unanimously recommends its approval and adoption by Cliffs
Drilling's stockholders.
 
     The Cliffs Drilling Board consulted with Cliffs Drilling's management, as
well as its legal counsel and financial advisors, and considered a number of
synergystic opportunities and strategic benefits expected to be realized by
Cliffs Drilling as a result of the Merger, including the following:
 
     - ability to reduce dependence on shallow water markets;
 
     - ability to reduce exposure to business cycles in the Gulf of Mexico and
       Venezuela;
 
                                       20
<PAGE>   30
 
     - greater geographical and equipment diversification;
 
     - greater access to equipment for international expansion;
 
     - access to existing infrastructure for expansion of well engineering and
       integrated services;
 
     - enhanced rig engineering and project management expertise; and
 
     - greater access to capital at a reduced cost.
 
     The Cliffs Drilling Board also considered the benefits currently
anticipated to be realized by the holders of Cliffs Drilling Common Stock as a
result of the Merger, including the following:
 
     - the opportunity to receive a premium over the market price immediately
       prior to announcement of the Merger for Cliffs Drilling Common Stock;
 
     - Merger Consideration consisting of R&B Falcon Common Stock which, based
       on historical information, has traded at higher earnings multiples, is
       more widely followed by the investment community, is less volatile, and
       provides greater liquidity, than Cliffs Drilling Common Stock; and
 
     - the opportunity to receive R&B Falcon Common Stock in a transaction that
       is intended to be non-taxable for federal income tax purposes.
 
     In reaching its decision to approve the Merger and the Merger Agreement,
the Cliffs Drilling Board also considered, among others, the following factors:
 
     - information concerning the financial performance and condition, business
       operations and prospects of each of Cliffs Drilling and R&B Falcon;
 
     - the recent historical performance of Cliffs Drilling Common Stock and R&B
       Falcon Common Stock;
 
     - current industry, economic and market conditions, which have encouraged
       business combinations and other strategic alliances in the oil and gas
       service industry;
 
     - the background and experience of R&B Falcon's management team;
 
     - the structure of the transaction and the terms of the Merger Agreement;
 
     - the premium offered with respect to the Cliffs Drilling Common Stock in
       the proposed Merger and a comparison of the valuation multiples implied
       in the exchange ratio to that of the other comparable publicly traded
       energy service companies and comparable transactions;
 
     - the financial analysis and Fairness Opinion of Jefferies described below,
       including Jefferies' conclusion that the consideration to be received in
       the Merger is fair, from a financial point of view, to the holders of
       Cliffs Drilling Common Stock; and
 
     - the ability of the Cliffs Drilling Board to entertain superior
       unsolicited alternative proposals, negotiate and give information to
       third parties and, subject to the payment to R&B Falcon of a $15 million
       termination fee and, under certain circumstances, a $30 million fee
       (against which Cliffs Drilling will be entitled to a credit for any
       termination fee previously paid to R&B Falcon), terminate the Merger
       Agreement if the Cliffs Drilling Board determines that any such action is
       necessary in order for the Cliffs Drilling Board to act in a manner
       consistent with its fiduciary obligations under applicable law.
 
     In view of the variety of factors considered in connection with its
evaluation of the Merger, the Cliffs Drilling Board considered the foregoing
factors as a whole and did not find it practicable or necessary to and did not
quantify or otherwise assign relative weights to the specific factors considered
in reaching its determination. In addition, individual members of the Cliffs
Drilling Board may have given different weights to different factors.
 
                                       21
<PAGE>   31
 
OPINION OF CLIFFS DRILLING'S FINANCIAL ADVISOR
 
     Cliffs Drilling retained Jefferies to act as Cliffs Drilling's financial
advisor in connection with the Merger. The Cliffs Drilling Board instructed
Jefferies, in its role as financial advisor, to evaluate the fairness, from a
financial point of view, of the Merger to Cliffs Drilling stockholders and, in
such regard, to conduct such investigations as Jefferies deemed appropriate for
such purpose. No limitations were imposed upon Jefferies with respect to the
investigations made or procedures followed by it in rendering its opinion.
 
     On August 20, 1998, Jefferies delivered its oral opinion to the Cliffs
Drilling Board (which was subsequently confirmed in writing) that, as of such
date and subject to certain considerations set forth in the written opinion, the
consideration to be received by the holders of shares of Cliffs Drilling Common
Stock pursuant to the Merger Agreement was fair from a financial point of view
to such holders.
 
     THE FULL TEXT OF THE FAIRNESS OPINION DATED AUGUST 20, 1998, WHICH SETS
FORTH, AMONG OTHER THINGS, ASSUMPTIONS MADE, PROCEDURES FOLLOWED, MATTERS
CONSIDERED, AND LIMITATIONS ON THE REVIEW UNDERTAKEN, IS ATTACHED AS APPENDIX B
TO THIS PROXY STATEMENT/PROSPECTUS. CLIFFS DRILLING STOCKHOLDERS ARE URGED TO,
AND SHOULD, READ THE FAIRNESS OPINION CAREFULLY AND IN ITS ENTIRETY. THE
FAIRNESS OPINION WAS PROVIDED TO THE CLIFFS DRILLING BOARD AND IS DIRECTED ONLY
TO THE FAIRNESS, FROM A FINANCIAL POINT OF VIEW, OF THE MERGER CONSIDERATION TO
BE RECEIVED BY THE HOLDERS OF SHARES OF CLIFFS DRILLING COMMON STOCK PURSUANT TO
THE MERGER AGREEMENT, AND IT DOES NOT ADDRESS ANY OTHER ASPECT OF THE MERGER.
THE SUMMARY OF THE FAIRNESS OPINION SET FORTH IN THE PROXY STATEMENT/PROSPECTUS
IS QUALIFIED IN ITS ENTIRETY BY REFERENCE TO THE FULL TEXT OF SUCH OPINION.
 
     In connection with rendering the Fairness Opinion, Jefferies, among other
things: (i) reviewed certain publicly available financial statements and other
information (including operating and construction project information provided
by R&B Falcon) of R&B Falcon; (ii) reviewed certain publicly available and
internal financial statements and other financial and operating data concerning
Cliffs Drilling prepared by the management of Cliffs Drilling; (iii) analyzed
certain financial projections prepared by the management of Cliffs Drilling;
(iv) discussed the past and current operations and financial condition and the
prospects of Cliffs Drilling and R&B Falcon with senior executives of Cliffs
Drilling and R&B Falcon; (v) compared the financial performance of Cliffs
Drilling and R&B Falcon with that of certain other comparable publicly traded
companies; (vi) reviewed the pro forma impact of the Merger on R&B Falcon's
earnings per share, cash flow, consolidated capitalization and financial ratios;
(vii) reviewed the financial terms, to the extent publicly available, of certain
comparable acquisition transactions; (viii) compared the financial performance
of Cliffs Drilling and R&B Falcon and the prices and trading activity of the R&B
Falcon Common Stock with that of certain other comparable publicly traded
companies and their securities; (ix) participated in discussions and
negotiations among representatives of Cliffs Drilling and R&B Falcon and their
financial and legal advisors; (x) reviewed the Merger Agreement and certain
related documents; and (xi) performed such other analyses and considered such
other factors as Jefferies deemed appropriate.
 
     In rendering the Fairness Opinion, Jefferies assumed and relied upon,
without independent verification, the accuracy and completeness of the
representations and warranties made by R&B Falcon and Cliffs Drilling in the
Merger Agreement, as well as all of the financial and other information publicly
available or provided to it by R&B Falcon's and Cliffs Drilling's management,
including without limitation, information with respect to the condition of
assets and material contract terms. Jefferies assumed that all financial
projections had been reasonably prepared on bases reflecting the best currently
available estimates and judgments of the future financial performance of Cliffs
Drilling and R&B Falcon. Jefferies did not make any independent valuation or
appraisal of the assets or liabilities of Cliffs Drilling or R&B Falcon, nor was
Jefferies furnished with any such appraisals. In addition, Jefferies assumed the
Merger would be consummated in accordance with the terms set forth in the Merger
Agreement. The Fairness Opinion is necessarily based on economic, market and
other conditions as in effect on, and the information made available to
Jefferies as of, the date of the Fairness Opinion.
 
     The following is a brief summary of the financial analyses performed by
Jefferies and reviewed with the Cliffs Drilling Board on August 20, 1998 in
connection with the preparation of the Fairness Opinion and with its
presentation to the Cliffs Drilling Board on such date.
                                       22
<PAGE>   32
 
     Historical Market Price Ratio Analysis. Jefferies analyzed the historical
ratios between the market prices for Cliffs Drilling Common Stock and R&B Falcon
Common Stock during the six months prior to the announcement date of the Merger,
from February 9 to August 10, 1998. Jefferies observed that the exchange ratio
of 1.70 is higher than the historical ratio between Cliffs Drilling Common Stock
and R&B Falcon Common Stock based on the closing sale prices on any trading day
in the period. Jefferies also observed that for selected time periods, including
the one, two, three and six month periods prior to the announcement of the
Merger, the average ratios between Cliffs Drilling Common Stock and R&B Falcon
Common Stock were 1.28, 1.38, 1.43 and 1.44, respectively, and the ratio on the
day prior to the announcement of the Merger, based on closing prices for Cliffs
Drilling and R&B Falcon on August 10, 1998, was 1.27.
 
     Premium Analysis. Jefferies analyzed implied share price premiums announced
or paid in selected negotiated transactions announced or completed in the oil
service industry since January 1, 1996. This analysis indicated that the average
premiums to the targets' share prices for the one day and one week periods prior
to announcement of the transactions were 23% and 24%, respectively, during this
period. Jefferies observed that an implied proposal price of $26.03 per Cliffs
Drilling share (the "Implied Price"), based upon the exchange ratio of 1.7
shares of R&B Falcon Common Stock for each share of Cliffs Drilling Common Stock
and R&B Falcon's closing price of $15.31 per share on August 10, 1998, implied
premiums to the share price of Cliffs Drilling Common Stock for the one day and
one week prior to August 11, 1998 of 34% and 31%, respectively, which are
significantly higher than the average premium for comparable transactions.
 
     Pro Forma Analysis of the Merger. Jefferies analyzed certain pro forma
financial effects of the Merger assuming that the Merger was treated as a
purchase transaction. Jefferies observed that, assuming $10.0 million of
operating synergies and cost savings, the issuance of R&B Falcon Common Stock in
the Merger would have an accretive effect on pro forma earnings per share to R&B
Falcon of approximately 9.8% for the year ended December 31, 1998 and
approximately 4.8% for the year ended December 31, 1999. In addition, the Merger
would have an accretive effect on pro forma cash flow per share to R&B Falcon of
approximately 13.5% for the year ended December 31, 1998 and approximately 7.4%
for the year ended December 31, 1999.
 
     Comparable Company Analysis. Comparable company analysis examines a
company's trading characteristics relative to a group of publicly traded peers.
Jefferies analyzed the trading characteristics of offshore drilling companies
including Atwood Oceanics, Inc., Diamond Offshore Drilling, Inc., ENSCO
International Incorporated, Global Marine Inc., Marine Drilling Companies, Inc.,
Noble Drilling Corporation, Parker Drilling Company, Pride International, Inc.
Rowan Companies, Inc., Santa Fe International Corporation and Transocean
Offshore Inc. (collectively the "Offshore Drilling Comparables"). Historical
financial information used in connection with the ratios provided below with
respect to the Offshore Drilling Comparables was as of the most recent financial
statements publicly available for each company. Market information used in
calculating the ratios was as of August 10, 1998, unless otherwise noted.
Earnings per share ("EPS"), cash flow per share ("CFPS") and earnings before
interest, taxes, depreciation and amortization ("EBITDA") estimates for Cliffs
Drilling, R&B Falcon and for the Offshore Drilling Comparables were obtained
from publicly available research analyst estimates.
 
     Jefferies analyzed the relative performance and value for Cliffs Drilling
and R&B Falcon compared to the Offshore Drilling Comparables. Among the market
trading information considered in the valuation analysis were the ratios of
market price to EPS estimates and market price to CFPS estimates for 1998 and
1999. This analysis indicated that (i) the ratios of market price to 1998 and
1999 EPS estimates for Cliffs Drilling were 5.5x and 4.3x, respectively, and the
ratios of market price to 1998 and 1999 EPS estimates for R&B Falcon were 11.0x
and 6.6x, respectively, (ii) the median ratios of market price to 1998 and 1999
EPS estimates for the Offshore Drilling Comparables were 10.2x and 7.6x,
respectively, (iii) the ratios of market price to 1998 and 1999 CFPS estimates
for Cliffs Drilling were 3.7x and 3.0x, respectively, and the ratios of market
price to 1998 and 1999 CFPS estimates for R&B Falcon were 8.0x and 4.7x,
respectively, and (v) the median ratios of market price to 1998 and 1999 CFPS
estimates for the Offshore Drilling Comparables were 6.3x and 4.8x,
respectively. Jefferies observed that the implied ratios derived from the
Implied Price to 1998 and 1999 estimates of EPS for Cliffs Drilling were 7.6x
and 6.0x, respectively. Jefferies also observed that the implied ratios derived
from the Implied Price to 1998 and 1999 estimates of CFPS for Cliffs Drilling
were 5.1x and 4.2x, respectively. In addition, Jefferies considered in the
valuation analysis the ratios of Total Enterprise
                                       23
<PAGE>   33
 
Value to estimated EBITDA for 1998 and 1999. For the purpose of this analysis,
Total Enterprise Value is defined as the total market value of common and
preferred equity, less the book value of total outstanding financial debt, plus
cash and cash equivalents. This analysis indicated that (i) the ratios of Total
Enterprise Value to 1998 and 1999 EBITDA estimates for Cliffs Drilling were 3.4x
and 2.9, respectively, and the ratios of Total Enterprise Value to 1998 and 1999
EBITDA estimates for R&B Falcon were 7.0x and 4.3x, respectively and (ii) the
median ratios of Total Enterprise Value to 1998 and 1999 EBITDA estimates for
the Offshore Drilling Comparables were 6.1x and 4.5x, respectively.
 
     Jefferies observed that as of August 10, 1998, Cliffs Drilling Common Stock
traded at multiples lower than those of the Offshore Drilling Comparables, while
R&B Falcon Common Stock generally traded at multiples in line with those of the
Offshore Drilling Comparables. Jefferies attributes Cliffs Drilling's lower
trading multiples relative to R&B Falcon and the Offshore Drilling Comparables
to Cliffs Drilling's relatively smaller size and the concentration of its
operations in the volatile Gulf of Mexico and Venezuela drilling markets.
 
     None of the Offshore Drilling Comparables is identical to Cliffs Drilling
or R&B Falcon. In evaluating the Offshore Drilling Comparables, Jefferies made
judgments and assumptions with regard to industry performance, general business,
economic, market and financial conditions and other matters, many of which are
beyond the control of Cliffs Drilling or R&B Falcon, such as the impact of
competition on the business of Cliffs Drilling and R&B Falcon and the industry
generally, industry growth and the absence of any material adverse change in the
financial condition and prospects of Cliffs Drilling or R&B Falcon or the
industry or in the financial markets in general. Due to the inherent differences
between the operations of Cliffs Drilling or R&B Falcon and the Offshore
Drilling Comparables, a purely quantitative mathematical analysis (such as
determining the average or median) is not in itself a meaningful method of using
comparable company data.
 
     Pro Forma Trading Analysis. Jefferies analyzed the implied equity value per
share to Cliffs Drilling's stockholders and to R&B Falcon's stockholders by
applying the median trading multiples, including market price to EPS estimates,
market price to CFPS estimates and Total Enterprise Value to EBITDA estimates
for 1998 and 1999, as of August 10, 1998, of offshore drilling companies with a
market capitalization greater than $2 billion (the "Large-Cap Peers"), to the
pro forma earnings, cash flow and EBITDA of the combined company for 1998 and
1999. The Large-Cap Peers include Diamond Offshore Drilling, Inc., Global Marine
Inc., Noble Drilling Corporation, R&B Falcon, Santa Fe International Corporation
and Transocean Offshore Inc. Jefferies observed that the implied equity value to
Cliffs Drilling stockholders and to R&B Falcon stockholders based on the pro
forma trading analysis and Merger Consideration was $32.40 per share and $19.06
per share, respectively, representing a 60.0% and 15.1% premium, respectively,
to the market value per share of Cliffs Drilling Common Stock and R&B Falcon
Common Stock as of August 10, 1998.
 
     The preparation of a fairness opinion is a complex process and is not
necessarily susceptible to a partial analysis or summary description. In
arriving at its opinion, Jefferies considered the results of all its analyses as
a whole and did not attribute any particular weight to any analysis or factor
considered by it. Jefferies believes that selecting any portion of its analyses,
without considering all analyses, would create an incomplete view of the process
underlying the Fairness Opinion. In addition, Jefferies may deem various
assumptions more or less probable than other assumptions, so that the ranges of
valuations resulting from any particular analysis described above should not be
taken to be Jefferies' view of the actual value of Cliffs Drilling.
 
     In performing its analyses, Jefferies made numerous assumptions with
respect to industry performance, general business and economic conditions and
other matters, many of which are beyond the control of Cliffs Drilling and R&B
Falcon. The analyses performed by Jefferies are not necessarily indicative of
actual values, which may be significantly more or less favorable than suggested
by such analyses. Such analyses were prepared solely as part of Jefferies'
analysis of the fairness, from a financial point of view, of the consideration
to be received by the holders of shares of Cliffs Drilling Common Stock pursuant
to the Merger Agreement and were conducted in connection with the delivery of
the Fairness Opinion. The analyses do not purport to be appraisals or to reflect
the prices at which Cliffs Drilling might actually be sold. Analyses based upon
projections of future results are not necessarily indicative of actual future
results, which may be significantly different from the results suggested by such
analyses. Because such analyses are inherently subject to uncertainty, being
based upon numerous factors or events beyond the control of the parties or their
respective
 
                                       24
<PAGE>   34
 
advisors, none of R&B Falcon, Cliffs Drilling, Jefferies or any other person
assumes any responsibility if future results are materially different from those
projected.
 
     As described above, the Fairness Opinion and the information provided by
Jefferies to the Cliffs Drilling Board were two of a number of factors taken
into consideration by the Cliffs Drilling Board in making its determination to
recommend approval of the Merger. Consequently, the Jefferies analyses described
above should not be viewed as determinative of the opinion of the entire Cliffs
Drilling Board or the view of the management with respect to the value of Cliffs
Drilling. The consideration to be received by the holders of shares of Cliffs
Drilling Common Stock pursuant to the Merger Agreement was determined through
negotiations between Cliffs Drilling and its advisors and R&B Falcon, and was
approved by the entire Cliffs Drilling Board.
 
     The Cliffs Drilling Board retained Jefferies based upon its experience and
expertise as financial advisors in the oil service industry and its familiarity
with Cliffs Drilling and its business. Jefferies is an internationally
recognized investment banking and advisory firm. As part of its investment
banking business, Jefferies is regularly engaged in the valuation of businesses
and securities in connection with mergers and acquisitions, negotiated
underwritings, competitive biddings, secondary distributions of listed and
unlisted securities, private placements and valuation for estate, corporate and
other purposes. Jefferies makes a market in Cliffs Drilling Common Stock. In the
ordinary course of its business, Jefferies and its affiliates may actively trade
the debt and equity securities and senior loans of R&B Falcon and Cliffs
Drilling for their own account and for the accounts of customers and,
accordingly may at times hold a long or short position in such securities. In
the past, Jefferies has provided financing services to R&B Falcon and Cliffs
Drilling for which services Jefferies received customary fees.
 
     Pursuant to an engagement letter dated August 10, 1998, Cliffs Drilling has
agreed to pay Jefferies (i) a fee, payable upon consummation of the Merger,
equal to 0.4% of the transaction value, defined as the total consideration to be
paid to or received by Cliffs Drilling or its stockholders in connection with
the Merger, including all indebtedness of Cliffs Drilling, whether assumed,
refinanced or extinguished, plus (ii) a fee of $350,000 upon rendering the
Fairness Opinion. In addition, Cliffs Drilling has agreed, among other things,
to reimburse Jefferies for all travel, legal and other expenses incurred in
connection with the services provided by Jefferies, and to indemnify and hold
harmless Jefferies and certain related parties from and against certain
liabilities and expenses, which may include certain liabilities under the
federal securities laws, in connection with its engagement.
 
ACCOUNTING TREATMENT OF THE MERGER
 
     R&B Falcon intends to account for the Merger under the purchase method of
accounting in accordance with Accounting Principles Board Opinion No. 16. Under
this method of accounting, the cost of acquiring all outstanding shares of
Cliffs Drilling Common Stock and the assumption of all outstanding Cliffs
Drilling stock options will be determined by the value of R&B Falcon Common
Stock (and cash in lieu of fractional shares) to be issued to holders of Cliffs
Drilling Common Stock and Cliffs Drilling stock options, plus the direct costs
associated with the Merger. R&B Falcon will allocate such costs in establishing
new accounting and reporting bases for the underlying acquired assets and
liabilities based on their estimated fair values at the Effective Time.
 
CERTAIN FEDERAL INCOME TAX CONSEQUENCES
 
     The following discussion is a general summary of certain federal income tax
consequences of the Merger. This discussion is based upon provisions of the
Internal Revenue Code of 1986, as amended (the "Code"), existing regulations
promulgated thereunder, judicial authorities and current rulings and
administrative practice of the U.S. Internal Revenue Service (the "Service"), in
each case as in effect as of the date hereof and all of which are subject to
change at any time, possibly with retroactive effect. For purposes of this
discussion, it is assumed that shares of Cliffs Drilling Common Stock are held
as "capital assets" within the meaning of Section 1221 of the Code (i.e.,
property held for investment). This discussion does not address all aspects of
federal income taxation that might be relevant to particular holders of Cliffs
Drilling Common
 
                                       25
<PAGE>   35
 
Stock in light of their status or personal investment circumstances; nor does it
discuss the consequences to such holders who are subject to special treatment
under the federal income tax laws such as foreign persons, dealers in
securities, regulated investment companies, life insurance companies, other
financial institutions, tax-exempt organizations, pass-through entities,
taxpayers who hold Cliffs Drilling Common Stock as part of a "straddle,"
"hedge", or "conversion transaction" or who have a "functional currency" other
than the United States dollar or to persons who have received their Cliffs
Drilling Common Stock as compensation. Further, this discussion does not address
the state, local or foreign tax consequences of the Merger. Holders of Cliffs
Drilling Common Stock are advised to consult their own tax advisers regarding
the federal income tax consequences of the Merger in light of their personal
circumstances and the consequences under state, local and foreign tax laws.
 
     The Merger is intended to qualify as a reorganization under Section 368(a)
of the Code. It is a condition to the obligation of Cliffs Drilling to
consummate the Merger that Cliffs Drilling shall have received from legal
counsel an opinion to the effect that, for federal income tax purposes: (i) the
Merger will be treated as a reorganization within the meaning of Section 368(a)
of the Code, (ii) R&B Falcon, Sub and Cliffs Drilling will each be a party to
that reorganization within the meaning of Section 368(b) of the Code, and (iii)
Cliffs Drilling and the stockholders of Cliffs Drilling will not recognize any
gain or loss as a result of the Merger, other than to the extent such
stockholders receive cash in lieu of fractional shares. Such opinion is subject
to certain assumptions and based on certain representations made by Cliffs
Drilling, R&B Falcon and Sub. Stockholders of Cliffs Drilling should be aware
that such opinions are not binding upon the Service and no assurance can be
given that the Service will not adopt a contrary position or that a contrary
Service position would not be sustained by a court. No ruling from the Service
has been or will be requested in connection with the Merger.
 
     Assuming the Merger qualifies as a reorganization under Section 368(a) of
the Code, the following federal income tax consequences will occur:
 
     - no gain or loss will be recognized by R&B Falcon, Sub or Cliffs Drilling
       in connection with the Merger;
 
     - no gain or loss will be recognized by a holder of Cliffs Drilling Common
       Stock who exchanges all of the holder's shares of Cliffs Drilling Common
       Stock solely for shares of R&B Falcon Common Stock in the Merger, except
       that gain or loss will be recognized by such holder on the receipt of
       cash in lieu of fractional shares;
 
     - the aggregate basis of the shares of R&B Falcon Common Stock to be
       received by a stockholder of Cliffs Drilling in the Merger will be the
       same as the aggregate basis of the shares of Cliffs Drilling Common Stock
       surrendered in exchange therefor (decreased by the amount of any tax
       basis allocable to any fractional share of R&B Falcon Common Stock for
       which cash is received);
 
     - the holding period of the shares of R&B Falcon Common Stock to be
       received by a stockholder of Cliffs Drilling in the Merger will include
       the holding period of the shares of Cliffs Drilling Common Stock
       surrendered in exchange therefor, provided that such shares of Cliffs
       Drilling Common Stock are held as capital assets at the Effective Time;
       and
 
     - a stockholder of Cliffs Drilling receiving cash in lieu of a fractional
       share will recognize gain or loss upon such payment equal to the
       difference, if any, between such stockholder's basis in the fractional
       share and the amount of cash received. Such gain or loss will be a
       capital gain or loss if the Cliffs Drilling Common Stock is held as a
       capital asset at the Effective Time.
 
     EACH HOLDER OF CLIFFS DRILLING COMMON STOCK IS URGED TO CONSULT WITH THE
HOLDER'S OWN TAX ADVISER WITH RESPECT TO THE TAX CONSEQUENCES OF THE MERGER,
INCLUDING THE APPLICATION AND EFFECT OF THE LAWS OF ANY STATE, MUNICIPAL,
FOREIGN OR OTHER TAXING JURISDICTION.
 
                                       26
<PAGE>   36
 
REGULATORY APPROVALS
 
     The HSR Act prohibits R&B Falcon and Cliffs Drilling from completing the
Merger until they have furnished certain information and materials to the
Federal Trade Commission (the "FTC") and the Antitrust Division of the United
States Department of Justice (the "Antitrust Division") and a required waiting
period has expired. Pursuant to the requirements of the HSR Act, R&B Falcon and
Cliffs Drilling have each filed a Notification and Report Form with the FTC and
the Antitrust Division for review under the HSR Act. On             , 1998, the
FTC notified R&B Falcon and Cliffs Drilling of the early termination of the
waiting period applicable under the HSR Act.
 
     Even after the HSR Act waiting period has expired or been terminated, the
FTC or the Antitrust Division could take such action under the antitrust laws as
it deems necessary or desirable in the public interest, including seeking
divestiture of substantial assets of R&B Falcon or Cliffs Drilling. Consummation
of the Merger is conditioned upon, among other things, the absence of any
pending or threatened governmental proceeding or any judgment, decree or order
of any governmental authority or court or any other legal restraint that would
prevent the consummation of the Merger. See "The Merger Agreement -- Conditions
to the Merger."
 
     R&B Falcon and Cliffs Drilling do not believe that any additional
governmental filings in the United States, other than the Certificate of Merger,
are required with respect to the Merger. R&B Falcon and Cliffs Drilling conduct
operations in a number of foreign countries where regulatory filings or
approvals may be required in connection with the consummation of the Merger. R&B
Falcon and Cliffs Drilling believe that all such material filings and approvals
have been, or will be, made or obtained, as the case may be.
 
RESALES OF R&B FALCON COMMON STOCK
 
     The shares of R&B Falcon Common Stock to be received by stockholders of
Cliffs Drilling in connection with the Merger have been registered under the
Securities Act and, except as set forth below, may be traded without
restriction. The shares of R&B Falcon Common Stock to be issued in the Merger
and received by persons who are deemed to be "affiliates" (as that term is
defined in Rule 144 under the Securities Act) of Cliffs Drilling prior to the
Merger may be resold by them only in transactions permitted by the resale
provisions of Rule 145 under the Securities Act (or, in the case of such persons
who become affiliates of R&B Falcon, Rule 144 under the Securities Act) or as
otherwise permitted under the Securities Act. Each affiliate of Cliffs Drilling
is required to execute a written agreement that such affiliate will not sell,
pledge, transfer or otherwise dispose of any shares of R&B Falcon Common Stock
issued to such affiliate pursuant to the Merger, except pursuant to an effective
registration statement or in compliance with Rule 145 under the Securities Act
or an exemption from the registration requirements of the Securities Act.
 
NYSE LISTING OF COMMON STOCK
 
     It is a condition to the Merger that the shares of R&B Falcon Common Stock
to be issued pursuant to the Merger be authorized for listing on the NYSE,
subject to official notice of issuance.
 
NO APPRAISAL RIGHTS
 
     Under the provisions of the DGCL, holders of Cliffs Drilling Common Stock
will not be entitled to any dissenters' rights of appraisal with respect to the
Merger.
 
INTERESTS OF CERTAIN PERSONS IN THE MERGER
 
     In considering the recommendations of the Cliffs Drilling Board with
respect to the Merger Agreement and the transactions contemplated thereby,
stockholders of Cliffs Drilling should be aware that certain members of the
management of Cliffs Drilling and the members of the Cliffs Drilling Board have
certain interests in the Merger that are in addition to the interests of the
stockholders generally and which may create potential conflicts of interest. The
Cliffs Drilling Board has considered these interests, among other matters, in
approving the Merger Agreement and the Merger.
 
                                       27
<PAGE>   37
 
     Election of Mr. Swanson to the R&B Falcon Board. As of the Effective Time,
Douglas E. Swanson, Chairman of the Board, President and Chief Executive Officer
of Cliffs Drilling, will be appointed as a director of R&B Falcon in the class
of directors with a term expiring at the annual meeting of R&B Falcon's
stockholders to be held in 2001.
 
     Waiver and Release Payments. The current executive officers of Cliffs
Drilling are Douglas E. Swanson, President and Chief Executive Officer; Charles
M. McCall, Senior Vice President -- Drilling Operations; Edward A. Guthrie, Vice
President -- Finance and Chief Financial Officer; James P. Mitchen, Vice
President -- Business Development; Jim R. Wise, Vice President -- Domestic
Drilling Operations; Gary W. Owen, Vice President -- Engineering Services; and
Cindy B. Taylor, Vice President -- Controller and Secretary. Each of Messrs.
Swanson, McCall, Guthrie and Mitchen is a party to an Executive Agreement with
Cliffs Drilling (the "Executive Agreements"). Pursuant to these Executive
Agreements, the consummation of the Merger would trigger the commencement of a
three-year (with respect only to Mr. Swanson) or a two-year (with respect to the
other three executive officers) employment period and the right to receive
severance payments and certain other benefits following any voluntary or
involuntary termination of employment during such employment period.
 
     Each Executive Agreement provides that, upon any termination of employment
(i) by the executive for good reason (as defined in the Executive Agreement),
(ii) by the executive for any reason during the 30-day period following the
change in control (as defined in the Executive Agreement) or any anniversary
thereof, or (iii) by the employer other than for cause (as defined in the
Executive Agreement), in each case prior to expiration of the applicable two- or
three-year term of the Executive Agreement, the executive becomes entitled to a
lump-sum severance payment equivalent to all compensation and benefits he would
have received for the remainder of the employment period, as though no
termination had occurred. Each Executive Agreement further provides that if any
payment to the executive is subject to excise tax under Section 4999 of the
Code, a "gross-up" payment will be made to place the executive in the same net
after-tax position as would have been the case if no excise tax had been
payable. Additionally, each Executive Agreement provides that any such
termination will result in the immediate vesting of (i) all stock appreciation
rights outstanding for at least six months on the date of change in control,
(ii) all stock options previously awarded to the executive; and (iii) all
restricted stock and deferred stock awards. The executive is also entitled to
other fringe benefits (i.e., outplacement services and counseling for 12 months,
certain life insurance policies, etc.). The assignment to the executive of
duties inconsistent with the executive's position, authority or
responsibilities, as well as any breach by the employer of the terms of the
Executive Agreement, shall constitute grounds for termination of employment by
the executive for "good reason."
 
     In addition, the Cliffs Drilling Board adopted an Amended and Restated
Retention Plan for Salaried Employees dated May 19, 1994, effective as of June
21, 1988 (the "Retention Plan"). Pursuant to the Retention Plan, the three
remaining executive officers, as well as other key employees, of Cliffs Drilling
would be entitled to receive, assuming a termination of employment within one
year following a change of control, specified severance benefits.
 
     Assuming that Messrs. Swanson, McCall, Guthrie and Mitchen resigned or were
terminated in anticipation of or immediately following the merger, such persons
would be entitled to receive cash and other quantifiable benefits pursuant to
the Executive Agreements in an amount of approximately $3,185,000, $745,000,
$745,000 and $574,000, respectively. Assuming that the employment of Messrs.
Wise and Owen and Ms. Taylor were terminated within one year following the
consummation of the Merger, such persons would be entitled to receive cash and
other quantifiable benefits pursuant to the Retention Plan in an amount of
approximately $219,600, $197,750 and $177,050, respectively. These amounts
include the estimated fair value of various benefits which the executives would
be entitled to receive and do not include any gross-up payments for excise taxes
that might be payable by the executive.
 
     The Merger Agreement provides that, as a condition to the Merger, Cliffs
Drilling shall obtain from each of its seven executive officers immediately
prior to the Effective Time a waiver and release of any and all rights and
claims existing under or arising pursuant to the Executive Agreements and/or the
Retention Plan, as applicable. The Merger Agreement provides that, in
conjunction with such waivers and releases, these
 
                                       28
<PAGE>   38
 
executive officers will receive in the aggregate approximately $7.1 million. The
Merger Agreement further provides that if any such payment to the executive
officers is subject to excise tax under Section 4999 of the Code, a "gross-up"
payment will be made to place the executive officers in the same net after-tax
position as would have been the case if no excise tax had been payable. The cash
amounts (excluding "gross-up" payments) to be made by Cliffs Drilling to Messrs.
Swanson, McCall, Guthrie, Mitchen, Wise and Owen and Ms. Taylor as required by
the Merger Agreement are $4,500,000, $650,000, $650,000, $494,000, $274,000,
$270,000 and $247,000, respectively. The payments required by the Merger
Agreement exceed the estimated value of the quantifiable benefits waived by an
aggregate amount of approximately $1.5 million, which amount is expected to be
expensed pursuant to the purchase method of accounting for business
combinations.
 
     In addition to the amount payable to Mr. Swanson reflected above, Cliffs
Drilling must also make a "gross up" payment of approximately $1.8 million to
Mr. Swanson in order to put him in the same net after-tax position as would have
been the case if no excise tax had been payable. Such "gross up" payment will
also compensate Mr. Swanson for any tax under Section 4999 of the Code with
respect to the acceleration of certain stock options described under
"Accelerated Vesting and Conversion of Stock Options" below. Approximately $5.1
million of the total amount required to be paid to Mr. Swanson is likely to be
characterized as an "excess parachute payment" (as defined in Section 280G(b)(1)
of the Code) subject to excise tax and will not be deductible by Cliffs Drilling
for federal income tax purposes.
 
     Employment Agreements. Pursuant to the Merger Agreement, the Surviving
Corporation will enter into employment agreements ("Employment Agreements") with
each of the seven executive officers of Cliffs Drilling. The Employment
Agreement for Mr. Swanson provides for his employment with the Surviving
Corporation for a three-year term following the Effective Time at an annual base
salary equal to his current base salary. In the event that Mr. Swanson's
employment with the Surviving Corporation is terminated by Mr. Swanson for good
reason (as defined in the Employment Agreement) or by the Surviving Corporation
other than for cause (as defined in the Employment Agreement), in each case
prior to expiration of the three-year term, Mr. Swanson is entitled to a lump
sum payment in an amount equal to (i) the annual base salary that would have
been received for the remainder of the employment period plus (ii) the highest
annual bonus awarded to Mr. Swanson during the previous three-year period
multiplied by a fraction, the numerator of which is the number of days since the
most recent bonus payment date through the date of termination date plus the
number of days remaining in the employment period, and the denominator of which
is 365. Mr. Swanson's Employment Agreement further provides that if any such
payment is subject to excise tax under Section 4999 of the Code, a "gross-up"
payment will be made to place Mr. Swanson in the same net after-tax position as
would have been the case if no excise tax had been payable. Additionally, the
Employment Agreement provides for the continuation of certain benefits to Mr.
Swanson from the date of termination to the end of the employment period. The
assignment of duties inconsistent with Mr. Swanson's position, authority or
responsibilities, as well as any breach by the employer of the terms of the
Employment Agreement, constitutes grounds for termination of employment by Mr.
Swanson for "good reason."
 
     The Employment Agreements for each of the remaining six executive officers
of Cliffs Drilling provides for employment of such executive by the Surviving
Corporation for a two-year term at an annual base salary equal to his or her
current base salary. In the event the employment of such executive is terminated
by the Surviving Corporation without cause, the executive shall be entitled to
receive his or her annual salary for the number of full months remaining in the
employment term had the executive not been so terminated.
 
     Accelerated Vesting and Conversion of Stock Options. As of August 21, 1998,
the date of execution of the Merger Agreement, there were unexercised options to
purchase an aggregate of approximately 621,500 shares of Cliffs Drilling Common
Stock that had previously been granted to officers, directors and employees of
Cliffs Drilling pursuant to its incentive equity plans. The Merger Agreement
provides that at the Effective Time of the Merger, each unexercised option to
purchase shares of Cliffs Drilling Common Stock shall be deemed to constitute an
option to acquire, on the same terms and conditions as were applicable under the
applicable Cliffs Drilling stock option plan, 1.7 shares of R&B Falcon Common
Stock (rounded downward to the nearest whole number), at a price per share
(rounded upward to the nearest whole cent) equal to the exercise price per share
for the shares of Cliffs Drilling Common Stock purchasable pursuant to such
option immediately prior to the Effective Time divided by 1.7. The various stock
option agreements governing stock
                                       29
<PAGE>   39
 
options previously awarded to the officers, directors and employees of Cliffs
Drilling pursuant to Cliffs Drilling's incentive equity plans provide that all
such stock options accelerate and vest in full upon the occurrence of a "change
in control" or a "potential change in control." Accordingly, all of the
outstanding Cliffs Drilling stock options that had not previously vested became
vested in full upon execution of the Merger Agreement. As of August 21, 1998,
Messrs. Swanson, McCall, Guthrie, Mitchen, Wise and Owen and Ms. Taylor held
unvested options to purchase 74,000, 32,500, 37,500, 27,000, 31,500, 29,500 and
27,000 shares of Cliffs Drilling Common Stock, respectively, and each member of
the Cliffs Drilling Board (other than Mr. Swanson) held unvested options to
purchase 2,000 shares of Cliffs Drilling Common Stock, that have become fully
vested and exercisable as a result of execution of the Merger Agreement. The
unvested options held by the directors and executive officers of Cliffs Drilling
described above consisted of options to purchase an aggregate of 46,500 shares
of Cliffs Drilling Common Stock at an exercise price of $14.00 per share,
options to purchase an aggregate of 27,500 shares at an exercise price of $32.75
per share, and options to purchase an aggregate of 197,000 shares at an exercise
price of $50.50 per share.
 
     R&B Falcon Stock Option Grants. The Merger Agreement requires R&B Falcon to
grant, as of the Effective Time, options to acquire an aggregate of 1,000,000
shares of R&B Falcon Common Stock to approximately 50 key employees (including
the executive officers) of Cliffs Drilling. These stock options will have a
ten-year term, an exercise price equal to the closing sale price of R&B Falcon
Common Stock as of the date on which the Effective Time occurs, and will vest
over a three year period, with 50% becoming exercisable on the first anniversary
of the grant date and 25% becoming exercisable on each of the next two
anniversaries of the grant date. Of the aggregate amount, options to purchase
300,000, 100,000, 100,000, 80,000, 80,000, 100,000 and 80,000 shares of R&B
Falcon Common Stock will be awarded to Messrs. Swanson, McCall, Guthrie,
Mitchen, Wise and Owen and Ms. Taylor, respectively.
 
     The R&B Falcon Board has authorized R&B Falcon's Chief Executive Officer to
make stock option grants and restricted stock awards to employees of R&B Falcon,
provided that he may not make any grants or awards to executive officers of R&B
Falcon. The authorization requires all stock option grants to vest one-third
annually and have an exercise price based upon the fair market value of R&B
Falcon Common Stock on the date of the grant, and requires all restricted stock
awards to vest at the end of three years following the date of the award. It is
expected that pursuant to this authorization, R&B Falcon will, prior to the
Merger, grant options to acquire approximately 1.9 million shares of R&B Falcon
Common Stock and make restricted stock awards aggregating approximately one
million shares of R&B Falcon Common Stock.
 
     Indemnification. The Merger Agreement provides that R&B Falcon and the
Surviving Corporation shall indemnify, defend and hold harmless each person who
is or has been at any time prior to the Effective Time an officer, director or
employee of Cliffs Drilling or any of its subsidiaries against all losses,
claims, damages, costs, expenses, liabilities or judgments or amounts paid in
settlement with the approval of the indemnifying party, based upon or arising
out of such person's service in such capacity, pertaining to any matter existing
or occurring at or prior to the Effective Time, to the same extent as he or she
would have been indemnified under the articles of incorporation, bylaws or
contractual indemnification agreements of Cliffs Drilling as were in effect on
August 11, 1998. The Merger Agreement further provides that the Surviving
Corporation shall purchase and maintain, for a period of six years after the
Effective Time, a directors and officers liability policy or runoff liability
coverage, in each case comparable to that currently maintained by Cliffs
Drilling, with respect to claims arising from facts or events that occurred
prior to the Effective Time.
 
RECENT DEVELOPMENT
 
     On August 26, 1998, Cliffs Drilling received notice that a class action
complaint against Cliffs Drilling and each member of the Cliffs Drilling Board
was filed by a stockholder, on behalf of all of the stockholders of Cliffs
Drilling, on August 12, 1998 in the Court of Chancery of the State of Delaware.
The complaint alleges that the directors of Cliffs Drilling are not acting in
accordance with their fiduciary duties to protect the interests of the
stockholders in connection with the transaction involving the proposed Merger.
The plaintiff seeks damages as well as injunctive relief. Cliffs Drilling
believes the allegations in the complaint are wholly without merit and intends
to vigorously defend the lawsuit.
 
                                       30
<PAGE>   40
 
                              THE MERGER AGREEMENT
 
     The detailed terms of and conditions of the Merger are contained in the
Merger Agreement, which is included in full as Appendix A to this Proxy
Statement/Prospectus and incorporated herein by reference. The following summary
description of certain provisions of the Merger Agreement is subject to the more
complete information set forth in the Merger Agreement.
 
THE MERGER
 
     At the Effective Time, Sub shall be merged with and into Cliffs Drilling.
As a result of the Merger, the separate corporate existence of Sub shall cease
and Cliffs Drilling shall continue as the Surviving Corporation, and all the
properties, rights, privileges, powers and franchises of Cliffs Drilling and Sub
shall vest in the Surviving Corporation, without any transfer or assignment
having occurred, and all debts, liabilities and duties of Cliffs Drilling and
Sub shall attach to the Surviving Corporation, all in accordance with the DGCL.
The Closing of the transactions contemplated by the Merger Agreement shall take
place as soon as practicable after the satisfaction or waiver of the conditions
set forth in the Merger Agreement or at such other time as R&B Falcon and Cliffs
Drilling shall agree. As soon as practicable after the Closing, the parties
hereto will cause the Merger to be consummated by filing with the Secretary of
State of Delaware a certificate of merger in accordance with the relevant
provisions of the DGCL. The Effective Time of the Merger will be contemporaneous
with the filing of a Certificate of Merger with the Secretary of State of the
State of Delaware or at such other time specified in the Certificate of Merger
as the effective time. Paul B. Loyd, Jr., Steven A. Webster, and Douglas E.
Swanson shall be the directors of the Surviving Corporation, and the officers of
Cliffs Drilling immediately prior to the Effective Time shall be the officers of
the Surviving Corporation. Such directors and officers shall hold office in
accordance with the certificate of incorporation and bylaws of the Surviving
Corporation until their respective successors are duly elected or appointed and
qualified.
 
CONVERSION OF SECURITIES
 
     Each share of Cliffs Drilling Common Stock issued and outstanding
immediately prior to the Effective Time, other than any shares of Cliffs
Drilling Common Stock to be canceled pursuant to the following sentence, shall
be converted, as of the Effective Time, into the right to receive 1.7 shares of
R&B Falcon Common Stock; provided, however, that no fractional shares of R&B
Falcon Common Stock shall be issued, and, in lieu thereof, a cash payment shall
be made as set forth below. Each share of Cliffs Drilling Common Stock held in
the treasury of Cliffs Drilling and each share of Cliffs Drilling Common Stock
owned by Sub, R&B Falcon or any direct or indirect wholly owned subsidiary of
R&B Falcon or of Cliffs Drilling immediately prior to the Effective Time shall
be canceled and extinguished without any conversion thereof and no payment shall
be made with respect thereto. Each share of common stock, par value $0.01 per
share, of Sub issued and outstanding immediately prior to the Effective Time
shall be converted into one share of common stock, $0.01 par value per share, of
the Surviving Corporation.
 
     No fraction of a share of R&B Falcon Common Stock shall be issued, but in
lieu thereof each holder of Cliffs Drilling Common Stock who would otherwise be
entitled to a fraction of a share of R&B Falcon Common Stock shall, upon
surrender of the certificate formerly representing Cliffs Drilling Common Stock
held by such holder to R&B Falcon or its transfer agent, be paid an amount in
cash equal to the value of such fraction of a share based upon the closing sales
price of R&B Falcon Common Stock, as reported on the NYSE, on the last day on
which there is a reported trade in the R&B Falcon Common Stock prior to the date
on which the Effective Time occurs. No interest shall be paid on such amount.
 
     DETAILED INSTRUCTIONS, INCLUDING A TRANSMITTAL LETTER, WILL BE MAILED TO
CLIFFS DRILLING STOCKHOLDERS PROMPTLY FOLLOWING THE EFFECTIVE TIME AS TO THE
METHOD OF EXCHANGING CERTIFICATES FORMALLY REPRESENTING SHARES OF CLIFFS
DRILLING COMMON STOCK. CLIFFS DRILLING STOCKHOLDERS SHOULD NOT FORWARD STOCK
CERTIFICATES TO THE PAYING AGENT UNTIL THEY HAVE
 
                                       31
<PAGE>   41
 
RECEIVED TRANSMITTAL LETTERS. CLIFFS DRILLING STOCKHOLDERS SHOULD NOT RETURN
STOCK CERTIFICATES WITH THE ENCLOSED PROXY.
 
REPRESENTATIONS AND WARRANTIES
 
     The Merger Agreement contains various representations and warranties of
Cliffs Drilling and R&B Falcon, relating, among other things, to the following:
(i) their organization and compliance with law, (ii) their capitalization, (iii)
their authorization to enter into the Merger Agreement and the validity of the
Merger Agreement, (iv) that no approvals or notices were required to consummate
the Merger and that the Merger would not conflict with certain instruments, (v)
the accuracy of their SEC filings and financial statements,(vi) the absence of
undisclosed liabilities, (vii) the conduct of their business in the ordinary
course and the absence of certain changes and events, and (viii) that no brokers
fees will be payable as a result of the Merger. Cliffs Drilling made additional
representations and warranties as to: (i) litigation, (ii) its employee benefit
plans, (iii) tax matters, (iv) environmental matters, (v) severance payments,
(vi) stockholder voting requirements with respect to the Merger, (vii) no excess
parachute payments or limitations on tax deductions under Section 162(m) of the
Internal Revenue Code, (viii) its labor relations, (ix) its insurance, (x)
compliance with state takeover laws and (xi) matters relating to the Cliffs
Drilling Rights Plan. R&B Falcon made additional representations and warranties
as to: (i) tax matters, (ii) the interim operations of Sub and (iii) no required
stockholder approval for the Merger.
 
     All representations and warranties of Cliffs Drilling and R&B Falcon, other
than those relating to the tax treatment of the Merger, expire at the Effective
Time, except for certain representations and warranties of R&B Falcon that
relate to tax matters.
 
CERTAIN COVENANTS
 
     Cliffs Drilling covenants in the Merger Agreement: (a) the business of
Cliffs Drilling and its subsidiaries shall be conducted only in, and Cliffs
Drilling and its subsidiaries shall not take any action except in, the ordinary
course of business and consistent with past practice; (b) Cliffs Drilling shall
not directly or indirectly: (i) issue, sell, pledge, dispose of or encumber, or
permit any of its subsidiaries to issue, sell, pledge, dispose of or encumber,
any capital stock of Cliffs Drilling or any such subsidiary except upon the
exercise of outstanding options to acquire Cliffs Drilling Common Stock; (ii)
amend or propose to amend the respective charters or bylaws of Cliffs Drilling
or any of its subsidiaries; (iii) split, combine or reclassify any outstanding
capital stock, or declare, set aside or pay any dividend or other distribution
payable in cash, stock, property or otherwise with respect to its capital stock
whether now or hereafter outstanding; (iv) redeem, purchase or acquire or offer
to acquire, or permit any of its subsidiaries to redeem, purchase or acquire or
offer to acquire, any of its or their capital stock; (v) enter into any
contract, agreement, commitment or arrangement with respect to any of these
matters; (vi) except as provided in the Merger Agreement, enter into, adopt or
(except as may be required by law and except for an amendment to the Cliffs
Drilling Stock Option Plans (or any option agreements existing thereunder) to
provide the Cliffs Drilling Board with the power to take the actions required
with respect to the conversion of options to acquire Cliffs Drilling Common
Stock into options to acquire R&B Falcon Common Stock pursuant to the Merger
Agreement) amend or terminate any bonus, profit sharing, compensation,
severance, termination, stock option, stock appreciation right, restricted
stock, performance unit, stock equivalent, stock purchase, pension, retirement,
deferred compensation, employment, severance or other employee benefit
agreement, trust, plan, fund or other arrangement for the benefit or welfare of
any director, officer or employee; (vii) except as provided in the Merger
Agreement, or in the ordinary course of business consistent with past practice
only with respect to non-executive officer employees, increase in any manner the
compensation or fringe benefits of any director, officer or employee; (viii)
except as provided in the Merger Agreement, pay to any director, officer or
employee any benefit not required by any employee benefit agreement, trust,
plan, fund or other arrangement as in effect on the date hereof; (ix) commence
any legal proceedings other than in accordance with past practice or settle any
legal proceedings or claims against Cliffs Drilling or any subsidiary of Cliffs
Drilling not covered by insurance for an amount or amounts in excess of
$5,000,000 in the aggregate; or (x) lend or advance any funds or otherwise
extend credit to any person other than Cliffs Drilling or a subsidiary of Cliffs
Drilling except for advances to
 
                                       32
<PAGE>   42
 
employees for business related expenses consistent with past practice and trade
credit extended in the ordinary course of business; (c) Cliffs Drilling shall
use its reasonable efforts (i) to preserve intact the business organization of
Cliffs Drilling and each of its subsidiaries, (ii) to maintain in effect any
authorizations or similar rights of Cliffs Drilling and each of its
subsidiaries, (iii) to keep available the services of the current officers and
key employees of Cliffs Drilling and its subsidiaries, (iv) to preserve the
goodwill of those having business relationships with it and its subsidiaries,
(v) to maintain and keep its properties and the properties of its subsidiaries
in as good a repair and condition as presently exists, except for deterioration
due to ordinary wear and tear and damage due to casualty; and (vi) to maintain
in full force and effect insurance comparable in amount and scope of coverage to
that currently maintained by it and its subsidiaries; (d) without the prior
written consent of R&B Falcon, which consent will not be unreasonably withheld,
Cliffs Drilling shall not make or agree to make, or permit any of its
subsidiaries to make or agree to make, capital expenditures that in the
aggregate exceed $40,000,000 (excluding any capital expenditures (i) funded with
insurance proceeds or (ii) accrued or incurred prior to June 30, 1998 and
reflected in Cliffs Drilling's previous filings with the SEC); (e) without the
prior written consent of R&B Falcon, which consent will not be unreasonably
withheld, Cliffs Drilling shall not, and shall not permit any of its
subsidiaries to (i) sell, pledge, dispose of or encumber any material portion of
its assets, (ii) incur, assume or guarantee indebtedness for money borrowed,
other than pursuant to existing credit facilities (within the limits of such
facilities as in effect on the date of the Merger Agreement) or for indebtedness
incurred in the ordinary course of business that does not exceed $5,000,000 in
the aggregate, or (iii) prepay any indebtedness or other material liability,
except prepayments pursuant to revolving lines of credit and prepayments made to
obtain prepayment discounts consistent with past practice; (f) Cliffs Drilling
shall not, and shall not permit any of its subsidiaries to, authorize, propose
or announce an intention to authorize or propose, or enter into an agreement
with respect to, any merger, consolidation or business combination (other than
the Merger) or any acquisition of a material amount of assets or securities, or
otherwise acquire direct or indirect control over any other person, except for
(i) purchases of U.S. Treasury securities or U.S. government agency securities,
which in either case have maturities of three years or less, (ii) other
investments in connection with cash management activities consistent with past
practice, or (iii) purchases of inventory, spares and replacements consistent
with past practice; (g) Cliffs Drilling shall, and shall cause its subsidiaries
to, perform their respective obligations under any contracts and agreements to
which any of them is a party or to which any of their assets is subject; (h)
Cliffs Drilling shall not, and shall not permit any of its subsidiaries to, take
any action that would, or that reasonably could be expected to, result in any of
the representations and warranties set forth in the Merger Agreement becoming
untrue or any of the conditions to the Merger not being satisfied. Cliffs
Drilling promptly shall advise R&B Falcon orally and in writing of any change or
event having, or which, insofar as reasonably can be foreseen, would have, a
material adverse effect on Cliffs Drilling; and (i) Cliffs Drilling shall, and
shall cause its subsidiaries to, make available to R&B Falcon and its
representatives such information with respect to the business and affairs of
Cliffs Drilling and its subsidiaries as R&B Falcon shall reasonably request, and
shall confer at all times as R&B Falcon may reasonably request with one or more
representatives of R&B Falcon with respect to Cliffs Drilling's material
operational matters and the general status of its operations. Cliffs Drilling
further covenants to (i) prepare and file with the Commission under the Exchange
Act, and to use its reasonable efforts to have cleared by the Commission, this
Proxy Statement with respect to the meeting of stockholders of Cliffs Drilling
and to cooperate with R&B Falcon in preparing the Registration Statement of
which this Prospectus is a part, (ii) to promptly take all action reasonably
necessary in accordance with the DGCL and the certificate of incorporation and
bylaws of Cliffs Drilling to convene a meeting of its stockholders to consider
and vote upon the adoption and approval of the Merger Agreement and the Merger,
(iii) subject to the terms and conditions set forth in the no solicitation
section of the Merger Agreement (A) to recommend at such meeting that the
stockholders of Cliffs Drilling vote to adopt and approve the Merger Agreement
and the Merger; (B) to use its reasonable efforts to solicit from stockholders
of Cliffs Drilling proxies in favor of such adoption and approval; and (C) to
take all other action reasonably necessary to secure a vote of its stockholders
in favor of the adoption and approval of the Merger Agreement and the Merger,
(iv) pay certain amounts to its executive officers in exchange for such
executive officers' execution of a waiver and release with respect to
obligations that would otherwise arise as a result of the Merger, and (v) to use
its reasonable effort to obtain an opinion that the Merger will qualify as a
tax-free reorganization and that Cliffs Drilling and the stockholders of Cliffs
 
                                       33
<PAGE>   43
 
Drilling will not recognize any gain or loss as a result of the Merger, other
than to the extent such stockholders receive cash in lieu of fractional shares.
 
     R&B Falcon covenants in the Merger Agreement: (i) the business of R&B
Falcon and its subsidiaries shall be conducted only in the ordinary course of
business consistent with past practice, (ii) R&B Falcon shall not, and shall not
permit any of its subsidiaries to, take any action (A) other than in the
ordinary course of business consistent with past practice or (B) that would, or
that reasonably could be expected to, result in any of R&B Falcon's
representations and warranties becoming untrue or any of the conditions to the
Merger not being satisfied (for purposes of the Merger Agreement, acquisitions
by R&B Falcon or any of its subsidiaries of entities or assets relating to or
involved in the energy service business shall be considered to be in the
ordinary course of R&B Falcon's business consistent with past practice), (iii)
R&B Falcon promptly shall advise Cliffs Drilling orally and in writing of any
change or event having, or which, insofar as reasonably can be foreseen, would
have, a material adverse effect on R&B Falcon, and (iv) R&B Falcon shall, and
shall cause its subsidiaries to, make available to Cliffs Drilling and its
representatives such information with respect to the business and affairs of R&B
Falcon and its subsidiaries as Cliffs Drilling shall reasonably request, and
shall confer at all times as Cliffs Drilling may reasonably request with one or
more representatives of Cliffs Drilling with respect to R&B Falcon's material
operational matters and the general status of its operations. R&B Falcon further
covenants that (i) it will file the Registration Statement of which this
Prospectus is a part, and R&B Falcon shall cooperate with Cliffs Drilling in
preparing this Proxy Statement with respect to the meeting of stockholders of
Cliffs Drilling, (ii) it shall ensure that it has adequate authorized and
unissued shares of R&B Falcon Common Stock as of the Effective Time to issue the
required number of shares of R&B Falcon Common Stock issuable pursuant to the
Merger and (iii) it shall use all reasonable efforts to cause the shares of R&B
Falcon Common Stock to be issued in the Merger and the shares of R&B Falcon
Common Stock to be reserved for issuance upon the exercise of outstanding
options to acquire Cliffs Drilling Common Stock to be assumed by R&B Falcon in
the Merger to be approved for listing on the NYSE, subject to official notice of
issuance, prior to the Closing Date.
 
NO SOLICITATION
 
     Cliffs Drilling has agreed, on behalf of itself and its affiliates, during
the term of the Merger Agreement that it will not: (i) solicit or knowingly
encourage, including by way of furnishing information, the initiation of any
inquiries or proposals regarding (A) any merger, tender offer, sale of shares of
capital stock or similar business combination transactions involving Cliffs
Drilling or its subsidiaries (other than (1) a merger of one or more wholly
owned subsidiaries of Cliffs Drilling with or into another wholly owned
subsidiary of Cliffs Drilling or Cliffs Drilling, (2) an issuance of Cliffs
Drilling Common Stock in exchange for assets of another entity, or (3) a merger
of a wholly owned subsidiary of Cliffs Drilling with or into another entity in
which the surviving entity is a wholly owned subsidiary of Cliffs Drilling and
the securities of such entity outstanding prior to such merger are converted
into shares of Cliffs Drilling Common Stock; provided that the aggregate number
of shares of Cliffs Drilling Common Stock issued in connection with any and all
transactions effected in reliance upon clause (2) or (3) do not exceed 15% of
the outstanding shares of Cliffs Drilling Common Stock as of the date of the
Merger Agreement), or (B) any sale of 15% or more of the assets of Cliffs
Drilling and its subsidiaries, taken as a whole (any of the foregoing
transactions being a "Cliffs Acquisition Transaction"), (ii) negotiate, explore
or otherwise engage in discussions with any person (other than R&B Falcon, Sub
or their respective directors, officers, employees, agents and representatives)
with respect to any Cliffs Acquisition Transaction, or (iii) enter into any
agreement, arrangement or understanding requiring it to abandon, terminate or
fail to consummate the Merger or any other transactions contemplated by the
Merger Agreement; provided, however, the members of the Cliffs Drilling Board
may (i) furnish information to (but only pursuant to a confidentiality
agreement) or enter into discussions or negotiations with any person or group
that makes an unsolicited bona fide written proposal for a Cliffs Acquisition
Transaction (an "Alternative Proposal"), if, and only to the extent that, (A)
the Cliffs Drilling Board, based on the written opinion of outside counsel,
determines in good faith that such action is required for the Cliffs Drilling
Board to comply with its fiduciary duties to stockholders imposed by law, and
(B) prior to furnishing such information to, or entering into discussions or
negotiations with, such person or entity, Cliffs Drilling provides written
notice to R&B Falcon to the effect that it is furnishing information to, or
entering into negotiations with, such
                                       34
<PAGE>   44
 
person or group; (ii) fail to make or withdraw or modify its recommendation of
the Merger if (A) there exists an Alternative Proposal and the Cliffs Drilling
Board, based on the written opinion of outside counsel, determines in good faith
that such action is required for the Cliffs Drilling Board to comply with its
fiduciary duties to stockholders imposed by law, (B) either such Alternative
Proposal is not conditioned on the receipt of financing or the Cliffs Drilling
Board has reasonably concluded in good faith that the person or group making
such Alternative Proposal will have adequate sources of financing to consummate
such Alternative Proposal, (C) the Cliffs Drilling Board has reasonably
determined in good faith that such Alternative Proposal is more favorable to the
stockholders of Cliffs Drilling than the Merger, and (D) the Cliffs Drilling
Board has received a written opinion from a nationally-recognized investment
banking firm to the effect that the consideration to be received by stockholders
of Cliffs Drilling in connection with such Alternative Proposal is superior,
from a financial point of view, to the consideration to be received by them in
the Merger; or (iii) to the extent applicable, comply with Rule 14e-2
promulgated under the Exchange Act with regard to an Alternative Proposal.
 
ADDITIONAL AGREEMENTS
 
     In addition to the foregoing covenants, the parties have agreed, among
other things, (i) to make all necessary filings with respect to the Merger and
the Merger Agreement under the HSR Act, the Securities Act, the Exchange Act and
applicable blue sky or similar securities laws and to use all reasonable efforts
to obtain required approvals and clearances with respect thereto, (ii) to obtain
all consents, waivers, approvals, authorizations and orders required in
connection with the authorization, execution and delivery of this Agreement and
the consummation of the Merger, (iii) to notify each other of events that would
be likely to cause any of their representations or warranties to be untrue or
inaccurate and of any material failure by them or any of their officers,
directors, employees or agents to comply with or satisfy any covenant, condition
or agreement to be complied with or satisfied by it under the Merger Agreement,
(iv) to cooperate and use their reasonable efforts to defend against and respond
to any claim, action, suit, investigation or other proceeding by any
governmental body or other person or other legal or administrative proceeding
that questions the validity or legality of the transactions contemplated by the
Merger Agreement, and (v) to use their reasonable efforts to cause the Merger to
be treated as a tax-free reorganization.
 
     In addition, R&B Falcon has agreed that the R&B Falcon Board will take
action to increase the number of directors comprising the full Board of
Directors of R&B Falcon at the Effective Time to eleven persons, and the R&B
Falcon Board shall elect Douglas E. Swanson (or, if Mr. Swanson shall decline or
be unable to serve, another person designated by Cliffs Drilling who is
reasonably acceptable to R&B Falcon) as a Class I director to fill the vacancy
created by the increase in the number of directors at or prior to the Effective
Time. R&B Falcon has also agreed that, as soon as practicable following the
Effective Time, it shall cause to be mailed to each holder of certificates that
represented shares of Cliffs Drilling Common Stock immediately prior to the
Effective Time, at such holder's address as it appears on Cliffs Drilling's
stock transfer records, a letter of transmittal and other information advising
such holder of the consummation of the Merger along with information and
instructions to enable such holder to effect the exchange of stock certificates
as contemplated by the Merger Agreement.
 
     Cliffs Drilling has additionally agreed to take or cause to be taken all
further action reasonably necessary pursuant to the Cliffs Drilling Rights Plan
in order to prevent the rights issuable thereunder from becoming exercisable as
a result of the execution of the Merger Agreement, the Merger or the
consummation of any of the transactions contemplated by the Merger Agreement.
 
EMPLOYEE MATTERS
 
     Pursuant to the Merger Agreement, the Surviving Corporation will enter into
employment agreements as of the Effective Time with the seven executive officers
of Cliffs Drilling, which agreements will provide for salaries equal to the
executive officers' current salaries and for a term of three years for Mr.
Swanson and two years for each of the other six executive officers. In addition,
R&B Falcon has agreed to grant, as of the effective time, options to purchase
1,000,000 shares, in the aggregate, of R&B Falcon Common Stock under the R&B
Falcon 1998 Employee Long-Term Incentive Plan to certain specified employees of
Cliffs Drilling,
                                       35
<PAGE>   45
 
including the seven executive officers of Cliffs Drilling. The exercise price of
such options shall be equal to the closing sales price of R&B Falcon Common
Stock, as reported on the NYSE, on the date on which the Effective Time occurs.
Such options shall have a term of ten years and shall vest as to 50% of such
options on the first anniversary of the grant date, as to an additional 25% on
the second anniversary of the grant date, and as to the remaining 25% on the
third anniversary of the grant date. Such options shall otherwise be on terms
and conditions consistent with employee stock options granted by R&B Falcon
prior to the Effective Time. See "The Merger -- Interests of Certain Persons in
the Merger."
 
     The Merger Agreement provides that employees of Cliffs Drilling and its
subsidiaries will receive bonuses under the Cliffs Drilling Incentive Bonus Plan
for the year ending December 31, 1998 based upon Cliffs Drilling's achievement
of certain previously-established financial and other targets for Cliffs
Drilling, in a manner consistent with such plan and with the administration of
such plan in prior years. The final amount of such bonuses shall be determined
by the Board of Directors of the Surviving Corporation and the Chief Executive
Officer of the Surviving Corporation as provided in the Cliffs Drilling
Incentive Bonus Plan. Bonuses under the Cliffs Drilling Incentive Bonus Plan
will be paid not later than February 28, 1999, and any employee of Cliffs
Drilling or a subsidiary of Cliffs Drilling who is terminated after the Closing
Date shall receive the full amount of any bonus to which such employee would
have been entitled under the Cliffs Drilling Incentive Bonus Plan but for the
termination of employment. The Merger Agreement contains provisions that provide
for participation as soon as practicable after the Effective Time by Cliffs
Drilling employees in R&B Falcon's 401(k) savings plan, defined benefit pension
plan and other welfare plans (health, disability and life insurance, etc.).
 
     Pursuant to the Merger Agreement, each outstanding option to purchase
shares of Cliffs Drilling Common Stock outstanding as of the Effective Time
under the two Cliffs Drilling stock option plans, whether vested or unvested,
shall be deemed to constitute an option to acquire, on the same terms and
conditions as were applicable under the applicable Cliffs Drilling stock option
plan, 1.7 shares of R&B Falcon Common Stock (rounded downward to the nearest
whole number), at a price per share (rounded upward to the nearest whole cent)
equal to (y) the exercise price per share for the shares of Cliffs Drilling
Common Stock purchasable pursuant to such option immediately prior to the
Effective Time divided by (z) 1.7. R&B Falcon is required, as soon as
practicable after the Effective Time, to file a registration statement on Form
S-8 (or any successor or other appropriate forms), or another appropriate form
with respect to the shares of R&B Falcon Common Stock subject to such options
and to use its reasonable efforts to maintain the effectiveness of such
registration statement or registration statements (and maintain the current
status of the prospectus or prospectuses contained therein) for so long as such
options remain outstanding. The Cliffs Drilling Board is required, prior to or
as of the Effective Time, to take all necessary actions to provide for such
conversion of the options to purchase Cliffs Drilling Common Stock into options
to purchase R&B Falcon Common Stock.
 
INDEMNIFICATION
 
     The Merger Agreement provides that, from and after the Effective Time, R&B
Falcon and the Surviving Corporation shall indemnify, defend and hold harmless
each person who was at the date of the Merger Agreement, or has been at any time
prior thereto or who becomes prior to the Effective Time, an officer, director
or employee of Cliffs Drilling or any of its subsidiaries (the "Indemnified
Parties") against losses, claims, damages, costs, expenses, liabilities or
judgments or amounts that are paid in settlement with the approval of the
indemnifying party (which approval shall not be unreasonably withheld) of or in
connection with a claim, action, suit, proceeding or investigation based in
whole or in part on or arising in whole or in part out of the fact that such
person is or was a director, officer or employee of Cliffs Drilling or any of
its subsidiaries, whether pertaining to any matter existing or occurring at or
prior to the Effective Time and whether reasserted or claimed prior to, or at or
after, the Effective Time ("Indemnified Liabilities"), including without
limitation, all Indemnified Liabilities based in whole or in part on, or arising
in whole or in part out of, or pertaining to the Merger Agreement, the Merger or
the transactions contemplated hereby, and specifically including any Indemnified
Liability That may be based on the sole or contributory negligence (whether
active, passive or gross) of any Indemnified Party, and R&B Falcon and the
Surviving Corporation shall pay expenses in advance of the final disposition of
any such action or proceeding to each Indemnified Party; provided,
 
                                       36
<PAGE>   46
 
however, that in no event shall R&B Falcon or the Surviving Corporation be
required to indemnify any Indemnified Party or advance any expenses on behalf of
any Indemnified Party to any greater extent than Cliffs Drilling would have been
required to so indemnify or advance expenses pursuant to the certificate of
incorporation or bylaws of Cliffs Drilling or contractual indemnification
agreements binding on Cliffs Drilling, each as in existence on August 11, 1998.
 
     The Merger Agreement also provides that the Surviving Corporation shall
purchase and maintain for a period of six years after the Effective Time
continuation coverage for runoff liability with respect to Cliffs Drilling's (i)
directors' and officers' liability insurance policy as in effect on August 11,
1998 (or obtain a directors' and officers' liability insurance policy for the
benefit of those persons covered by Cliffs Drilling's current directors' and
officers' liability insurance policy with comparable coverage) and (ii)
fiduciary liability policy, commercial crime policy and special crime policy as
in effect on August 11, 1998 (or obtain similar policies for those persons
currently covered thereby with comparable coverage). In addition, the Merger
Agreement requires R&B Falcon to cause its fiduciary liability policy to be
endorsed to cover the individuals acting as fiduciaries for Cliffs Drilling
subsequent to the Effective Date.
 
CONDITIONS TO THE MERGER
 
  Conditions to the Obligations of Each Party to Consummate the Merger
 
     The respective obligations of each party to effect the Merger shall be
subject to the fulfillment at or prior to the Closing Date of the following
conditions: (a) the Merger Agreement shall have been approved and adopted by the
requisite vote of the stockholders of Cliffs Drilling; (b) the waiting period
applicable to the consummation of the Merger under the HSR Act shall have
expired or been terminated; (c) no order shall have been entered and remain in
effect in any action or proceeding before any foreign, federal or state court or
governmental agency or other foreign, federal or state regulatory or
administrative agency or commission that would prevent or make illegal the
consummation of the Merger; (d) the Registration Statement of which this
Prospectus is a part shall be effective (and remain effective on the Closing
Date), and all post-effective amendments filed shall have been declared
effective or shall have been withdrawn; and no stop-order suspending the
effectiveness thereof shall have been issued and no proceedings for that purpose
shall have been initiated or, to the knowledge of the parties, threatened by the
Commission; (e) there shall have been obtained any and all material permits,
approvals and consents of securities or blue sky commissions of any
jurisdiction, and of any other governmental body or agency, that reasonably may
be deemed necessary so that the consummation of the Merger and the transactions
contemplated thereby will be in compliance with applicable laws, the failure to
comply with which would have a material adverse effect on the business,
financial condition or results of operations of the Surviving Corporation and
its subsidiaries, taken as a whole, after consummation of the Merger; (f) the
shares of R&B Falcon Common Stock issuable upon consummation of the Merger and
the shares of R&B Falcon Common Stock issuable upon exercise of any options to
purchase Cliffs Drilling Common Stock that are to become options to purchase R&B
Falcon Common Stock pursuant to the Merger Agreement shall have been approved
for listing on the NYSE, subject to official notice of issuance; and (g) all
approvals of private persons or corporations, (i) the granting of which is
necessary for the consummation of the Merger or the transactions contemplated in
connection therewith and (ii) the non-receipt of which would have a material
adverse effect on the business, financial condition or results of operations of
the Surviving Corporation and its subsidiaries, taken as a whole after the
consummation of the Merger, shall have been obtained.
 
  Additional Conditions to the Obligations of R&B Falcon
 
     The obligations of R&B Falcon to consummate the Merger are subject to the
satisfaction of the following further conditions: (a) the representations and
warranties of Cliffs Drilling in the Merger Agreement shall be accurate as of
the date of the Merger Agreement and (except to the extent such representations
and warranties speak specifically as of an earlier date) as of the Closing Date
as though such representations and warranties had been made at and as of that
time; all of the terms, covenants and conditions of the Merger Agreement to be
complied with and performed by Cliffs Drilling on or before the Closing Date
shall have been duly complied with and performed in all material respects; and a
certificate to the foregoing effect dated the
 
                                       37
<PAGE>   47
 
Closing Date and signed by the chief executive officer of Cliffs Drilling shall
have been delivered to R&B Falcon; (b) since the date of the Merger Agreement,
no material adverse change in the financial condition, results of operations or
business of Cliffs Drilling and its subsidiaries, taken as a whole, shall have
occurred (other than as a result of material adverse changes affecting the
contract drilling industry generally or the U.S. economy generally), and R&B
Falcon shall have received a certificate signed by the chief executive officer
of Cliffs Drilling dated the Closing Date to such effect; (c) the R&B Falcon
Board shall have received from its financial advisor a written opinion, dated as
of the date of the Merger Agreement, satisfactory in form and substance to the
R&B Falcon Board, to the effect that the conversion ratio of 1.7 shares of R&B
Falcon Common Stock to be issued for each share of Cliffs Drilling Common Stock
pursuant to the Merger is fair to the stockholders of R&B Falcon from a
financial point of view, which opinion shall have been confirmed in writing to
the R&B Falcon Board as of the date this Proxy Statement/Prospectus is first
mailed to the stockholders of Cliffs Drilling and shall not have been
subsequently withdrawn; (d) Cliffs Drilling shall have received, and furnished
written copies to R&B Falcon of, each of the Cliffs Drilling affiliate letters
required by the Merger Agreement; (e) Cliffs Drilling shall have received, and
furnished written copies to R&B Falcon of, the waivers and releases of the
Cliffs Drilling executive officers required by the Merger Agreement; and (f) R&B
Falcon shall have received from Cliffs Drilling's legal counsel an opinion dated
the Closing Date in form and substance reasonably acceptable to R&B Falcon
covering such matters as are customary in similar transactions.
 
  Additional Conditions to the Obligations of Cliffs Drilling
 
     The obligations of Cliffs Drilling to consummate the Merger are subject to
the satisfaction of the following further conditions: (a) the representations
and warranties of R&B Falcon and Sub in the Merger Agreement shall be accurate
as of the date of the Merger Agreement and (except to the extent such
representations and warranties speak specifically as of an earlier date) as of
the Closing Date as though such representations and warranties had been made at
and as of that time; all the terms, covenants and conditions of the Merger
Agreement to be complied with and performed by R&B Falcon or Sub on or before
the Closing Date shall have been duly complied with and performed in all
material respects; and a certificate to the foregoing effect dated the Closing
Date and signed by the chief executive officer of R&B Falcon shall have been
delivered to Cliffs Drilling; (b) since the date of the Merger Agreement, no
material adverse change in the financial condition, results of operations or
business of R&B Falcon and its subsidiaries, taken as a whole, shall have
occurred (other than as a result of material adverse changes affecting the
contract drilling industry generally or the U.S. economy generally), and Cliffs
Drilling shall have received a certificate signed by the chief executive officer
of R&B Falcon dated the Closing Date to such effect; (c) the Cliffs Drilling
Board shall have received from its financial advisor a written opinion, dated as
of the date of the Merger Agreement, satisfactory in form and substance to the
Cliffs Drilling Board, to the effect that the conversion ratio of 1.7 shares of
R&B Falcon Common Stock to be issued for each share of Cliffs Drilling Common
Stock pursuant to the Merger is fair to the stockholders of Cliffs Drilling from
a financial point of view, which opinion shall have been confirmed in writing to
the Cliffs Drilling Board as of the date this Proxy Statement/ Prospectus is
first mailed to the stockholders of Cliffs Drilling and shall not have been
subsequently withdrawn; (d) Cliffs Drilling shall have received from R&B
Falcon's legal counsel an opinion dated the Closing Date in form and substance
reasonably acceptable to Cliffs Drilling covering such matters as are customary
in similar transactions; and (e) Cliffs Drilling shall have received a written
opinion dated as of the Closing Date to the effect that for U.S. federal income
tax purposes (i) the Merger will be treated as a reorganization within the
meaning of Section 368(a) of the Code, (ii) R&B Falcon, Sub and Cliffs Drilling
will each be a party to that reorganization within the meaning of Section 368(b)
of the Code, and (iii) Cliffs Drilling and the stockholders of Cliffs Drilling
will not recognize any gain or loss as a result of the Merger, other than to the
extent such stockholders receive cash in lieu of fractional shares.
 
TERMINATION
 
     The Merger Agreement may be terminated and the Merger and the other
transactions contemplated by the Merger Agreement may be abandoned at any time
prior to the Effective Time, whether prior to or after approval by the
stockholders of Cliffs Drilling: (a) by mutual consent of R&B Falcon and Cliffs
Drilling;
                                       38
<PAGE>   48
 
(b) by either R&B Falcon or Cliffs Drilling if the Merger has not been effected
on or before February 28, 1999; provided, however, that this right to terminate
the Merger Agreement shall not be available to a party whose failure to fulfill
any obligation under the Merger Agreement has been the cause of or resulted in
the failure of the Merger to occur on or before such date; (c) by R&B Falcon if
it does not receive the fairness opinion from its financial advisor or the
opinion is not confirmed as of the date of mailing this Proxy
Statement/Prospectus or the opinion is subsequently withdrawn; (d) by Cliffs
Drilling if it does not receive the fairness opinion from its financial advisor
or the opinion is not confirmed as of the date of mailing this Proxy
Statement/Prospectus or the opinion is subsequently withdrawn; (e) by either R&B
Falcon or Cliffs Drilling if a final, unappealable order of a judicial or
administrative authority of competent jurisdiction to restrain, enjoin or
otherwise prevent a consummation of the Merger Agreement or the transactions
contemplated in connection therewith shall have been entered; (f) by either R&B
Falcon or Cliffs Drilling if the required approval of the stockholders of Cliffs
Drilling is not received in a vote duly taken at the Cliffs Drilling
stockholders' meeting; (g) by R&B Falcon if (i) since the date of the Merger
Agreement there has been a material adverse change in the results of operations,
financial condition or business of Cliffs Drilling and its subsidiaries, taken
as a whole (other than as a result of material adverse changes affecting the
contract drilling industry generally or the U.S. economy generally), or (ii)
there has been a breach of any representation or warranty or covenant set forth
in the Merger Agreement by Cliffs Drilling which breach has not been cured
within 30 days following receipt by Cliffs Drilling of notice of such breach;
(h) by Cliffs Drilling if (i) since the date of the Merger Agreement there has
been a material adverse change in the results of operations, financial condition
or business of R&B Falcon and its subsidiaries, taken as a whole (other than as
a result of material adverse changes affecting the contract drilling industry
generally or the U.S. economy generally), or (ii) there has been a breach of any
representation or warranty or covenant set forth in the Merger Agreement by R&B
Falcon which breach has not been cured within 30 days following receipt by R&B
Falcon of notice of such breach; or (i) by R&B Falcon if the Cliffs Drilling
Board exercises its right pursuant to the no solicitation section of the Merger
Agreement not to convene a meeting of the Cliffs Drilling stockholders to
approve the Merger or to withdraw or otherwise change its recommendation that
the Cliffs Drilling stockholders approve the Merger.
 
EXPENSES AND TERMINATION FEES
 
     Except as set forth below, R&B Falcon and Cliffs Drilling will each pay
their own costs and expenses in connection with the transactions contemplated by
the Merger.
 
     The Merger Agreement provides that: (a) in the event of any termination of
the Merger Agreement, such termination shall not relieve any party from
liability for any breach of the Merger Agreement, provided that a party's
liability for any such breach shall be limited to that set forth in the
following clauses; (b) if the Merger Agreement is terminated (i) by Cliffs
Drilling because it has not received the fairness opinion from its financial
advisor or the opinion is not confirmed as of the date of mailing this Proxy
Statement/Prospectus or the opinion is subsequently withdrawn and there has not
been a material adverse change in the results of operations, financial condition
or business of R&B Falcon and its subsidiaries, taken as a whole (other than as
a result of material adverse changes affecting the contract drilling industry
generally or the U.S. economy generally), (ii) by Cliffs Drilling or R&B Falcon
because the Cliffs Drilling stockholders do not approve the Merger, or (iii) by
R&B Falcon because Cliffs Drilling breaches a representation, warranty or
covenant and does not timely cure such breach or because the Cliffs Drilling
Board exercises its right pursuant to the no solicitation section of the Merger
Agreement not to convene a meeting of the Cliffs Drilling stockholders to
approve the Merger or to withdraw or otherwise change its recommendation that
the Cliffs Drilling stockholders approve the Merger, then Cliffs Drilling shall
promptly, but in no event later than five business days after written request by
R&B Falcon, pay to R&B Falcon an amount equal to $15,000,000 as liquidated
damages; (c) if the Merger Agreement is terminated (i) by R&B Falcon because it
has not received the fairness opinion from its financial advisor or the opinion
is not confirmed as of the date of mailing this Proxy Statement/Prospectus or
the opinion is subsequently withdrawn and there has not been a material adverse
change in the results of operations, financial condition or business of Cliffs
Drilling and its subsidiaries, taken as a whole (other than as a result of
material adverse changes affecting the contract drilling industry generally or
the U.S. economy generally), or (ii) by Cliffs Drilling because R&B Falcon
breaches a representation,
                                       39
<PAGE>   49
 
warranty or covenant and does not timely cure such breach, then R&B Falcon shall
promptly, but in no event later than five business days after written request by
Cliffs Drilling, pay to Cliffs Drilling an amount equal to $15,000,000 as
liquidated damages; and (d) if the Merger Agreement is terminated (i) by Cliffs
Drilling because it has not received the fairness opinion from its financial
advisor or the opinion is not confirmed as of the date of mailing this Proxy
Statement/Prospectus or the opinion is subsequently withdrawn and there has not
been a material adverse change in the results of operations, financial condition
or business of R&B Falcon and its subsidiaries, taken as a whole (other than as
a result of material adverse changes affecting the contract drilling industry
generally or the U.S. economy generally), (ii) by Cliffs Drilling or R&B Falcon
because the Cliffs Drilling stockholders do not approve the Merger, (iii) by R&B
Falcon because Cliffs Drilling breaches a representation, warranty or covenant
and does not timely cure such breach or because the Cliffs Drilling Board
exercises its right pursuant to the no solicitation section of the Merger
Agreement not to convene a meeting of the Cliffs Drilling stockholders to
approve the Merger or to withdraw or otherwise change its recommendation that
the Cliffs Drilling stockholders approve the Merger, or (iv) by Cliffs Drilling
because the Merger has not been consummated by February 28, 1999, and (A) after
the date of the Merger Agreement but at or before the time the Merger Agreement
is terminated a Cliffs Acquisition Transaction shall have been made known to
Cliffs Drilling or shall have been made directly to Cliffs Drilling stockholders
or any person shall have publicly announced an intention to effect a Cliffs
Acquisition Transaction, and (B) any Cliffs Acquisition Transaction (whether the
same or different from the one referenced in clause (A)) is consummated at any
time within one year after the date of termination of the Merger Agreement, then
Cliffs Drilling shall promptly pay to R&B Falcon the sum of $30,000,000, less
any amounts previously paid by Cliffs Drilling to R&B Falcon pursuant clause (b)
above.
 
AMENDMENT AND WAIVER
 
     The Merger Agreement provides that any provision of the Merger Agreement
may be waived at any time by the party that is, or whose stockholders are,
entitled to the benefits thereof. The Merger Agreement may not be amended or
supplemented at any time, except by an instrument in writing signed on behalf of
each party hereto, provided that after the Merger Agreement has been approved
and adopted by the stockholders of Cliffs Drilling, it may be amended only as
may be permitted by applicable provisions of the DGCL. The waiver by any party
hereto of any condition or of a breach of another provision of the Merger
Agreement shall not operate or be construed as a waiver of any other condition
or subsequent breach. The waiver by any party of any of the conditions precedent
to its obligations under the Merger Agreement shall not preclude it from seeking
redress for breach of the Merger Agreement other than with respect to the
condition so waived.
 
                                       40
<PAGE>   50
 
          UNAUDITED PRO FORMA CONDENSED COMBINED FINANCIAL STATEMENTS
 
     The following unaudited pro forma condensed combined financial statements
are presented assuming the Merger will be accounted for under the purchase
method of accounting in accordance with Accounting Principles Board Opinion No.
16. The unaudited pro forma condensed combined statements of operations are
presented as if the Merger and certain other acquisition and financing
transactions were consummated at the beginning of the respective periods. The
unaudited pro forma condensed combined balance sheet is presented as if the
Merger and certain other acquisition and financing transactions were consummated
at the date of the balance sheet. The unaudited pro forma condensed combined
financial statements do not reflect any anticipated cost savings which may be
realized after consummation of the Merger.
 
     The pro forma data does not purport to represent what R&B Falcon and Cliffs
Drilling's combined results of operations actually would have been if the Merger
had occurred as of the date indicated or will be for any future periods. The
unaudited pro forma condensed combined financial statements should be read in
conjunction with the historical financial statements and the notes thereto of
R&B Falcon and Cliffs Drilling contained elsewhere or incorporated by reference
in this Proxy Statement/Prospectus.
 
              UNAUDITED PRO FORMA CONDENSED COMBINED BALANCE SHEET
                              AS OF JUNE 30, 1998
 
<TABLE>
<CAPTION>
                                                                       HISTORICAL                  PRO FORMA
                                                              ----------------------------   ----------------------
                                                              R&B FALCON   CLIFFS DRILLING   ADJUSTMENTS   COMBINED
                                                              ----------   ---------------   -----------   --------
                                                                                  (IN MILLIONS)
<S>                                                           <C>          <C>               <C>           <C>
                                                      ASSETS
CURRENT ASSETS:
  Cash and cash equivalents.................................   $   69.5        $  17.3         $(14.1)     $   72.7
  Short-term investments....................................       63.1             --             --          63.1
  Accounts receivable.......................................      249.0           76.1             --         325.1
  Inventories...............................................       21.1            9.6             --          30.7
  Drilling contracts in progress............................         --           12.7             --          12.7
  Other current assets......................................       18.7           13.3             --          32.0
                                                               --------        -------         ------      --------
        Total current assets................................      421.4          129.0          (14.1)        536.3
                                                               --------        -------         ------      --------
PROPERTY AND EQUIPMENT:
  Drilling and related equipment............................    2,395.6          493.7           86.8       2,976.1
  Other assets..............................................      122.6           17.5             --         140.1
                                                               --------        -------         ------      --------
        Total property and equipment........................    2,518.2          511.2           86.8       3,116.2
  Accumulated depreciation..................................     (466.0)        (114.6)         114.6        (466.0)
                                                               --------        -------         ------      --------
        Net property and equipment..........................    2,052.2          396.6          201.4       2,650.2
                                                               --------        -------         ------      --------
DEFERRED CHARGES AND OTHER ASSETS...........................       38.6            7.0           28.6          74.2
                                                               --------        -------         ------      --------
NET ASSETS OF DISCONTINUED OPERATIONS.......................       19.0             --             --          19.0
                                                               --------        -------         ------      --------
        TOTAL ASSETS........................................   $2,531.2        $ 532.6         $215.9      $3,279.7
                                                               ========        =======         ======      ========
 
                                       LIABILITIES AND STOCKHOLDERS' EQUITY
 
CURRENT LIABILITIES:
  Short-term obligations....................................   $   96.7        $    --         $   --      $   96.7
  Long-term obligations due within one year.................       32.3             --             --          32.3
  Accounts payable..........................................       37.9           36.7             --          74.6
  Accrued expenses..........................................      106.1           27.5             --         133.6
                                                               --------        -------         ------      --------
        Total current liabilities...........................      273.0           64.2             --         337.2
LONG-TERM OBLIGATIONS.......................................    1,172.9          203.3             --       1,376.2
OTHER NON-CURRENT LIABILITIES...............................       36.2            1.3             --          37.5
DEFERRED INCOME TAXES.......................................      129.9           18.1           70.5         218.5
                                                               --------        -------         ------      --------
        Total liabilities...................................    1,612.0          286.9           70.5       1,969.4
                                                               --------        -------         ------      --------
MINORITY INTEREST...........................................       56.7             --             --          56.7
                                                               --------        -------         ------      --------
STOCKHOLDERS' EQUITY:
  Common stock..............................................        1.7             .2             .1           2.0
  Capital in excess of par..................................      677.2          182.7          208.1       1,068.0
  Retained earnings.........................................      204.5           69.7          (69.7)        204.5
  Other.....................................................      (20.9)          (6.9)           6.9         (20.9)
                                                               --------        -------         ------      --------
        Total stockholders' equity..........................      862.5          245.7          145.4       1,253.6
                                                               --------        -------         ------      --------
        TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY..........   $2,531.2        $ 532.6         $215.9      $3,279.7
                                                               ========        =======         ======      ========
</TABLE>
 
See Notes to Unaudited Pro Forma Condensed Combined Balance Sheet as of June 30,
                                     1998.
 
                                       41
<PAGE>   51
 
               R&B FALCON CORPORATION AND CLIFFS DRILLING COMPANY
 
         NOTES TO UNAUDITED PRO FORMA CONDENSED COMBINED BALANCE SHEET
                              AS OF JUNE 30, 1998
 
     The following is a summary of the significant assumptions and adjustments
included in the unaudited pro forma condensed combined balance sheet as of June
30, 1998:
 
          a) Cash and Cash Equivalents -- Other costs related to the merger as
     shown below (in millions):
 
<TABLE>
<CAPTION>
DESCRIPTION                                           AMOUNT
- -----------                                           ------
<S>                                                   <C>
Investment advisors.................................  $ 5.3
Executive waiver and release payments...............    7.4
Printing, legal and accounting fees.................    1.4
                                                      -----
          Total other cash costs....................  $14.1
                                                      =====
</TABLE>
 
          In addition to the foregoing, it is expected that, upon completion of
     the Merger, approximately $1.5 million of the aggregate executive waiver
     and release payments, representing that portion of the payments not
     directly attributable to the waiver and release of quantifiable benefits
     due such executive officers under existing contractual obligations, will be
     expensed.
 
          b) Net Property and Equipment and Deferred Income Taxes -- In
     accordance with Accounting Principles Board Opinion No. 16, Business
     Combinations, using the purchase method of accounting, the values of the
     acquired assets were adjusted to their estimated fair value. This resulted
     in an increase to net property and equipment of $201.4 million.
     Additionally, in accordance with Statement of Financial Accounting
     Standards No. 109, Accounting for Income Taxes, a corresponding increase of
     $70.5 million was recorded in deferred income taxes.
 
          c) Deferred Charges and Other Assets -- The excess of the investment
     in the net assets of Cliffs Drilling results in excess cost over net assets
     acquired of $28.6 million. Included in the cost of the acquisition are the
     cash costs described in note a) above.
 
          d) Stockholders' Equity -- The following table shows the effects of
     issuing approximately 27.1 million new shares of R&B Falcon at a per share
     price of $14.2125, a value of approximately $6.2 million assigned to the
     conversion of existing options of Cliffs Drilling into R&B Falcon options
     determined consistent with Statement of Financial Accounting Standards No.
     123, Accounting for Stock-Based Compensation, and the elimination of the
     current equity of Cliffs Drilling (in millions):
 
<TABLE>
<CAPTION>
                                              R&B FALCON     CLIFFS DRILLING    NET PRO
                                              SHARES AND         EQUITY          FORMA
                                            OPTIONS ISSUED     ELIMINATED      ADJUSTMENT
                                            --------------   ---------------   ----------
<S>                                         <C>              <C>               <C>
Common stock, par value $.01 per share....      $   .3           $   (.2)        $   .1
Capital in excess of par..................       390.8            (182.7)         208.1
Retained earnings.........................          --             (69.7)         (69.7)
Other.....................................          --               6.9            6.9
                                                ------           -------         ------
          Total stockholders' equity......      $391.1           $(245.7)        $145.4
                                                ======           =======         ======
</TABLE>
 
                                       42
<PAGE>   52
 
               R&B FALCON CORPORATION AND CLIFFS DRILLING COMPANY
 
         UNAUDITED PRO FORMA CONDENSED COMBINED STATEMENT OF OPERATIONS
                      FOR THE YEAR ENDED DECEMBER 31, 1997
 
<TABLE>
<CAPTION>
                                                             HISTORICAL                  PRO FORMA
                                                    ----------------------------   ----------------------
                                                    R&B FALCON   CLIFFS DRILLING   ADJUSTMENTS   COMBINED
                                                    ----------   ---------------   -----------   --------
                                                           (IN MILLIONS, EXCEPT PER SHARE AMOUNTS)
<S>                                                 <C>          <C>               <C>           <C>
OPERATING REVENUES................................   $ 942.1         $263.6          $ 21.6      $1,227.3
                                                     -------         ------          ------      --------
COSTS AND EXPENSES:
  Operating expenses..............................     447.6          145.2*           13.4         606.2
  Depreciation and amortization...................      82.9           20.4            10.2         113.5
  General and administrative......................      51.9            8.7              --          60.6
  Merger expenses.................................      66.4             --              --          66.4
                                                     -------         ------          ------      --------
          Total costs and expenses................     648.8          174.3            23.6         846.7
                                                     -------         ------          ------      --------
OPERATING INCOME..................................     293.3           89.3            (2.0)        380.6
                                                     -------         ------          ------      --------
OTHER INCOME (EXPENSE):
  Interest expense, net of capitalized interest...     (46.3)         (17.8)            3.3         (60.8)
  Interest income.................................       5.8            1.9              --           7.7
  Other, net......................................      (2.7)          (1.6)             --          (4.3)
                                                     -------         ------          ------      --------
          Total other income (expense)............     (43.2)         (17.5)            3.3         (57.4)
                                                     -------         ------          ------      --------
INCOME FROM CONTINUING OPERATIONS BEFORE INCOME
  TAX EXPENSE AND MINORITY INTEREST...............     250.1           71.8             1.3         323.2
Income tax expense................................      84.7           25.1              .8         110.6
                                                     -------         ------          ------      --------
INCOME FROM CONTINUING OPERATIONS BEFORE MINORITY
  INTEREST........................................     165.4           46.7              .5         212.6
Minority interest.................................       9.4             --              --           9.4
                                                     -------         ------          ------      --------
INCOME FROM CONTINUING OPERATIONS.................   $ 156.0         $ 46.7          $   .5      $  203.2
                                                     =======         ======          ======      ========
INCOME FROM CONTINUING OPERATIONS PER SHARE:
  Basic...........................................   $   .95         $ 3.06                      $   1.07
                                                     =======         ======                      ========
  Diluted.........................................   $   .94         $ 3.01                      $   1.05
                                                     =======         ======                      ========
WEIGHTED AVERAGE COMMON SHARES OUTSTANDING:
  Basic...........................................     164.1           15.2            11.3         190.6
                                                     =======         ======          ======      ========
  Diluted.........................................     166.2           15.5            11.6         193.3
                                                     =======         ======          ======      ========
</TABLE>
 
- ---------------
 
<TABLE>
<S>                                                         <C>    <C>
*Reclassification of Cliffs Drilling's Statement of
  Operations:
     Operating Expenses as previously reported............  $148.2
     Less Gain on Disposition of Assets...................    (3.2)
     Plus Exchange Rate (Gain)/Loss.......................      .2
                                                            ------
     Operating Expenses Reclassified......................  $145.2
                                                            ======
</TABLE>
 
See Schedule of Adjustments to Unaudited Pro Forma Condensed Combined Statements
                                 of Operations.
 
                                       43
<PAGE>   53
 
               R&B FALCON CORPORATION AND CLIFFS DRILLING COMPANY
 
         UNAUDITED PRO FORMA CONDENSED COMBINED STATEMENT OF OPERATIONS
                     FOR THE SIX MONTHS ENDED JUNE 30, 1998
 
<TABLE>
<CAPTION>
                                                              HISTORICAL                  PRO FORMA
                                                     ----------------------------   ----------------------
                                                     R&B FALCON   CLIFFS DRILLING   ADJUSTMENTS   COMBINED
                                                     ----------   ---------------   -----------   --------
                                                            (IN MILLIONS, EXCEPT PER SHARE AMOUNTS)
<S>                                                  <C>          <C>               <C>           <C>
OPERATING REVENUES.................................    $560.4         $175.0           $  --       $735.4
                                                       ------         ------           -----       ------
COSTS AND EXPENSES:
  Operating expenses...............................     251.9          103.1*             --        355.0
  Depreciation and amortization....................      43.5           13.7             1.7         58.9
  General and administrative.......................      28.1            4.5              --         32.6
  Merger expenses..................................      (1.0)            --              --         (1.0)
                                                       ------         ------           -----       ------
          Total costs and expenses.................     322.5          121.3             1.7        445.5
                                                       ------         ------           -----       ------
OPERATING INCOME...................................     237.9           53.7            (1.7)       289.9
                                                       ------         ------           -----       ------
OTHER INCOME (EXPENSE):
  Interest expense, net of capitalized interest....     (29.1)         (10.0)            1.7        (37.4)
  Interest income..................................       4.4            1.0              --          5.4
  Other, net.......................................       (.4)           (.4)             --          (.8)
                                                       ------         ------           -----       ------
          Total other income (expense).............     (25.1)          (9.4)            1.7        (32.8)
                                                       ------         ------           -----       ------
INCOME FROM CONTINUING OPERATIONS BEFORE INCOME TAX
  EXPENSE AND MINORITY INTEREST....................     212.8           44.3              --        257.1
Income tax expense.................................      77.5           15.5              .1         93.1
                                                       ------         ------           -----       ------
INCOME FROM CONTINUING OPERATIONS BEFORE MINORITY
  INTEREST.........................................     135.3           28.8             (.1)       164.0
Minority interest..................................       5.1             --              --          5.1
                                                       ------         ------           -----       ------
INCOME FROM CONTINUING OPERATIONS..................    $130.2         $ 28.8           $ (.1)      $158.9
                                                       ======         ======           =====       ======
INCOME FROM CONTINUING OPERATIONS PER SHARE:
  Basic............................................    $  .79         $ 1.82                       $  .83
                                                       ======         ======                       ======
  Diluted..........................................    $  .78         $ 1.80                       $  .82
                                                       ======         ======                       ======
WEIGHTED AVERAGE COMMON SHARES OUTSTANDING:
  Basic............................................     165.1           15.8            11.1        192.0
                                                       ======         ======           =====       ======
  Diluted..........................................     166.5           16.0            11.2        193.7
                                                       ======         ======           =====       ======
</TABLE>
 
- ---------------
 
<TABLE>
<S>                                                         <C>    <C>
*Reclassification of Cliffs Drilling's Statement of Operations:
     Operating Expenses as previously reported............  $102.6
     Less Gain on Disposition of Assets...................     (.1)
     Plus Exchange Rate (Gain)/Loss.......................      .6
                                                            ------
     Operating Expenses Reclassified......................  $103.1
                                                            ======
</TABLE>
 
See Schedule of Adjustments to Unaudited Pro Forma Condensed Combined Statements
                                 of Operations.
 
                                       44
<PAGE>   54
 
               R&B FALCON CORPORATION AND CLIFFS DRILLING COMPANY
 
SCHEDULE OF ADJUSTMENTS TO UNAUDITED PRO FORMA CONDENSED COMBINED STATEMENTS OF
                                   OPERATIONS
<TABLE>
<CAPTION>
 
                                                                                                       INCOME
                                                     OPERATING   OPERATING                  INTEREST     TAX
                                                     REVENUES    EXPENSES    DEPRECIATION   EXPENSE    EXPENSE
                                                     ---------   ---------   ------------   --------   -------
                                                                           (IN MILLIONS)
<S>  <C>                                             <C>         <C>         <C>            <C>        <C>
FOR THE YEAR ENDED DECEMBER 31, 1997
a)   To include operating results for all of 1997
     for the drilling and production units acquired
     from Well Services (Marine) Limited by Cliffs
     Drilling on December 29, 1997.................    $17.3       $11.1        $ 2.6                   $ 1.3
b)   To consolidate the operating results of the
     West Indies Joint Venture for all of 1997. The
     remaining 50% interest in the venture was
     acquired by Cliffs Drilling on August 1, 1997:
     Record 100% of results........................      5.3         2.3           .6        $ (.5)        .7
     Reverse equity in earnings....................     (1.0)                                             (.4)
c)   To adjust interest expense for Cliffs Drilling
     as if the $50 million Senior Notes issued on
     August 7, 1997 had been issued January 1,
     1997..........................................                                           (2.7)       (.9)
d)   To adjust interest expense for R&B Falcon as
     if the $1.1 billion Senior Notes issued in
     April 1998 had been issued January 1, 1997.
     Interest rates on the new Senior Notes are
     less than on the debt retired.................                                            6.5        2.3
e)   To record additional depreciation due to the
     additions to property and equipment as a
     result of recording Cliffs Drilling's assets
     at their estimated fair value.................                               6.3                    (2.2)
f)   To record amortization of excess cost over net
     assets acquired based on a 40 year
     amortization period...........................                                .7
g)   Additional shares for conversion of Cliffs
     Drilling's shares at a ratio of 1.7 to 1 for
     R&B Falcon shares.............................
                                                       -----       -----        -----        -----      -----
     Totals for the year ended December 31, 1997...    $21.6       $13.4        $10.2        $ 3.3      $  .8
                                                       =====       =====        =====        =====      =====
FOR THE SIX MONTHS ENDED JUNE 30, 1998
a)   To adjust interest expense for R&B Falcon as
     if the $1.1 billion Senior Notes issued in
     April 1998 had been issued January 1, 1998.
     Interest rates on the new Senior Notes are
     less than on the debt retired.................                                          $ 1.7      $  .6
b)   To record additional depreciation due to the
     additions to property and equipment as a
     result of recording Cliffs Drilling's assets
     at their estimated fair value.................                             $ 1.3                     (.5)
c)   To record amortization of excess cost over net
     assets acquired based on a 40 year
     amortization period...........................                                .4
d)   Additional shares for conversion of Cliffs
     Drilling's shares at a ratio of 1.7 to 1 for
     R&B Falcon shares.............................
                                                       -----       -----        -----        -----      -----
     Totals for six months ended June 30, 1998.....    $  --       $  --        $ 1.7        $ 1.7      $  .1
                                                       =====       =====        =====        =====      =====
 
<CAPTION>
      WEIGHTED AVERAGE
        COMMON SHARES
     -------------------
     BASIC       DILUTED
     -----       -------
        (IN MILLIONS)
<S>  <C>         <C>
FOR
a)     .7           .7
b)
c)
d)
e)
f)
g)   10.6         10.9
     ----         ----
     11.3         11.6
     ====         ====
FOR
a)
b)
c)
d)   11.1         11.2
     ----         ----
     11.1         11.2
     ====         ====
</TABLE>
 
                                       45
<PAGE>   55
 
                        COMPARISON OF STOCKHOLDER RIGHTS
 
     R&B Falcon and Cliffs Drilling are both incorporated under the laws of the
State of Delaware. Upon consummation of the Merger, the holders of Cliffs
Drilling Common Stock upon exchange of their shares will become holders of R&B
Falcon Common Stock, and their rights as such will be governed by the DGCL, the
Amended and Restated Certificate of Incorporation of R&B Falcon and the Amended
and Restated Bylaws of R&B Falcon (the "R&B Falcon Certificate" and the "R&B
Falcon Bylaws," respectively), and the R&B Falcon Rights Plan, each as in effect
at the Effective Time. The following is a comparison of the material rights of
the holders of R&B Falcon Common Stock and Cliffs Drilling Common Stock.
 
     The following summary does not purport to be a complete statement of the
provisions affecting, and the differences between, the rights of holders of R&B
Falcon Common Stock and Cliffs Drilling Common Stock. This summary is qualified
in its entirety by reference to the DGCL, the R&B Falcon Certificate and the R&B
Falcon Bylaws and the Certificate of Incorporation, as amended, and Bylaws of
Cliffs Drilling (the "Cliffs Drilling Certificate" and the "Cliffs Drilling
Bylaws," respectively).
 
AUTHORIZED CAPITAL STOCK
 
     The Cliffs Drilling Certificate authorizes 30,000,000 shares of Cliffs
Drilling Common Stock and 3,000,000 shares of Cliffs Drilling preferred stock,
no par value per share.
 
     The R&B Falcon Certificate authorizes 550,000,000 shares of R&B Falcon
Common Stock and 50,000,000 Shares of R&B Falcon preferred stock, par value $.01
per share.
 
RIGHTS PLANS
 
     Both Cliffs Drilling and R&B Falcon have adopted rights plans that are
intended to protect stockholders from hostile takeovers. The Cliffs Drilling
Rights Plan and the R&B Falcon Rights Plan are substantially similar. The Cliffs
Drilling Rights Plan has been amended so that the signing of the Merger
Agreement and the consummation of the Merger and related transactions will not
trigger the provisions of the plan.
 
BOARD OF DIRECTORS
 
     The Cliffs Drilling Certificate provides that the number of directors
comprising the Cliffs Drilling Board shall be as stated in the Cliffs Drilling
Bylaws, provided that the Cliffs Drilling Board consist of not less than three
and not more than fifteen persons. The Cliffs Drilling Board can change the
number of directors without stockholder approval. The Cliffs Drilling Board
currently consists of seven directors. The Cliffs Drilling Board is divided into
three classes of directors as equal in number as possible. The term of office of
each class is three years, each term expiring in a different year.
 
     The R&B Falcon Certificate provides that the number of directors shall be
fixed from time to time by, or in the manner provided in, the R&B Falcon Bylaws.
The R&B Falcon Board can amend the R&B Falcon Bylaws to change the number of
directors without stockholder approval. The R&B Falcon Bylaws provide that the
R&B Falcon Board consist of not less than one nor more than fifteen persons. The
R&B Falcon Board currently consists of ten directors. The R&B Falcon Certificate
also provides for a staggered Board of Directors consisting of three classes,
Class I, Class II and Class III. The current terms of the directors in Class I,
Class II and Class III expire at the annual stockholders meeting in 2001, 1999
and 2000, respectively. Directors serve for terms expiring on the third annual
stockholders meeting following the stockholders meeting at which they are
elected. Directors elected to fill a vacancy or newly created directorship shall
serve the unexpired portion of the term of the class to which they are elected.
The R&B Falcon Certificate also requires that no more than a minority of the
directors necessary to constitute a quorum of the R&B Falcon Board may be
non-United States citizens.
 
MONETARY LIABILITY OF DIRECTORS
 
     The Cliffs Drilling Certificate and the R&B Falcon Certificate each provide
for the elimination of personal monetary liability of directors to the fullest
extent permissible under the DGCL.
                                       46
<PAGE>   56
 
VOTING RIGHTS
 
     Each share of Cliffs Drilling Common Stock and R&B Falcon Common Stock is
entitled to one vote.
 
FOREIGN OWNERSHIP LIMITATION
 
     The Cliffs Drilling Certificate does not contain any restrictions on the
foreign ownership of the stock of Cliffs Drilling.
 
     The R&B Falcon Certificate provides that transfers of any class of R&B
Falcon Common Stock that would result in persons who are not citizens of the
United States owning in excess of 24% of the outstanding shares of R&B Falcon
Common Stock will be void and ineffective.
 
REMOVAL OF DIRECTORS AND FILLING VACANCIES ON THE BOARD OF DIRECTORS
 
     Under the DGCL, a director of a corporation with a classified board may be
removed only for cause, unless the certificate of incorporation provides
otherwise. The Cliffs Drilling Certificate provides that directors may be
removed only for cause by the affirmative vote of 80% or more of the voting
power of the outstanding capital stock of Cliffs Drilling entitled to vote at an
election of directors. The Cliffs Drilling Certificate provides that any
vacancy, whether arising through death, resignation or removal of a director, or
through an increase in the number of directors of any class, shall be filled by
a majority vote of the remaining directors then in office, even if less than a
quorum exists.
 
     The R&B Falcon Certificate is silent on the removal of directors, and under
the DGCL, R&B Falcon stockholders representing a majority of the voting power of
the outstanding shares entitled to vote at an election of directors may remove
an R&B director, but only for cause. The R&B Falcon Certificate provides that
vacancies on the R&B Falcon Board, however created, may only be filled by a
majority vote of the remaining directors then in office, even if less than a
quorum exists.
 
STOCKHOLDER ACTION WITHOUT A MEETING
 
     Both the Cliffs Drilling Certificate and the R&B Falcon Certificate
prohibit action by written consent of stockholders.
 
SPECIAL MEETINGS OF STOCKHOLDERS
 
     The Cliffs Drilling Certificate provides that a special meeting of
stockholders may be called only by the Chairman of the Cliffs Drilling Board and
shall be called by the Chairman at the request in writing of a majority of the
Cliffs Drilling Board.
 
     The R&B Falcon Certificate provides that a special meeting of stockholders
may be called by the Chairman or the President and shall be called by the
Chairman, the President or the Secretary at the request in writing of a majority
of the R&B Falcon Board.
 
CHARTER AND BYLAW AMENDMENTS
 
     The Cliffs Drilling Certificate provides that the affirmative vote of the
holders of 80% of the outstanding shares of capital stock entitled to vote in
the election of directors is required to amend, modify or repeal any the
provisions set forth in Article SEVENTH (which contains, among other things,
provisions with respect to the staggered board and the filling of vacancies and
newly created directorships). In addition, the Cliffs Drilling Certificate
requires the affirmative vote of the holders of at least 80% of the voting power
of the outstanding shares of capital stock to amend, modify or repeal the
charter provisions with respect to (i) unanimous written consent of stockholders
and (ii) calling special meetings of stockholders. See "-- Stockholder Action
Without a Meeting" and "-- Special Meetings of Stockholders" above. The Cliffs
Drilling Certificate and the Cliffs Drilling Bylaws provide that the provisions
of the Cliffs Drilling Bylaws relating to (i) prior notice of stockholder
proposals, (ii) nomination of directors, (iii) the number of directors and the
staggered board and (iv) amendments to the Cliffs Drilling Bylaws may be altered
or repealed only by
 
                                       47
<PAGE>   57
 
the affirmative vote of the holders of at least 80% of the voting power of the
outstanding shares of Cliffs Drilling capital stock, and the provision of the
Cliffs Drilling Certificate so requiring also may only be amended, modified or
repealed by the affirmative vote of the holders of at least 80% of the voting
power of the outstanding shares of Cliffs Drilling capital stock.
 
     The R&B Falcon Certificate provides that the affirmative vote of the
holders of 66 2/3% of all classes of capital stock entitled to vote in the
election of directors is required to alter, amend or adopt any charter
provisions inconsistent with Article EIGHTH (which contains, among other things,
provisions with respect to the supermajority stockholder vote required for Bylaw
amendments, the staggered board, removal and replacement of directors, written
consent and the calling of special stockholder meetings). The R&B Falcon
Certificate also provides that a majority of the total number of authorized
directors has the power to adopt, amend or repeal the R&B Falcon Bylaws and that
the affirmative vote of the holders of 66 2/3% of the voting power of the then
issued and outstanding shares of capital stock entitled to vote in the election
of directors is required to adopt, amend or repeal the R&B Falcon Bylaws.
 
              BENEFICIAL OWNERSHIP OF CLIFFS DRILLING COMMON STOCK
 
     The following table shows the number of shares of Cliffs Drilling Common
Stock beneficially owned as of September 1, 1998 by each director, by certain
executive officers and by all directors and executive officers as a group. No
person or group (as that term is used in the Exchange Act) is known to Cliffs
Drilling to beneficially own more than 5% of the outstanding shares of Cliffs
Drilling Common Stock as of September 1, 1998. Unless otherwise indicated in the
footnotes to the table, to the knowledge of Cliffs Drilling, each of the named
persons and members of the group has sole voting and investment (dispositive)
power with respect to the shares shown.
 
<TABLE>
<CAPTION>
                          NAME                                AMOUNT       PERCENTAGE
                          ----                            ---------------  ----------
<S>                                                       <C>       <C>    <C>
Douglas E. Swanson......................................  109,224   (1,2)      *
Michael M. Cone.........................................   22,000   (3)        *
Joseph E. Reid..........................................    6,000   (3)        *
Donald W. Keller........................................    5,000   (3)        *
John D. Weil............................................    4,005   (3,4)      *
H. Robert Hirsch........................................    4,000   (3)        *
Robert M. McInnes.......................................    3,000   (3)        *
Edward A Guthrie........................................   71,000   (1,2)      *
Gary W. Owen............................................   46,000   (1,2)      *
Charles M. McCall.......................................   44,000   (1,2)      *
Jim R. Wise.............................................   43,000   (1,2)      *
All directors and executive officers as a group (13
  persons)..............................................  456,429   (1,5)     2.8%
</TABLE>
 
- ---------------
 
 *  less than 1.0% of class
 
(1) Does not include shares of Common Stock owned by Cliffs Drilling's 401(k)
    Plan for the benefit of employees of Cliffs Drilling, consisting of 9,883,
    5,270, 2,529, 6,576 and 300 shares for Messrs. Swanson, Guthrie, Owen,
    McCall and Wise, respectively, and 31,369 shares for the directors and
    executive officers as a group (13 persons), as of June 30, 1998.
 
(2) Includes 98,000, 65,000, 34,000, 40,000 and 43,000 shares which may be
    acquired upon the exercise of options granted to Messrs. Swanson, Guthrie,
    Owen, McCall and Wise, respectively.
 
(3) Includes 2,000 shares of Common Stock which may be acquired upon the
    exercise of options.
 
(4) The information shown above was obtained in part from a Form 4 dated June
    15, 1998, as filed with the Securities and Exchange Commission (the
    "Commission") by John D. Weil.
 
(5) In addition to the options specifically described in the foregoing
    footnotes, includes 88,000 shares which may be acquired upon the exercise of
    options granted to two executive officers excluding those named.
 
                                       48
<PAGE>   58
 
                             STOCKHOLDER PROPOSALS
 
     If the merger is approved by the stockholders of Cliffs Drilling and
consummated, Cliffs Drilling will not hold an Annual Meeting of Stockholders in
1998. If the Merger is not approved by the stockholders of Cliffs Drilling or
otherwise not consummated, Cliffs Drilling intends to hold an Annual Meeting of
Stockholders in May 1999. Any proposals of stockholders of Cliffs Drilling
intended to be presented at the Annual Meeting of Stockholders of Cliffs
Drilling must be submitted not less than 80 days prior to the meeting; provided,
that in the event of less than 90 days notice or prior public disclosure of the
date of the meeting, then notice by the stockholder to be timely must be
received not later than the close of business on the tenth day following the
date on which such notice of the date of the annual meeting was mailed or such
public disclosure made. Such proposals are required to be addressed to the
Secretary of Cliffs Drilling at 1200 Smith Street, Suite 300, Houston, Texas
77002.
 
                         INDEPENDENT PUBLIC ACCOUNTANTS
 
     Representatives of Ernst & Young LLP are expected to be present at the
Cliffs Drilling Special Meeting to respond to appropriate questions of
stockholders and to make a statement if they so desire.
 
                                 LEGAL MATTERS
 
     The validity of the shares of R&B Falcon Common Stock to be issued in
connection with the Merger will be passed upon by Gardere Wynne Sewell & Riggs,
L.L.P., Houston, Texas. Certain tax consequences of the Merger will be passed
upon for Cliffs Drilling by Griggs & Harrison, P.C., Houston, Texas.
 
                                    EXPERTS
 
     The consolidated financial statements included in the R&B Falcon Annual
Report on Form 10-K for the year ended December 31, 1997, incorporated herein by
reference, have been audited by Arthur Andersen LLP, independent public
accountants, as indicated in their report with respect thereto, and are
incorporated by reference herein in reliance upon the authority of said firm as
experts in accounting and auditing in giving said report.
 
     With respect to the unaudited interim financial information of R&B Falcon
for the quarters ended March 31, 1998 and 1997 and the six months ended June 30,
1998 and 1997, Arthur Andersen LLP has applied limited procedures in accordance
with professional standards for a review of that information. However, their
separate report thereon states that they did not audit and they do not express
an opinion on that interim financial information. Accordingly, the degree of
reliance on their report on that information should be restricted in light of
the limited nature of the review procedures applied. In addition, the
accountants are not subject to the liability provisions of Section 11 of the
Securities Act for their report on the unaudited interim financial information
because that report is not a "report" or a "part" of the registration statement
prepared or certified by the accountants within the meaning of Sections 7 and 11
of the Securities Act.
 
     The consolidated financial statements of Cliffs Drilling appearing in
Cliffs Drilling's Annual Report (Form 10-K) for the year ended December 31,
1997, have been audited by Ernst & Young LLP, independent auditors, as set forth
in their report thereon and incorporated herein by reference. Such consolidated
financial statements are incorporated herein by reference in reliance upon such
report given upon the authority of such firm as experts in accounting and
auditing.
 
                                       49
<PAGE>   59
 
                                                                      APPENDIX A
 
                          AGREEMENT AND PLAN OF MERGER
                                     AMONG
                            R&B FALCON CORPORATION,
                          RBF CLIFFS ACQUISITION CORP.
                                      AND
                            CLIFFS DRILLING COMPANY
 
                                AUGUST 21, 1998
<PAGE>   60
 
                               TABLE OF CONTENTS
 
<TABLE>
<CAPTION>
                                                               PAGE
                                                               ----
<S>                                                            <C>
ARTICLE I -- THE MERGER.....................................    A-1
  1.1 The Merger............................................    A-1
  1.2 Closing Date..........................................    A-1
  1.3 Consummation of the Merger............................    A-1
  1.4 Effects of the Merger.................................    A-2
  1.5 Certificate of Incorporation; Bylaws..................    A-2
  1.6 Directors and Officers................................    A-2
  1.7 Conversion of Securities..............................    A-2
  1.8 Exchange of Certificates; Fractional Shares...........    A-2
  1.9 Lost Certificates.....................................    A-3
  1.10 Taking of Necessary Action; Further Action...........    A-3
ARTICLE II -- REPRESENTATIONS AND WARRANTIES................    A-3
  2.1 Representations and Warranties of R&B Falcon and
     Sub....................................................    A-3
     (a) Organization and Compliance with Law...............    A-3
     (b) Capitalization.....................................    A-4
     (c) Authorization and Validity of Agreement............    A-5
     (d) No Approvals or Notices Required; No Conflict with
         Instruments to which R&B Falcon or any of the R&B
         Falcon Subsidiaries is a Party.....................    A-5
     (e) Commission Filings; Financial Statements...........    A-5
     (f) Absence of Undisclosed Liabilities.................    A-6
     (g) Conduct of Business in the Ordinary Course; Absence
         of Certain Changes and Events......................    A-6
     (h) Tax Representation.................................    A-6
     (i) Brokers............................................    A-7
     (j) Interim Operations of Sub..........................    A-7
     (k) Stockholder Approval...............................    A-7
  2.2 Representations and Warranties of Cliffs..............    A-7
     (a) Organization and Compliance with Law...............    A-7
     (b) Capitalization.....................................    A-7
     (c) Authorization and Validity of Agreement............    A-8
     (d) No Approvals or Notices Required; No Conflict with
         Instruments to which Cliffs or any of the Cliffs
         Subsidiaries is a Party............................    A-8
     (e) Commission Filings; Financial Statements...........    A-9
     (f) Absence of Undisclosed Liabilities.................    A-9
     (g) Conduct of Business in the Ordinary Course; Absence
         of Certain Changes and Events......................    A-9
     (h) Litigation.........................................   A-10
     (i) Employee Benefit Plans.............................   A-10
     (j) Taxes..............................................   A-11
     (k) Environmental Matters..............................   A-12
     (l) Severance Payments.................................   A-13
</TABLE>
 
                                        i
<PAGE>   61
 
<TABLE>
<CAPTION>
                                                               PAGE
                                                               ----
<S>                                                            <C>
     (m) Voting Requirements................................   A-14
     (n) No Excess Parachute Payments; Section 162(m) of the
         Code...............................................   A-14
     (o) Brokers............................................   A-14
     (p) Labor Relations....................................   A-14
     (q) Insurance..........................................   A-14
     (r) State Takeover Laws................................   A-14
     (s) Cliffs Rights Plan.................................   A-14
ARTICLE III -- COVENANTS OF CLIFFS PRIOR TO THE EFFECTIVE
  TIME......................................................   A-15
  3.1 Conduct of Business by Cliffs Pending the Merger......   A-15
  3.2 Proxy Statement.......................................   A-16
  3.3 Meeting of Stockholders of Cliffs.....................   A-17
  3.4 No Solicitation.......................................   A-17
  3.5 Affiliate Letters.....................................   A-18
  3.6 Waivers and Releases..................................   A-18
  3.7 Obtain Tax Opinion....................................   A-18
ARTICLE IV -- COVENANTS OF R&B FALCON PRIOR TO THE EFFECTIVE
  TIME......................................................   A-18
  4.1 Conduct of Business by R&B Falcon Pending the
     Merger.................................................   A-18
  4.2 Registration Statement................................   A-18
  4.3 Adequate R&B Falcon Common Stock......................   A-19
  4.4 Stock Exchange Listing................................   A-19
ARTICLE V -- ADDITIONAL AGREEMENTS..........................   A-19
  5.1 Accountants Letters...................................   A-19
  5.2 Filings; Consents; Reasonable Efforts.................   A-19
  5.3 Notification of Certain Matters.......................   A-19
  5.4 Agreement to Defend...................................   A-20
  5.5 Expenses..............................................   A-20
  5.6 R&B Falcon's Board of Directors.......................   A-20
  5.7 Employment Agreements.................................   A-20
  5.8 Cliffs Employee Benefits..............................   A-20
  5.9 Cliffs Stock Options..................................   A-21
  5.10 New R&B Falcon Option Grants.........................   A-22
  5.11 Post-Effective Time Mailing..........................   A-22
  5.12. Tax-Free Reorganization.............................   A-22
  5.13 Indemnification......................................   A-22
  5.14 Cliffs Rights Plan...................................   A-23
ARTICLE VI -- CONDITIONS....................................   A-23
  6.1 Conditions to Obligation of Each Party to Effect the
     Merger.................................................   A-23
  6.2 Additional Conditions to Obligations of R&B Falcon....   A-24
  6.3 Additional Conditions to Obligations of Cliffs........   A-25
ARTICLE VII -- MISCELLANEOUS................................   A-26
  7.1 Termination...........................................   A-26
  7.2 Effect of Termination.................................   A-26
  7.3 Waiver and Amendment..................................   A-27
  7.4 Nonsurvival of Representations, Warranties and
     Agreements.............................................   A-27
  7.5 Public Statements.....................................   A-27
  7.6 Assignment............................................   A-27
  7.7 Notices...............................................   A-27
  7.8 Governing Law.........................................   A-28
  7.9 Severability..........................................   A-28
  7.10 Counterparts.........................................   A-28
</TABLE>
 
                                       ii
<PAGE>   62
 
<TABLE>
<CAPTION>
                                                               PAGE
                                                               ----
<S>                                                            <C>
  7.11 Headings.............................................   A-28
  7.12 Entire Agreement; Third Party Beneficiaries..........   A-28
  7.13 Disclosure Letters...................................   A-28
</TABLE>
 
                                    EXHIBITS
 
  Exhibit A -- Form of Affiliate Letter
 
                                   SCHEDULES
 
  Schedule 3.6 -- Cliffs Executives -- Waiver and Release Payments
  Schedule 5.7 -- Cliffs Executives -- Employment Agreement Terms
  Schedule 5.10 -- Option Grants
 
                                       iii
<PAGE>   63
 
                          AGREEMENT AND PLAN OF MERGER
 
     This Agreement and Plan of Merger, dated as of the 21st day of August, 1998
(the "Agreement"), is among R&B Falcon Corporation, a Delaware corporation ("R&B
Falcon"), RBF Cliffs Acquisition Corp., a newly formed Delaware corporation and
a wholly owned subsidiary of R&B Falcon ("Sub"), and Cliffs Drilling Company, a
Delaware corporation ("Cliffs").
 
                                  WITNESSETH:
 
     WHEREAS, subject to and in accordance with the terms and conditions of this
Agreement, the respective Boards of Directors of R&B Falcon, Sub and Cliffs, and
R&B Falcon as sole stockholder of Sub, after determining that it is in the best
interests of their respective stockholders, have approved the merger of Sub with
and into Cliffs (the "Merger"), whereby each issued and outstanding share of
common stock, $0.01 par value per share, of Cliffs ("Cliffs Common Stock") not
owned directly or indirectly by Cliffs will be converted into the right to
receive 1.7 shares of common stock, $0.01 par value per share, of R&B Falcon
("R&B Falcon Common Stock"), as provided herein;
 
     WHEREAS, for federal income tax purposes, it is intended that the Merger
shall qualify as a reorganization within the meaning of Section 368(a) of the
Internal Revenue Code of 1986, as amended (the "Code");
 
     WHEREAS, the Merger is intended to be treated as an acquisition for
accounting purposes; and
 
     WHEREAS, the parties hereto desire to set forth certain representations,
warranties and covenants made by each to the other as an inducement to the
consummation of the Merger;
 
     NOW, THEREFORE, in consideration of the premises and of the mutual
representations, warranties and covenants herein contained, the parties hereto
hereby agree as follows:
 
                                   ARTICLE I
 
                                   THE MERGER
 
     1.1  The Merger. Subject to and in accordance with the terms and conditions
of this Agreement and in accordance with the General Corporation Law of the
State of Delaware (the "DGCL"), at the Effective Time (as defined in Section
1.3) Sub shall be merged with and into Cliffs. As a result of the Merger, the
separate corporate existence of Sub shall cease and Cliffs shall continue as the
surviving corporation (sometimes referred to herein as the "Surviving
Corporation"), and all the properties, rights, privileges, powers and franchises
of Cliffs and Sub shall vest in the Surviving Corporation, without any transfer
or assignment having occurred, and all debts, liabilities and duties of Cliffs
and Sub shall attach to the Surviving Corporation, all in accordance with the
DGCL.
 
     1.2  Closing Date. The closing of the transactions contemplated by this
Agreement (the "Closing") shall take place at the offices of Gardere Wynne
Sewell & Riggs, L.L.P., 333 Clay, Suite 800, Houston, Texas 77002, as soon as
practicable after the satisfaction or waiver of the conditions set forth in
Article VI or at such other time and place and on such other date as R&B Falcon
and Cliffs shall agree; provided, that the closing conditions set forth in
Article VI shall have been satisfied or waived at or prior to such time. The
date on which the Closing occurs is herein referred to as the "Closing Date."
 
     1.3  Consummation of the Merger. As soon as practicable on the Closing
Date, the parties hereto will cause the Merger to be consummated by filing with
the Secretary of State of Delaware a certificate of merger in such form as
required by, and executed in accordance with, the relevant provisions of the
DGCL. The "Effective Time" of the Merger as that term is used in this Agreement
shall mean such time as the certificate of merger is duly filed with the
Secretary of State of Delaware or at such later time (not to exceed 90 days from
the date the certificate is filed) as is specified in the certificate of merger
pursuant to the mutual agreement of R&B Falcon and Cliffs.
 
                                       A-1
<PAGE>   64
 
     1.4  Effects of the Merger. The Merger shall have the effects set forth in
the applicable provisions of the DGCL.
 
     1.5  Certificate of Incorporation; Bylaws. At the Effective Time, the
Certificate of Incorporation and Bylaws of Cliffs, as in effect immediately
prior to the Effective Time, shall be the Certificate of Incorporation and
Bylaws, respectively, of Surviving Corporation.
 
     1.6  Directors and Officers. At and after the Effective Time, Douglas E.
Swanson, Steven A. Webster, and Paul B. Loyd shall be the directors of the
Surviving Corporation, and shall serve as such until the next annual meeting of
the Surviving Corporation (or until their earlier resignation or removal) or
until their respective successors are duly elected and qualified. The officers
of Cliffs immediately prior to the Effective Time shall be the officers of the
Surviving Corporation at and after the Effective Time, to serve in such
capacities until their successors are duly elected or until their earlier
resignation or removal.
 
     1.7  Conversion of Securities. Subject to the terms and conditions of this
Agreement, at the Effective Time, by virtue of the Merger and without any action
on the part of R&B Falcon, Cliffs, Sub or their stockholders:
 
          (a) Each share of Cliffs Common Stock issued and outstanding
     immediately prior to the Effective Time, other than any shares of Cliffs
     Common Stock to be canceled pursuant to Section 1.7(b), shall be converted
     into the right to receive 1.7 shares of R&B Falcon Common Stock; provided,
     however, that no fractional shares of R&B Falcon Common Stock shall be
     issued, and, in lieu thereof, a cash payment shall be made in accordance
     with Section 1.8(d) hereof.
 
          (b) Each share of Cliffs Common Stock held in the treasury of Cliffs
     and each share of Cliffs Common Stock owned by Sub, R&B Falcon or any
     direct or indirect wholly owned subsidiary of R&B Falcon or of Cliffs
     immediately prior to the Effective Time shall be canceled and extinguished
     without any conversion thereof and no payment shall be made with respect
     thereto.
 
          (c) Each share of common stock, par value $0.01 per share, of Sub
     issued and outstanding immediately prior to the Effective Time shall be
     converted into one share of common stock, $0.01 par value per share, of the
     Surviving Corporation.
 
     1.8  Exchange of Certificates; Fractional Shares.
 
          (a) As soon as practicable after the Effective Time, each holder of a
     certificate that prior thereto represented shares of Cliffs Common Stock
     shall be entitled, upon surrender thereof to R&B Falcon or its transfer
     agent, to receive in exchange therefor, a certificate or certificates
     representing the number of whole shares of R&B Falcon Common Stock into
     which the shares of Cliffs Common Stock so surrendered shall have been
     converted as aforesaid, in such denominations and registered in such names
     as such holder may request. Each holder of shares of Cliffs Common Stock
     who would otherwise be entitled to a fraction of a share of R&B Falcon
     Common Stock shall, upon surrender of the certificates representing such
     shares held by such holder to R&B Falcon or its transfer agent, be paid an
     amount in cash in accordance with the provisions of Section 1.8(d). Until
     so surrendered and exchanged, each certificate that prior to the Effective
     Time represented shares of Cliffs Common Stock shall represent solely the
     right to receive R&B Falcon Common Stock and cash in lieu of fractional
     shares, if any. Unless and until any such certificates shall be so
     surrendered and exchanged, no dividends or other distributions payable to
     the holders of R&B Falcon Common Stock, as of any time on or after the
     Effective Time, shall be paid to the holders of such certificates that
     prior to the Effective Time represented shares of Cliffs Common Stock;
     provided, however, that, upon any such surrender and exchange of such
     certificates, there shall be paid to the record holders of the certificates
     issued and exchanged therefor the amount, without interest thereon, of
     dividends and other distributions, if any, that theretofore were declared
     and became payable after the Effective Time with respect to the number of
     whole shares of R&B Falcon Common Stock issued to such holder.
 
          (b) All shares of R&B Falcon Common Stock issued upon the surrender
     for exchange of certificates that prior to the Effective Time represented
     shares of Cliffs Common Stock in accordance
 
                                       A-2
<PAGE>   65
 
     with the terms hereof (together with any cash paid pursuant to Section
     1.8(d)) shall be deemed to have been issued in full satisfaction of all
     rights pertaining to such shares of Cliffs Common Stock. At and after the
     Effective Time, there shall be no further registration of transfers on the
     stock transfer books of the Surviving Corporation of the shares of Cliffs
     Common Stock that were outstanding immediately prior to the Effective Time.
     If, after the Effective Time, certificates which prior to the Effective
     Time represented shares of Cliffs Common Stock are presented to the
     Surviving Corporation for any reason, they shall be canceled and exchanged
     as provided in this Article I.
 
          (c) If any certificate for shares of R&B Falcon Common Stock is to be
     issued in a name other than that in which the certificate surrendered in
     exchange therefor is registered, it shall be a condition of the issuance
     thereof that the certificate so surrendered shall be properly endorsed and
     otherwise in proper form for transfer and that the person requesting such
     exchange shall have paid to R&B Falcon or its transfer agent any transfer
     or other taxes required by reason of the issuance of a certificate for
     shares of R&B Falcon Common Stock in any name other than that of the
     registered holder of the certificate surrendered, or established to the
     satisfaction of R&B Falcon or its transfer agent that such tax has been
     paid or is not payable.
 
          (d) No fraction of a share of R&B Falcon Common Stock shall be issued,
     but in lieu thereof each holder of Cliffs Common Stock who would otherwise
     be entitled to a fraction of a share of R&B Falcon Common Stock shall, upon
     surrender of the certificate formerly representing Cliffs Common Stock held
     by such holder to R&B Falcon or its transfer agent, be paid an amount in
     cash equal to the value of such fraction of a share based upon the closing
     sales price of R&B Falcon Common Stock, as reported on the New York Stock
     Exchange, on the last day on which there is a reported trade in the R&B
     Falcon Common Stock prior to the date on which the Effective Time occurs.
     No interest shall be paid on such amount. All shares of Cliffs Common Stock
     held by a record holder shall be aggregated for purposes of computing the
     number of shares of R&B Falcon Common Stock to be issued pursuant to this
     Article I and cash in lieu of fractional shares payable hereunder.
 
          (e) None of R&B Falcon, Sub, Cliffs, the Surviving Corporation or
     their transfer agents shall be liable to a holder of shares of Cliffs
     Common Stock for any amount properly paid to a public official pursuant to
     applicable property, escheat or similar laws.
 
     1.9  Lost Certificates. If any certificate representing shares of Cliffs
Common Stock shall have been lost, stolen or destroyed, upon the making of an
affidavit of that fact by the person claiming such certificate to be lost,
stolen or destroyed and, if required by R&B Falcon, the posting by such person
of a bond in such reasonable amount as R&B Falcon may direct as indemnity
against any claim that may be made against it or the Surviving Corporation with
respect to such certificate, the shares of R&B Falcon Common Stock issuable in
exchange for the shares represented by such lost, stolen or destroyed
certificate shall be issued to such person and, if applicable, any cash in lieu
of fractional shares shall be paid to such person.
 
     1.10  Taking of Necessary Action; Further Action. The parties hereto shall
take all such reasonable and lawful action as may be necessary or appropriate in
order to effectuate the Merger as promptly as possible. If, at any time after
the Effective Time, any such further action is necessary or desirable to carry
out the purposes of this Agreement and to vest the Surviving Corporation with
full right, title and possession to all assets, property, rights, privileges,
powers and franchises of Cliffs or Sub, such corporations shall direct their
respective officers and directors to take all such lawful and necessary action.
 
                                   ARTICLE II
 
                         REPRESENTATIONS AND WARRANTIES
 
     2.1  Representations and Warranties of R&B Falcon and Sub. R&B Falcon and
Sub hereby jointly and severally represent and warrant to Cliffs that:
 
          (a) Organization and Compliance with Law. Each of R&B Falcon and its
     consolidated subsidiaries (the "R&B Falcon Subsidiaries") is a corporation
     duly organized, validly existing and in good
                                       A-3
<PAGE>   66
 
     standing under the laws of the jurisdiction in which it is chartered or
     organized and has all requisite corporate power and authority and all
     necessary governmental authorizations to own, lease and operate all of its
     properties and assets and to carry on its business as now being conducted,
     except where the failure to be so organized, existing or in good standing
     or to have such governmental authority would not have a material adverse
     effect on the financial condition, results of operations or business of R&B
     Falcon and the R&B Falcon Subsidiaries, taken as a whole (a "R&B Falcon
     MAE"). A R&B Falcon MAE shall not be deemed to include material adverse
     effects caused by circumstances or occurrences that similarly affect the
     contract drilling industry generally or the United States economy
     generally. Except as set forth in Section 2.1(a) of the disclosure letter
     delivered by R&B Falcon to Cliffs on the date hereof (the "R&B Falcon
     Disclosure Letter"), each of R&B Falcon and the R&B Falcon Subsidiaries is
     duly qualified as a foreign corporation to do business, and is in good
     standing, in each jurisdiction in which the property owned, leased or
     operated by it or the nature of the business conducted by it makes such
     qualification necessary, except in such jurisdictions where the failure to
     be duly qualified does not and would not, either individually or in the
     aggregate, have a R&B Falcon MAE. Each of R&B Falcon and the R&B Falcon
     Subsidiaries is in compliance with all applicable laws, judgments, orders,
     rules and regulations, domestic and foreign, except where failure to be in
     such compliance would not have a R&B Falcon MAE.
 
          (b) Capitalization.
 
             (i) The authorized capital stock of R&B Falcon consists of
        550,000,000 shares of R&B Falcon Common Stock and 50,000,000 shares of
        preferred stock, par value $0.01 per share ("R&B Falcon Preferred
        Stock"), of which 1,688,000 shares of R&B Falcon Preferred Stock has
        been designated Series A Junior Participating Preferred Stock. As of
        August 1, 1998, there were issued and outstanding 166,226,374 shares of
        R&B Falcon Common Stock, no shares of R&B Falcon Common Stock were held
        as treasury shares, and no shares of R&B Falcon Preferred Stock were
        issued and outstanding. All issued shares of R&B Falcon Common Stock
        were duly authorized and validly issued and are fully paid and
        nonassessable and no holder thereof is entitled to preemptive rights.
        All shares of R&B Falcon Common Stock to be issued pursuant to the
        Merger, when issued in accordance with this Agreement, will be duly
        authorized and validly issued, fully paid and nonassessable and will not
        violate the preemptive rights of any person. Except as set forth in
        Section 2.1(b) of the R&B Falcon Disclosure Letter, R&B Falcon is not a
        party to, and is not aware of, any voting agreement, voting trust or
        similar agreement or arrangement relating to any class or series of its
        capital stock, or any agreement or arrangement providing for
        registration rights with respect to any capital stock or other
        securities of R&B Falcon as to which the registration statement has not
        already become effective.
 
             (ii) As of August 1, 1998, there were outstanding options to
        purchase 4,536,442 shares of R&B Falcon Common Stock ("R&B Falcon
        Options"). Other than (A) as set forth in this Section 2.1(b), (B) as
        described in Section 2.1(b) of the R&B Falcon Disclosure Letter, (C) as
        contemplated by this Agreement, (D) pursuant to the exercise of R&B
        Falcon Options, and (E) pursuant to the Rights Agreement between R&B
        Falcon and American Stock Transfer & Trust Company dated December 23,
        1997, R&B Falcon will not, prior to the Effective Time, issue, commit to
        issue or grant rights to acquire in excess of an aggregate of 75,000,000
        additional shares of R&B Falcon Common Stock.
 
             (iii) Except as set forth in Section 2.1(b) of the R&B Falcon
        Disclosure Letter, all outstanding shares of capital stock of the R&B
        Falcon Subsidiaries (A) are owned by R&B Falcon or a wholly owned
        subsidiary of R&B Falcon, free and clear of all liens, charges,
        encumbrances, adverse claims and options of any nature, (B) were duly
        authorized and validly issued and are fully paid and nonassessable, and
        (C) have not been issued in violation of any preemptive rights. There
        are not now, and at the Effective Time there will not be, any
        outstanding options, warrants, scrip, rights to subscribe for, calls or
        commitments of any character whatsoever relating to, or securities or
        rights convertible into or exchangeable for, shares of any class of
        capital stock of the R&B Falcon Subsidiaries, or contracts,
        understandings or arrangements to which R&B Falcon or a R&B Falcon
        Subsidiary is a party, or by which any of them is or may be bound, to
        issue additional shares of
                                       A-4
<PAGE>   67
 
        capital stock or options, warrants, scrip or rights to subscribe for, or
        securities or rights convertible into or exchangeable for, any
        additional shares of capital stock of any R&B Falcon Subsidiary.
 
             (iv) As of the date hereof, the authorized capital stock of Sub
        consists of 1,000 shares of common stock, par value $0.01 per share, all
        of which were duly authorized and validly issued and are fully paid and
        nonassessable and are owned by R&B Falcon.
 
          (c) Authorization and Validity of Agreement. R&B Falcon and Sub have
     all requisite corporate power and authority to enter into this Agreement
     and to perform their obligations hereunder. The execution and delivery by
     R&B Falcon and Sub of this Agreement and the consummation by each of them
     of the transactions contemplated hereby have been duly authorized by all
     necessary corporate action. This Agreement has been duly executed and
     delivered by R&B Falcon and Sub and is the valid and binding obligation of
     R&B Falcon and Sub, enforceable against R&B Falcon and Sub in accordance
     with its terms.
 
          (d) No Approvals or Notices Required; No Conflict with Instruments to
     which R&B Falcon or any of the R&B Falcon Subsidiaries is a Party. Neither
     the execution and delivery of this Agreement nor the performance by R&B
     Falcon or Sub of its obligations hereunder, nor the consummation of the
     transactions contemplated hereby by R&B Falcon and Sub, will (i) conflict
     with the certificate of incorporation or the bylaws of R&B Falcon or the
     charter or bylaws of any of the R&B Falcon Subsidiaries; (ii) assuming
     satisfaction of the requirements set forth in clause (iii) below, violate
     any provision of law applicable to R&B Falcon or any of the R&B Falcon
     Subsidiaries; (iii) except for (A) requirements of Federal or state
     securities laws, (B) requirements arising out of the Hart-Scott-Rodino
     Antitrust Improvements Act of 1976 (the "HSR Act"),(C) requirements of
     notice filings in such foreign jurisdictions as may be applicable, and (D)
     the filing of a certificate of merger by Sub in accordance with the DGCL,
     require any consent or approval of, or filing with or notice to, any public
     body or authority, domestic or foreign, under any provision of law
     applicable to R&B Falcon or any of the R&B Falcon Subsidiaries; or (iv)
     require any consent, approval or notice under, or violate, breach, be in
     conflict with or constitute a default (or an event that, with notice or
     lapse of time or both, would constitute a default) under, or permit the
     termination of any provision of, or result in the creation or imposition of
     any lien upon any properties, assets or business of R&B Falcon or any of
     the R&B Falcon Subsidiaries under, any note, bond, indenture, mortgage,
     deed of trust, lease, franchise, permit, authorization, license, contract,
     instrument or other agreement or commitment or any order, judgment or
     decree to which R&B Falcon or any of the R&B Falcon Subsidiaries is a party
     or by which R&B Falcon or any of the R&B Falcon Subsidiaries or any of its
     or their assets or properties is bound or encumbered, except (A) those that
     have already been given, obtained or filed, (B) those that are required
     pursuant to bank loan agreements, as set forth in Section 2.1(d) of the R&B
     Falcon Disclosure Letter, which R&B Falcon will use its reasonable efforts
     to obtain prior to the Effective Time, and (C) those that, in the
     aggregate, would not have a R&B Falcon MAE.
 
          (e) Commission Filings; Financial Statements. R&B Falcon and each of
     the R&B Falcon Subsidiaries have timely filed all reports, registration
     statements and other filings, together with any amendments required to be
     made with respect thereto, that they have been required to file with the
     Securities and Exchange Commission (the "Commission")under the Securities
     Act of 1933, as amended (the "Securities Act"), and the Securities Exchange
     Act of 1934, as amended (the "Exchange Act"). All reports, registration
     statements and other filings (including all notes, exhibits and schedules
     thereto and documents incorporated by reference therein) filed by R&B
     Falcon with the Commission since January 1, 1998, through the date of this
     Agreement, together with any amendments thereto, are sometimes collectively
     referred to as the "R&B Falcon Commission Filings." As of the respective
     dates of their filing with the Commission, the R&B Falcon Commission
     Filings complied in all material respects with the Securities Act, the
     Exchange Act and the rules and regulations of the Commission thereunder,
     and did not contain any untrue statement of a material fact or omit to
     state a material fact required to be stated therein or necessary to make
     the statements made therein, in light of the circumstances under which they
     were made, not misleading.
 
                                       A-5
<PAGE>   68
 
          Each of the consolidated financial statements (including any related
     notes or schedules) included in the R&B Falcon Commission Filings was
     prepared in accordance with generally accepted accounting principles
     applied on a consistent basis (except as may be noted therein or in the
     notes or schedules thereto) and complied with all applicable rules and
     regulations of the Commission. Such consolidated financial statements
     fairly present the consolidated financial position of R&B Falcon and the
     R&B Falcon Subsidiaries as of the dates thereof and the results of
     operations, cash flows and changes in stockholders' equity for the periods
     then ended (subject, in the case of the unaudited interim financial
     statements, to normal year end audit adjustments on a basis consistent with
     past periods).
 
          (f) Absence of Undisclosed Liabilities.  Except as disclosed in
     Section 2.1(f) of the R&B Falcon Disclosure Letter, as of the date of this
     Agreement, neither R&B Falcon nor any of the R&B Falcon Subsidiaries has
     any liabilities that are reasonably likely to have, individually or in the
     aggregate, a R&B Falcon MAE, except liabilities which are accrued or
     reserved against in the consolidated balance sheet of R&B Falcon as of
     December 31, 1997 or June 30, 1998, included in the R&B Falcon Commission
     Filings or reflected in the notes thereto. Neither R&B Falcon nor any R&B
     Falcon Subsidiary has incurred or paid any liability since June 30, 1998,
     except for liabilities incurred or paid (i) in the ordinary course of
     business consistent with past practice, (ii) in connection with
     transactions contemplated by this Agreement, or (iii) pursuant to
     transactions not prohibited by this Agreement.
 
          (g) Conduct of Business in the Ordinary Course; Absence of Certain
     Changes and Events. Since January 1, 1998, except as contemplated by this
     Agreement or as disclosed in the R&B Falcon Commission Filings or as set
     forth in Section 2.1(g) of the R&B Falcon Disclosure Letter, R&B Falcon and
     the R&B Falcon Subsidiaries have conducted their business only in the
     ordinary and usual course, and there has not been (i) any R&B Falcon MAE or
     any condition, event or development that reasonably may be expected to
     result in a R&B Falcon MAE; (ii) any material change by R&B Falcon in its
     accounting methods, principles or practices; (iii) any revaluation by R&B
     Falcon or any of the R&B Falcon Subsidiaries of any of its or their assets,
     including, without limitation, writing down the value of inventory or
     writing off notes or accounts receivable other than in the ordinary course
     of business; (iv) any declaration, setting aside or payment of any
     dividends or distributions in respect of the R&B Falcon Common Stock, or
     any redemption, purchase or other acquisition of any of its securities or
     any securities of any of the R&B Falcon Subsidiaries; (v) any damage,
     destruction or loss (whether or not covered by insurance) materially
     adversely affecting the properties or business of R&B Falcon and the R&B
     Falcon Subsidiaries, taken as a whole; (vi) any increase in indebtedness
     for borrowed money other than borrowings under existing credit facilities
     or indebtedness incurred in the ordinary course of business; (vii) any
     granting of a security interest or lien on any material property or assets
     of R&B Falcon and the R&B Falcon Subsidiaries, taken as a whole, other than
     (A) liens for taxes not due and payable or which are being contested in
     good faith; (B) maritime liens and mechanics', warehousemen's and other
     statutory liens incurred in the ordinary course of business; (C) defects
     and irregularities in title and encumbrances which are not substantial in
     character or amount and do not materially impair the use of the property or
     asset in question; and (D) liens securing indebtedness incurred in the
     ordinary course of business (collectively, "Permitted Liens"); or (viii)
     any entry by R&B Falcon or a R&B Falcon Subsidiary into any transaction or
     commitment that could reasonably be expected to have a R&B Falcon MAE.
 
          (h) Tax Representation. R&B Falcon has no present plan or intention to
     (i) liquidate the Surviving Corporation, (ii) merge the Surviving
     Corporation with or into another corporation, (iii) sell or otherwise
     dispose of the stock of the Surviving Corporation, except as permitted
     under Section 368 of the Code, (iv) cause or permit the Surviving
     Corporation to sell or otherwise dispose of any of the assets of Cliffs or
     the assets of Sub vested in the Surviving Corporation except for
     dispositions made in the ordinary course of business or except as otherwise
     permitted under Section 368 of the Code, (v) reacquire any of the R&B
     Falcon Common Stock issued to the Cliffs stockholders pursuant to the
     Merger, or (vi) cause or permit the Surviving Corporation to either
     discontinue the historic business of Cliffs or fail to use a substantial
     amount of Cliffs' historic business assets in a business.
 
                                       A-6
<PAGE>   69
 
          (i) Brokers. All negotiations relative to this Agreement and the
     transactions contemplated hereby have been carried out by R&B Falcon
     directly with Cliffs, without the intervention of any person on behalf of
     R&B Falcon in such manner as to give rise to any valid claim by any person
     against Cliffs, the Surviving Corporation, R&B Falcon or any of their
     subsidiaries for a finders' fee, brokerage commission or similar payment,
     other than the fee payable to Donaldson, Lufkin & Jenrette Securities
     Corporation for acting as R&B Falcon's financial advisor and rendering a
     fairness opinion in connection with the Merger. R&B Falcon has provided
     Cliffs with a true, correct and complete copy of the agreement between R&B
     Falcon and Donaldson, Lufkin & Jenrette Securities Corporation, and R&B
     Falcon has no other agreements or understandings (written or oral) with
     respect to such services.
 
          (j) Interim Operations of Sub. Sub was formed solely for the purpose
     of engaging in the transactions contemplated hereby, has engaged in no
     other business activities and has conducted its operations only as
     contemplated hereby.
 
          (k) Stockholder Approval. The approval of the stockholders of R&B
     Falcon is not required under applicable law or stock exchange rules to
     authorize the consummation of the Merger.
 
     2.2  Representations and Warranties of Cliffs. Cliffs hereby represents and
warrants to R&B Falcon that:
 
          (a) Organization and Compliance with Law. Each of Cliffs and its
     consolidated subsidiaries (the "Cliffs Subsidiaries") is a corporation duly
     organized, validly existing and in good standing under the laws of the
     jurisdiction in which it is chartered or organized and has all requisite
     corporate power and authority and all necessary governmental authorizations
     to own, lease and operate all of its properties and assets and to carry on
     its business as now being conducted, except where the failure to be so
     organized, existing or in good standing or to have such governmental
     authority would not have a material adverse effect on the financial
     condition, results of operations or business of Cliffs and the Cliffs
     Subsidiaries, taken as a whole (a "Cliffs MAE"). A Cliffs MAE shall not be
     deemed to include material adverse effects caused by circumstances or
     occurrences that similarly affect the contract drilling industry generally
     or the United States economy generally. Except as set forth in Section
     2.2(a) of the disclosure letter delivered by Cliffs to R&B Falcon on the
     date hereof (the "Cliffs Disclosure Letter"), each of Cliffs and the Cliffs
     Subsidiaries is duly qualified as a foreign corporation to do business, and
     is in good standing, in each jurisdiction in which the property owned,
     leased or operated by it or the nature of the business conducted by it
     makes such qualification necessary, except in such jurisdictions where the
     failure to be duly qualified does not and would not, either individually or
     in the aggregate, have a Cliffs MAE. Each of Cliffs and the Cliffs
     Subsidiaries is in compliance with all applicable laws, judgments, orders,
     rules and regulations, domestic and foreign, except where failure to be in
     such compliance would not have a Cliffs MAE.
 
          (b) Capitalization.
 
             (i) The authorized capital stock of Cliffs consists of 30,000,000
        shares of Cliffs Common Stock and 3,000,000 shares of preferred stock,
        without par value, of which 500,000 shares have been designated as
        Series A Junior Participating Preferred Stock (the "Cliffs Preferred
        Stock"). As of August 20, 1998, there were issued and outstanding
        15,943,326 shares of Cliffs Common Stock, 395,399 shares of Cliffs
        Common Stock were held as treasury shares, and no shares of Cliffs
        Preferred Stock were issued and outstanding. All issued shares of Cliffs
        Common Stock were duly authorized and validly issued and are fully paid
        and nonassessable and no holder thereof is entitled to preemptive
        rights. Except as set forth in Section 2.2(b) of the Cliffs Disclosure
        Letter, Cliffs is not a party to, and is not aware of, any voting
        agreement, voting trust or similar agreement or arrangement relating to
        any class or series of its capital stock, or any agreement or
        arrangement providing for registration rights with respect to any
        capital stock or other securities of Cliffs as to which the registration
        statement has not already become effective.
 
             (ii) As of the date hereof, there are outstanding options (the
        "Cliffs Options") to purchase an aggregate of 621,500 shares of Cliffs
        Common Stock under the Cliffs 1988 Incentive Equity Plan or the Cliffs
        1998 Incentive Equity Plan (collectively, the "Cliffs Stock Option
        Plans"). Other than as
                                       A-7
<PAGE>   70
 
        set forth in this Section 2.2(b), there are not now, and at the
        Effective Time there will not be, any (A) shares of capital stock or
        other equity securities of Cliffs outstanding other than Cliffs Common
        Stock issued pursuant to the exercise of Cliffs Options or issued from
        treasury to satisfy matching obligations pursuant to the Cliffs Drilling
        Company Savings Plan (As Amended and Restated Effective June 21, 1988)
        (the "Cliffs Savings Plan"), or (B) outstanding options, warrants,
        scrip, rights to subscribe for, calls or commitments of any character
        whatsoever relating to, or securities or rights convertible into or
        exchangeable for, shares of any class of capital stock of Cliffs, or
        contracts, understandings or arrangements to which Cliffs is a party, or
        by which it is or may be bound, to issue additional shares of its
        capital stock or options, warrants, scrip or rights to subscribe for, or
        securities or rights convertible into or exchangeable for, any
        additional shares of its capital stock, other than (x) rights to acquire
        shares of Cliffs Preferred Stock pursuant to that certain Rights
        Agreement dated as of June 17, 1997 (the "Cliffs Rights Plan") between
        Cliffs and Harris Trust and Savings Bank, as rights agent and (y) an
        obligation of Cliffs to issue 3,800 shares of Cliffs Common Stock
        pursuant to the Cliffs Drilling Company Compensation Deferral Plan, as
        amended (the "Cliffs Compensation Deferral Plan").
 
             (iii) Except as set forth in Section 2.2(b) of the Cliffs
        Disclosure Letter, all outstanding shares of capital stock of the Cliffs
        Subsidiaries (A) are owned by Cliffs or a wholly owned subsidiary of
        Cliffs, free and clear of all liens, charges, encumbrances, adverse
        claims and options of any nature, (B) were duly authorized and validly
        issued and are fully paid and nonassessable, and (C) have not been
        issued in violation of any preemptive rights. There are not now, and at
        the Effective Time there will not be, any outstanding options, warrants,
        scrip, rights to subscribe for, calls or commitments of any character
        whatsoever relating to, or securities or rights convertible into or
        exchangeable for, shares of any class of capital stock of the Cliffs
        Subsidiaries, or contracts, understandings or arrangements to which
        Cliffs or a Cliffs Subsidiary is a party, or by which any of them is or
        may be bound, to issue additional shares of capital stock or options,
        warrants, scrip or rights to subscribe for, or securities or rights
        convertible into or exchangeable for, any additional shares of capital
        stock of any Cliffs Subsidiary. There are not now, and at the Effective
        Time there will not be, any outstanding contractual obligations of
        Cliffs or any of the Cliffs Subsidiaries to repurchase, redeem or
        otherwise acquire any outstanding shares of capital stock or other
        ownership interests of any Cliffs Subsidiary or to provide funds to or
        make any investment (in the form of a loan, capital contribution or
        otherwise), in any Cliffs Subsidiary or any other entity.
 
          (c) Authorization and Validity of Agreement. Cliffs has all requisite
     corporate power and authority to enter into this Agreement and to perform
     its obligations hereunder. The execution and delivery by Cliffs of this
     Agreement and the consummation by it of the transactions contemplated
     hereby have been duly authorized by all necessary corporate action (subject
     only, with respect to the Merger, to approval of this Agreement by its
     stockholders as provided for in Section 3.3). On or prior to the date
     hereof the Board of Directors of Cliffs has determined to recommend
     approval of the Merger to the stockholders of Cliffs, and such
     determination is in effect as of the date hereof. This Agreement has been
     duly executed and delivered by Cliffs and is the valid and binding
     obligation of Cliffs, enforceable against Cliffs in accordance with its
     terms.
 
          (d) No Approvals or Notices Required; No Conflict with Instruments to
     which Cliffs or any of the Cliffs Subsidiaries is a Party. Except as set
     forth in Section 2.2(d) of the Cliffs Disclosure Letter, neither the
     execution and delivery of this Agreement nor the performance by Cliffs of
     its obligations hereunder, nor the consummation of the transactions
     contemplated hereby by Cliffs, will (i) conflict with the certificate of
     incorporation or the bylaws of Cliffs or the charter or bylaws of any of
     the Cliffs Subsidiaries; (ii) assuming satisfaction of the requirements set
     forth in clause (iii) below, violate any provision of law applicable to
     Cliffs or any of the Cliffs Subsidiaries; (iii) except for (A) requirements
     of Federal or state securities laws, (B) requirements arising out of the
     HSR Act, (C) requirements of notice filings in such foreign jurisdictions
     as may be applicable, and (D) the filing of a certificate of merger in
     accordance with the DGCL, require any consent or approval of, or filing
     with or notice to, any public body or authority, domestic or foreign, under
     any provision of law applicable to Cliffs or any of the
 
                                       A-8
<PAGE>   71
 
     Cliffs Subsidiaries; or (iv) require any consent, approval or notice under,
     or violate, breach, be in conflict with or constitute a default (or an
     event that, with notice or lapse of time or both, would constitute a
     default) under, or permit the termination of any provision of, or result in
     the creation or imposition of any lien upon any properties, assets or
     business of Cliffs or any of the Cliffs Subsidiaries under, any note, bond,
     indenture, mortgage, deed of trust, lease, franchise, permit,
     authorization, license, contract, instrument or other agreement or
     commitment or any order, judgment or decree to which Cliffs or any of the
     Cliffs Subsidiaries is a party or by which Cliffs or any of the Cliffs
     Subsidiaries or any of its or their assets or properties is bound or
     encumbered, except (A) those that have already been given, obtained or
     filed, (B) those that are required pursuant to bank loan agreements or
     leasing arrangements, as set forth in Section 2.2(d) of the Cliffs
     Disclosure Letter, which Cliffs will use its reasonable efforts to obtain
     prior to the Effective Time, and (C) those that, in the aggregate, would
     not have a Cliffs MAE.
 
          (e) Commission Filings; Financial Statements. Cliffs and each of the
     Cliffs Subsidiaries have timely filed all reports, registration statements
     and other filings, together with any amendments required to be made with
     respect thereto, that they have been required to file with the Commission
     under the Securities Act and the Exchange Act. All reports, registration
     statements and other filings (including all notes, exhibits and schedules
     thereto and documents incorporated by reference therein) filed by Cliffs
     with the Commission since January 1, 1996 through the date of this
     Agreement, together with any amendments thereto, are sometimes collectively
     referred to as the "Cliffs Commission Filings." As of the respective dates
     of their filing with the Commission, the Cliffs Commission Filings complied
     in all material respects with the Securities Act, the Exchange Act and the
     rules and regulations of the Commission thereunder, and did not contain any
     untrue statement of a material fact or omit to state a material fact
     required to be stated therein or necessary to make the statements made
     therein, in light of the circumstances under which they were made, not
     misleading.
 
          Each of the consolidated financial statements (including any related
     notes or schedules) included in the Cliffs Commission Filings was prepared
     in accordance with generally accepted accounting principles applied on a
     consistent basis (except as may be noted therein or in the notes or
     schedules thereto) and complied with the rules and regulations of the
     Commission. Such consolidated financial statements fairly present the
     consolidated financial position of Cliffs and the Cliffs Subsidiaries as of
     the dates thereof and the results of operations, cash flows and changes in
     stockholders' equity for the periods then ended (subject, in the case of
     the unaudited interim financial statements, to normal year end audit
     adjustments on a basis consistent with past periods).
 
          (f) Absence of Undisclosed Liabilities. Except as disclosed in Section
     2.2(f) of the Cliffs Disclosure Letter, as of the date of this Agreement,
     neither Cliffs nor any of the Cliffs Subsidiaries has any liabilities that
     are reasonably likely to have, individually or in the aggregate, a Cliffs
     MAE, except liabilities which are accrued or reserved against in the
     consolidated balance sheet of Cliffs as of December 31, 1997 or June 30,
     1998, included in the Cliffs Commission Filings or reflected in the notes
     thereto. Neither Cliffs nor any Cliffs Subsidiary has incurred or paid any
     liability since June 30, 1998, except for liabilities incurred or paid (i)
     in the ordinary course of business consistent with past practice, (ii) in
     connection with transactions contemplated by this Agreement, or (iii)
     pursuant to transactions not prohibited by this Agreement.
 
          (g) Conduct of Business in the Ordinary Course; Absence of Certain
     Changes and Events. Since January 1, 1998, except as contemplated by this
     Agreement or as disclosed in the Cliffs Commission Filings or as set forth
     in Section 2.2(g) of the Cliffs Disclosure Letter, Cliffs and the Cliffs
     Subsidiaries have conducted their business only in the ordinary and usual
     course, and there has not been (i) any Cliffs MAE, or any condition, event
     or development that reasonably may be expected to result in a Cliffs MAE;
     (ii) any material change by Cliffs in its accounting methods, principles or
     practices; (iii) any revaluation by Cliffs or any of the Cliffs
     Subsidiaries of any of its or their assets, including, without limitation,
     writing down the value of inventory or writing off notes or accounts
     receivable other than in the ordinary course of business; (iv) any entry by
     Cliffs or any of the Cliffs Subsidiaries into any commitment or transaction
     material to Cliffs and the Cliffs Subsidiaries, taken as a whole; (v) any
     declaration, setting aside or payment of any dividends or distributions in
     respect of the Cliffs Common Stock or any redemption,
                                       A-9
<PAGE>   72
 
     purchase or other acquisition of any of its securities or any securities of
     any of the Cliffs Subsidiaries; (vi) any damage, destruction or loss
     (whether or not covered by insurance) materially adversely affecting the
     properties or business of Cliffs and the Cliffs Subsidiaries, taken as a
     whole; (vii) any increase in indebtedness for borrowed money other than (A)
     borrowings under existing credit facilities or (B) indebtedness incurred in
     the ordinary course of business that does not exceed $5,000,000 in the
     aggregate; (viii) any granting of a security interest or lien on any
     material property or assets of Cliffs and the Cliffs Subsidiaries, taken as
     a whole, other than Permitted Liens; or (ix) any increase in or
     establishment of any bonus, insurance, severance, deferred compensation,
     pension, retirement, profit sharing, stock option (including, without
     limitation, the granting of stock options, stock appreciation rights,
     performance awards or restricted stock awards), stock purchase or other
     employee benefit plan or any other increase in the compensation payable or
     to become payable to any executive officers of Cliffs or any of the Cliffs
     Subsidiaries.
 
          (h) Litigation. Except as disclosed in the Cliffs Commission Filings
     or as set forth in Section 2.2(h) of the Cliffs Disclosure Letter, there
     are no claims, actions, suits, investigations, inquiries or proceedings
     pending or, to the knowledge of Cliffs, overtly threatened against or
     affecting Cliffs or any of the Cliffs Subsidiaries or any of their
     respective properties at law or in equity, or any of their respective
     employee benefit plans or fiduciaries of such plans, or before or by any
     federal, state, municipal or other governmental agency or authority, or
     before any arbitration board or panel, wherever located, that individually
     or in the aggregate if adversely determined could have a Cliffs MAE, or
     that involve the risk of criminal liability.
 
          (i) Employee Benefit Plans.
 
             (i) Section 2.2(i) of the Cliffs Disclosure Letter provides a list
        of each of the following which is sponsored, maintained or contributed
        to by Cliffs, a Cliffs Subsidiary or any corporation, trade, business or
        entity under common control with Cliffs or a Cliffs Subsidiary within
        the meaning of Section 414(b), (c), (m) or (o) of the Code or Section
        4001 of ERISA (a "Cliffs ERISA Affiliate") for the benefit of its
        employees, or has been so sponsored, maintained or contributed to within
        six years prior to the Closing Date:
 
                (A) each "employee benefit plan," as such term is defined in
           Section 3(3) of the Employee Retirement Income Security Act of 1974,
           as amended ("ERISA"), ("Plan"); and
 
                (B) each personnel policy, stock option plan, collective
           bargaining agreement, bonus plan or arrangement, incentive award plan
           or arrangement, vacation policy, severance pay plan, policy or
           agreement, deferred compensation agreement or arrangement, executive
           compensation or supplemental income arrangement, consulting
           agreement, employment agreement and each other employee benefit plan,
           agreement, arrangement, program, practice or understanding that is
           not described in Section 2.1(i)(i)(A) ("Benefit Program or
           Agreement").
 
        True, correct and complete copies of each of the Plans, Benefit Programs
        or Agreements, related trusts, if applicable, and all amendments
        thereto, have been or upon request will be furnished to R&B Falcon.
 
             (ii) Except as otherwise set forth in Section 2.2(i) of the Cliffs
        Disclosure Letter:
 
                (A) None of Cliffs, any Cliffs Subsidiary or any Cliffs ERISA
           Affiliate contributes to or has an obligation to contribute to, or
           has at any time contributed to or had an obligation to contribute to,
           a plan subject to Title IV of ERISA, including, without limitation, a
           multiemployer plan within the meaning of Section 3(37) of ERISA;
 
                (B) Each Plan and each Benefit Program or Agreement has been
           administered, maintained and operated in all material respects in
           accordance with the terms thereof and in compliance with its
           governing documents and applicable law (including, where applicable,
           ERISA and the Code);
 
                                      A-10
<PAGE>   73
 
                (C) There is no matter pending with respect to any of the Plans
           before any governmental agency, and there are no actions, suits or
           claims pending (other than routine claims for benefits) or, to the
           knowledge of Cliffs, threatened against, or with respect to, any of
           the Plans or Benefit Programs or Agreements or their assets;
 
                (D) No act, omission or transaction has occurred which would
           result in imposition on Cliffs, any Cliffs Subsidiary or any Cliffs
           ERISA Affiliate of breach of fiduciary duty liability damages under
           Section 409 of ERISA, a civil penalty assessed pursuant to
           Subsections (c), (i) or (l) of Section 502 of ERISA or a tax imposed
           pursuant to Chapter 43 of Subtitle D of the Code; and
 
                (E) Except as provided in Sections 3.6, 5.7, 5.8, 5.9 or 5.10,
           the execution and delivery of this Agreement and the consummation of
           the transactions contemplated hereby will not require Cliffs, any
           Cliffs Subsidiary or any Cliffs ERISA Affiliate to make a larger
           contribution to, or pay greater benefits under, any Plan, Benefit
           Program or Agreement than it otherwise would or create or give rise
           to any additional vested rights or service credits under any Plan or
           Benefit Program or Agreement.
 
             (iii) Termination of employment of any employee of Cliffs, any
        Cliffs Subsidiary or any Cliffs ERISA Affiliate immediately after
        consummation of the transactions contemplated by this Agreement would
        not result in payments under the Plans, Benefit Programs or Agreements
        which, in the aggregate, would result in imposition of the sanctions
        imposed under Sections 280G and 4999 of the Code.
 
             (iv) Each Plan which is an "employee welfare benefit plan," as such
        term is defined in Section 3(1) of ERISA, provides that it may be
        unilaterally amended or terminated in its entirety, and no such plan
        provides for the accrual of additional liability after such amendment or
        termination.
 
             (v) None of the employees of Cliffs, any of the Cliffs Subsidiaries
        or any Cliffs ERISA Affiliate are subject to union or collective
        bargaining agreements.
 
          (j) Taxes. Except as set forth in Section 2.2(j) of the Cliffs
     Disclosure Letter, all federal and all material state, local, foreign
     returns, declarations, reports, including claims for refunds, estimates,
     information returns and statements (including any amendments thereof) ("Tax
     Returns") of or relating to any Tax that are required to be filed on or
     before the Closing Date by or with respect to Cliffs or any of the Cliffs
     Subsidiaries, or any other corporation that is or was a member of an
     affiliated group (within the meaning of Section 1504(a) of the Code) of
     corporations of which Cliffs was a member for any period ending on or prior
     to the Closing Date, have been or will be duly and timely filed with
     appropriate governmental authorities, and all Taxes, including interest and
     penalties, due and payable pursuant to such Tax Returns or otherwise
     required to be duly paid or deposited by or with respect to Cliffs or any
     of the Cliffs Subsidiaries have been paid or adequately provided for in
     reserves established by Cliffs, except where the failure to file, pay or
     provide for would not have a Cliffs MAE. Except as set forth in Section
     2.2(j) of the Cliffs Disclosure Letter, all U.S. Federal income Tax Returns
     of or with respect to Cliffs or any of the Cliffs Subsidiaries have been
     audited by the applicable governmental authority, or the applicable statute
     of limitations has expired, for all periods up to and including the tax
     year ended December 31, 1994. There is no material claim against Cliffs or
     any of the Cliffs Subsidiaries with respect to any Taxes, and no material
     assessment, deficiency or adjustment has been asserted or proposed with
     respect to any Tax Return of or with respect to Cliffs or any of the Cliffs
     Subsidiaries that has not been adequately provided for in reserves
     established by Cliffs in the consolidated financial statements included in
     the Cliffs Commission Filings. The total amounts set up as liabilities for
     current and deferred Taxes in the consolidated financial statements
     included in the Cliffs Commission Filings have been prepared in accordance
     with generally accepted accounting principles and are sufficient to cover
     the payment of all material Taxes, including any penalties or interest
     thereon and whether or not assessed or disputed, that are, or are hereafter
     found to be, or to have been, due with respect to the operations of Cliffs
     and the Cliffs Subsidiaries through the periods covered thereby. Cliffs and
     each of the Cliffs Subsidiaries have
                                      A-11
<PAGE>   74
 
     (and as of the Closing Date will have) made all deposits (including
     estimated tax payments for taxable years for which the consolidated federal
     income tax return is not yet due) required with respect to Taxes. Except as
     set forth in Section 2.2(j) of the Cliffs Disclosure Letter, no waiver or
     extension of any statute of limitations as to any federal, state, local or
     foreign Tax matter has been given by or requested from Cliffs or any of the
     Cliffs Subsidiaries. Except for statutory liens for current Taxes not yet
     due, no liens for Taxes exist upon the assets of either Cliffs or the
     Cliffs Subsidiaries. Except as set forth in Section 2.2(j) of the Cliffs
     Disclosure Letter, neither Cliffs nor any of the Cliffs Subsidiaries (i)
     has filed consolidated income Tax Returns with any corporation, other than
     consolidated federal and state income Tax Returns with Cliffs, for any
     taxable period which is not now closed by the applicable statute of
     limitations, (ii) is a party to any tax sharing or indemnity agreement, or
     (iii) has any liability for Taxes of any other person (other than current
     members of the Cliffs affiliated group of corporations) under Treasury
     Regulation sec. 1.1502-6 (or any similar provision of state, local or
     foreign law), as a transferee or successor, by contract or otherwise.
     Neither Cliffs nor the Cliffs Subsidiaries has any deferred intercompany
     gain as defined in Treasury Regulation Section 1.1502-13.
 
          Cliffs and the Cliffs Subsidiaries have made or upon request will make
     available to R&B Falcon true and correct copies of all federal, state and
     local income and franchise Tax Returns, examination reports and statements
     of deficiencies asserted or assessed against or agreed to by Cliffs or any
     Cliff Subsidiary for all open Tax periods. None of the assets of Cliffs or
     the Cliffs Subsidiaries (i) is property that is required to be treated as
     being owned by any other person pursuant to the "safe harbor lease"
     provisions of former Section 168(f)(8) of the Code, (ii) is "tax-exempt use
     property" within the meaning of Section 168(h) of the Code, or (iii)
     secures any debt the interest on which is tax-exempt under Section 103(a)
     of the Code.
 
          In the Merger, at least 90% of the fair market value of Cliffs's net
     assets and at least 70% of the fair market value of Cliffs's gross assets
     held immediately prior to the Merger will be held by the Surviving
     Corporation. For purposes of this representation, amounts paid by Cliffs to
     its stockholders who receive cash or other property, amounts used by Cliffs
     to pay reorganization expenses, and all redemptions and distributions
     (except for regular, normal dividends) made by Cliffs will be included as
     assets of Cliffs immediately prior to the Merger. As of the Closing Date,
     Cliffs has not redeemed, or made any distributions (except for regular,
     normal dividends) with respect to, shares of Cliffs Common Stock in
     connection with the Merger.
 
          For purposes of this Agreement, "Tax" or "Taxes" means any and all
     taxes, fees, levies, duties, tariffs, imposts and other charges of any kind
     (together with any and all interest, penalties, additions to tax and
     additional amounts imposed with respect thereto) imposed by any government
     or taxing authority, including, without limitation: taxes or other charges
     on or with respect to income, franchises, windfall profits, severance,
     gross receipts, property, sales, use, capital stock, payroll, employment,
     social security, workers' compensation, unemployment compensation,
     disability or net worth; taxes or other charges in the nature of excise,
     withholding, ad valorem, stamp, transfer, value added or gains taxes;
     license, registration and documentation fees; and custom duties, tariffs
     and similar charges whether or not disputed.
 
          (k) Environmental Matters. Except for matters disclosed in Section
     2.2(k) of the Cliffs Disclosure Letter and except for matters that in the
     aggregate would not have a Cliffs MAE, (i) the properties, operations and
     activities of Cliffs and the Cliffs Subsidiaries comply with all applicable
     Environmental Laws (as hereinafter defined); (ii) Cliffs and the Cliffs
     Subsidiaries and the properties and operations of Cliffs and the Cliffs
     Subsidiaries are not subject to any existing, pending or, to the knowledge
     of Cliffs, threatened action, suit, investigation, inquiry or proceeding by
     or before any governmental authority under any Environmental Law; (iii) all
     notices, permits, licenses or similar authorizations, if any, required to
     be obtained or filed by Cliffs or the Cliffs Subsidiaries under any
     Environmental Law in connection with any aspect of the business of Cliffs
     or the Cliffs Subsidiaries, including without limitation those relating to
     the treatment, storage, disposal or release of a hazardous substance or
     solid waste, have been duly obtained or filed and will remain valid and in
     effect after the Merger, and Cliffs and the Cliffs Subsidiaries are in
     compliance with the terms and conditions of all such notices, permits,
     licenses and
                                      A-12
<PAGE>   75
 
     similar authorizations; (iv) Cliffs and the Cliffs Subsidiaries have
     satisfied and are currently in compliance with all financial responsibility
     requirements applicable to their operations and imposed by the U.S. Coast
     Guard and Minerals Management Service pursuant to OPA (as hereinafter
     defined) or by any other governmental authority under any other
     Environmental Law, and Cliffs and the Cliffs Subsidiaries have not received
     any notice of noncompliance with any such financial responsibility
     requirements; (v) to the knowledge of Cliffs, there are no physical or
     environmental conditions existing on any property of Cliffs and the Cliffs
     Subsidiaries or resulting from Cliffs' or the Cliffs Subsidiaries'
     operations or activities, past or present, at any location, that would give
     rise to any on-site or off-site remedial obligations under any
     Environmental Laws; (vi) to the knowledge of Cliffs, since the effective
     date of the relevant requirements of all applicable Environmental Laws, all
     hazardous substances or solid wastes generated by Cliffs or any of the
     Cliffs Subsidiaries or used in connection with any of their properties or
     operations have been transported only by carriers authorized under
     Environmental Laws to transport such substances and wastes, and disposed of
     only at treatment, storage and disposal facilities authorized under
     Environmental Laws to treat, store or dispose of such substances and
     wastes, and, to the knowledge of Cliffs, such carriers and facilities have
     been and are operating in compliance with such authorizations and are not
     the subject of any existing, pending or overtly threatened action,
     investigation, or inquiry by any governmental authority in connection with
     any Environmental Laws; (vii) there has been no exposure of any person or
     property to hazardous substances, solid waste, or any pollutant or
     contaminant, nor has there been any release of hazardous substances, solid
     waste, or any pollutant or contaminant into the environment by Cliffs or
     the Cliffs Subsidiaries or in connection with any of their properties or
     operations that could reasonably be expected to give rise to any claim for
     damages or compensation; and (viii) Cliffs and the Cliffs Subsidiaries have
     made or upon request will make available to R&B Falcon true and correct
     copies of all internal and external environmental audits and studies and
     all correspondence on substantial environmental matters in the possession
     of Cliffs and the Cliffs Subsidiaries relating to any of the current or
     former properties or operations of Cliffs and the Cliffs Subsidiaries.
 
          For purposes of this Agreement, the term "Environmental Laws" shall
     mean any and all laws, statutes, ordinances, rules, regulations, orders or
     determinations of any Governmental Authority (as hereinafter defined)
     pertaining to health or the environment currently in effect in any
     jurisdiction in which the party in question and its subsidiaries own
     property or conduct business, or has owned property or conducted business,
     including without limitation, the Clean Air Act, as amended, the
     Comprehensive Environmental, Response, Compensation, and Liability Act of
     1980 ("CERCLA"), as amended, the Federal Water Pollution Control Act, as
     amended, the Occupational Safety and Health Act of 1970, as amended, the
     Resource Conservation and Recovery Act of 1976 ("RCRA"), as amended, the
     Safe Drinking Water Act, as amended, the Toxic Substances Control Act, as
     amended, the Hazardous & Solid Waste Amendments Act of 1984, as amended,
     the Superfund Amendments and Reauthorization Act of 1986, as amended, the
     Hazardous Materials Transportation Act, as amended, the Oil Pollution Act
     of 1990 ("OPA"), any state laws pertaining to the handling of oil and gas
     exploration and production wastes or the use, maintenance and closure of
     pits and impoundments, and all other environmental conservation or
     protection laws. For purposes of this Agreement, the terms "hazardous
     substance" and "release" have the meanings specified in CERCLA, and the
     terms "solid waste" and "disposal" have the meanings specified in RCRA;
     provided, however, that to the extent the laws of the state in which the
     property is located establish a meaning for "hazardous substance,"
     "release," "solid waste" or "disposal" that is broader than that specified
     in either CERCLA or RCRA, such broader meaning shall apply. For purposes of
     this Agreement, the term "Governmental Authority" includes the United
     States, the state, county, city and political subdivisions in which the
     party in question owns property or conducts business, or has owned property
     or conducted business, and any agency, department, commission, board,
     bureau or instrumentality of any of them that exercises jurisdiction over
     the party in question.
 
          (l) Severance Payments. Except as set forth in Section 2.2(l) of the
     Cliffs Disclosure Letter or as contemplated by Section 3.6 hereof, none of
     Cliffs or the Cliffs Subsidiaries will owe a severance payment or similar
     obligation to any of their respective employees, officers or directors as a
     result of the Merger or the transactions contemplated by this Agreement,
     nor will any of such persons be entitled to severance
                                      A-13
<PAGE>   76
 
     payments or other benefits as a result of the Merger or the transactions
     contemplated by this Agreement in the event of the subsequent termination
     of their employment.
 
          (m) Voting Requirements. The affirmative vote of the holders of a
     majority of the outstanding shares of Cliffs Common Stock is the only vote
     of the holders of any class or series of the capital stock of Cliffs
     necessary to approve this Agreement and the Merger.
 
          (n) No Excess Parachute Payments; Section 162(m) of the Code.
 
             (i) Except as disclosed in Section 2.2(n) of the Cliffs Disclosure
        Letter, any amount that could be received (whether in cash or property
        or the vesting of property) as a result of any of the transactions
        contemplated by this Agreement by any employee, officer or director of
        Cliffs or any of its affiliates who is a "Disqualified Individual" (as
        such term is defined in proposed Treasury Regulation 1.280G-1) under any
        employment, severance or termination agreement, other compensation
        arrangement or benefit plan currently in effect would not be
        characterized as an "Excess Parachute Payment" (as such term is defined
        in Section 280G(b)(1) of the Code).
 
             (ii) Except as disclosed in Section 2.2(n) of the Cliffs Disclosure
        Letter, the disallowance of a deduction under Section 162(m) of the Code
        for employee remuneration will not apply to any amount paid or payable
        by Cliffs or the Surviving Corporation or any of their subsidiaries
        under any contract, benefit plan, program, arrangement or understanding
        currently in effect.
 
          (o) Brokers. All negotiations relative to this Agreement and the
     transactions contemplated hereby have been carried out by Cliffs directly
     with R&B Falcon, without the intervention of any person on behalf of Cliffs
     in such manner as to give rise to any valid claim by any person against
     Cliffs, the Surviving Corporation, R&B Falcon or any of their subsidiaries
     for a finders' fee, brokerage commission or similar payment, other than the
     fee payable to Jefferies & Company, Inc. for acting as Cliffs' financial
     advisor and rendering a fairness opinion in connection with the Merger.
     Cliffs has provided R&B Falcon with a true, correct and complete copy of
     the agreement between Cliffs and Jefferies & Company, Inc., and Cliffs has
     no other agreements or understandings (written or oral) with respect to
     such services.
 
          (p) Labor Relations. Except as set forth in Section 2.2(p) of the
     Cliffs Disclosure Letter, neither Cliffs nor any of the Cliffs Subsidiaries
     is a party to, or bound by, any collective bargaining agreement, contract
     or other agreement or understanding with respect to a labor union or labor
     organization, and to the knowledge of Cliffs, there are no organizational
     efforts with respect to the formation of a collective bargaining unit
     presently being made or threatened involving employees of Cliffs or any of
     the Cliffs Subsidiaries. There are no unfair labor practice complaints
     against Cliffs or any of the Cliffs Subsidiaries pending before the
     National Labor Relations Board and there is no labor strike, dispute, slow
     down or stoppage, or any union organizing campaign, actually pending or, to
     the knowledge of Cliffs, threatened against Cliffs or any of the Cliffs
     Subsidiaries, except for any such proceedings which would not reasonably be
     expected to have a Cliffs MAE.
 
          (q) Insurance. Section 2.2(q) of the Cliffs Disclosure Letter sets
     forth a list and brief description of the insurance policies of Cliffs and
     the Cliffs Subsidiaries relating to their properties and the conduct of
     their business. All premiums due and arising thereon have been paid and
     such policies are in full force and effect. True, correct and complete
     copies of all such insurance policies have been or upon request will be
     made available to R&B Falcon.
 
          (r) State Takeover Laws. Cliffs and the Cliffs Subsidiaries have taken
     all necessary action to approve the transactions contemplated by this
     Agreement pursuant to Section 203 of the DGCL.
 
          (s) Cliffs Rights Plan. The Board of Directors of Cliffs has approved
     and Cliffs has executed, and contemporaneously with the execution of this
     Agreement Cliffs has caused the rights agent under the Cliffs Rights Plan
     to execute and deliver, an amendment to the Cliffs Rights Plan that
     provides and specifically confirms that: (i) neither this Agreement, the
     Merger nor any of the other transactions contemplated hereby (A) will cause
     R&B Falcon or Sub to become an "Acquiring Person," or result in the
     occurrence of a "Shares Acquisition Date," a "Flip-In Event," a "Flip-Over
     Event" or a "Distribution Date" (as defined in the Cliffs Rights Plan), or
     (B) will permit any Person to have the right under
 
                                      A-14
<PAGE>   77
 
     the Cliffs Rights Plan to acquire, or to make the rights under the Cliffs
     Rights Plan ever exercisable for, any securities of R&B Falcon; and (ii)
     this Agreement, the Merger, the other transactions and all actions of R&B
     Falcon, Sub, the R&B Falcon Subsidiaries and any of their affiliates
     contemplated hereby will not cause the rights under the Cliffs Rights Plan
     to become separated from the Cliffs Common Stock or to become exercisable.
 
                                  ARTICLE III
 
                COVENANTS OF CLIFFS PRIOR TO THE EFFECTIVE TIME
 
     Cliffs covenants and agrees as follows:
 
     3.1  Conduct of Business by Cliffs Pending the Merger. From the date of
this Agreement until the Effective Time, unless R&B Falcon shall otherwise agree
in writing or as otherwise expressly contemplated by this Agreement or set forth
in Section 3.1 of the Cliffs Disclosure Letter:
 
          (a) the business of Cliffs and the Cliffs Subsidiaries shall be
     conducted only in, and Cliffs and the Cliffs Subsidiaries shall not take
     any action except in, the ordinary course of business and consistent with
     past practice;
 
          (b) Cliffs shall not directly or indirectly: (i) issue, sell, pledge,
     dispose of or encumber, or permit any Cliffs Subsidiary to issue, sell,
     pledge, dispose of or encumber, any capital stock of Cliffs or any Cliffs
     Subsidiary except upon the exercise of Cliffs Options; (ii) amend or
     propose to amend the respective charters or bylaws of Cliffs or any Cliffs
     Subsidiary; (iii) split, combine or reclassify any outstanding capital
     stock, or declare, set aside or pay any dividend or other distribution
     payable in cash, stock, property or otherwise with respect to its capital
     stock whether now or hereafter outstanding; (iv) redeem, purchase or
     acquire or offer to acquire, or permit any of the Cliffs Subsidiaries to
     redeem, purchase or acquire or offer to acquire, any of its or their
     capital stock; (v) enter into any contract, agreement, commitment or
     arrangement with respect to any of the matters set forth in this Section
     3.1(b); (vi) except as provided in Sections 3.6, 5.7, 5.8, 5.9 and 5.10,
     enter into, adopt or (except as may be required by law and except for an
     amendment to the Cliffs Stock Option Plans (or any option agreements
     existing thereunder) to provide the Board of Directors of Cliffs with the
     power to take the actions required pursuant to Section 5.9) amend or
     terminate any bonus, profit sharing, compensation, severance, termination,
     stock option, stock appreciation right, restricted stock, performance unit,
     stock equivalent, stock purchase, pension, retirement, deferred
     compensation, employment, severance or other employee benefit agreement,
     trust, plan, fund or other arrangement for the benefit or welfare of any
     director, officer or employee; (vii) except as provided in Sections 3.6,
     5.7, 5.8, 5.9 and 5.10, or in the ordinary course of business consistent
     with past practice only with respect to non-executive officer employees,
     increase in any manner the compensation or fringe benefits of any director,
     officer or employee; (viii) except as provided in Sections 3.6, 5.7, 5.8,
     5.9 and 5.10, pay to any director, officer or employee any benefit not
     required by any employee benefit agreement, trust, plan, fund or other
     arrangement as in effect on the date hereof; (ix) commence any legal
     proceedings other than in accordance with past practice or settle any legal
     proceedings or claims against Cliffs or any Cliffs Subsidiary not covered
     by insurance for an amount or amounts in excess of $5,000,000 in the
     aggregate; or (x) lend or advance any funds or otherwise extend credit to
     any person other than Cliffs or a Cliffs Subsidiary except for advances to
     employees for business related expenses consistent with past practice and
     trade credit extended in the ordinary course of business;
 
          (c) Cliffs shall use its reasonable efforts (i) to preserve intact the
     business organization of Cliffs and each of the Cliffs Subsidiaries, (ii)
     to maintain in effect any authorizations or similar rights of Cliffs and
     each of the Cliffs Subsidiaries, (iii) to keep available the services of
     the current officers and key employees of Cliffs and the Cliffs
     Subsidiaries, (iv) to preserve the goodwill of those having business
     relationships with it and the Cliffs Subsidiaries, (v) to maintain and keep
     its properties and the properties of the Cliffs Subsidiaries in as good a
     repair and condition as presently exists, except for deterioration due to
     ordinary wear and tear and damage due to casualty; and (vi) to maintain in
     full force and effect
 
                                      A-15
<PAGE>   78
 
     insurance comparable in amount and scope of coverage to that currently
     maintained by it and the Cliffs Subsidiaries;
 
          (d) Without the prior written consent of R&B Falcon, which consent
     will not be unreasonably withheld, Cliffs shall not make or agree to make,
     or permit any of the Cliffs Subsidiaries to make or agree to make, capital
     expenditures that in the aggregate exceed $40,000,000 (excluding any
     capital expenditures (i) funded with insurance proceeds or (ii) accrued or
     incurred prior to June 30, 1998 and reflected in the Cliffs SEC Filings);
 
          (e) Without the prior written consent of R&B Falcon, which consent
     will not be unreasonably withheld, Cliffs shall not, and shall not permit
     any of the Cliffs Subsidiaries to (i) sell, pledge, dispose of or encumber
     any material portion of its assets, (ii) incur, assume or guarantee
     indebtedness for money borrowed, other than pursuant to existing credit
     facilities (within the limits of such facilities as in effect on the date
     hereof) or for indebtedness incurred in the ordinary course of business
     that does not exceed $5,000,000 in the aggregate, or (iii) prepay any
     indebtedness or other material liability, except prepayments pursuant to
     revolving lines of credit and prepayments made to obtain prepayment
     discounts consistent with past practice;
 
          (f) Cliffs shall not, and shall not permit any of the Cliffs
     Subsidiaries to, authorize, propose or announce an intention to authorize
     or propose, or enter into an agreement with respect to, any merger,
     consolidation or business combination (other than the Merger) or any
     acquisition of a material amount of assets or securities, or otherwise
     acquire direct or indirect control over any other person, except for (i)
     purchases of U.S. Treasury securities or U.S. government agency securities,
     which in either case have maturities of three years or less, (ii) other
     investments in connection with cash management activities consistent with
     past practice, or (iii) purchases of inventory, spares and replacements
     consistent with past practice;
 
          (g) Cliffs shall, and shall cause the Cliffs Subsidiaries to, perform
     their respective obligations under any contracts and agreements to which
     any of them is a party or to which any of their assets is subject; and
 
          (h) Cliffs shall not, and shall not permit any of the Cliffs
     Subsidiaries to, take any action that would, or that reasonably could be
     expected to, result in any of the representations and warranties set forth
     in this Agreement becoming untrue or any of the conditions to the Merger
     set forth in Article VI not being satisfied. Cliffs promptly shall advise
     R&B Falcon orally and in writing of any change or event having, or which,
     insofar as reasonably can be foreseen, would have, a Cliffs MAE; and
 
          (i) Cliffs shall, and shall cause the Cliffs Subsidiaries to, make
     available to R&B Falcon and its representatives such information with
     respect to the business and affairs of Cliffs and the Cliffs Subsidiaries
     as R&B Falcon shall reasonably request, and shall confer at all times as
     R&B Falcon may reasonably request with one or more representatives of R&B
     Falcon with respect to Cliffs' material operational matters and the general
     status of its operations.
 
     3.2  Proxy Statement. Promptly after the date of this Agreement, Cliffs
shall prepare and file with the Commission under the Exchange Act, and shall use
its reasonable efforts to have cleared by the Commission, a proxy statement (the
"Proxy Statement") with respect to the meeting of stockholders of Cliffs
referred to in Section 3.3 and Cliffs shall cooperate with R&B Falcon in
preparing the Registration Statement (as defined in Section 4.2). Cliffs shall
cause (i) the Proxy Statement (except with respect to information concerning R&B
Falcon and the R&B Falcon Subsidiaries furnished in writing by or on behalf of
R&B Falcon specifically for use therein, for which information R&B Falcon shall
be responsible) to comply as to form in all material respects with the
requirements of the Exchange Act and the rules and regulations adopted
thereunder, and (ii) the Registration Statement (with respect to information
concerning Cliffs and the Cliffs Subsidiaries furnished in writing by or on
behalf of Cliffs specifically for use therein) and the Proxy Statement (except
with respect to information concerning R&B Falcon and the R&B Falcon
Subsidiaries furnished in writing by or on behalf of R&B Falcon specifically for
use therein, for which information R&B Falcon shall be responsible) to not
contain any untrue statement of a material fact or omit to state any material
fact required
                                      A-16
<PAGE>   79
 
to be stated therein or necessary to make the statements therein not misleading.
Subject to the terms and conditions of Section 3.4, the Proxy Statement shall
contain the recommendation of the Board of Directors of Cliffs that the
stockholders of Cliffs vote to approve and adopt this Agreement and the Merger.
Cliffs will advise R&B Falcon promptly in writing if prior to the Effective Time
it shall obtain knowledge of any facts that would make it necessary to amend or
supplement the Proxy Statement or the Registration Statement in order to make
the statements therein not misleading or to comply with applicable law.
 
     3.3  Meeting of Stockholders of Cliffs. Subject to the terms and conditions
set forth in Section 3.4, Cliffs shall promptly take all action reasonably
necessary in accordance with the DGCL and the certificate of incorporation and
bylaws of Cliffs to convene a meeting of its stockholders to consider and vote
upon the adoption and approval of this Agreement and the Merger. Subject to the
terms and conditions set forth in Section 3.4, the Board of Directors of Cliffs
(i) shall recommend at such meeting that the stockholders of Cliffs vote to
adopt and approve this Agreement and the Merger; (ii) shall use its reasonable
efforts to solicit from stockholders of Cliffs proxies in favor of such adoption
and approval; and (iii) shall take all other action reasonably necessary to
secure a vote of its stockholders in favor of the adoption and approval of this
Agreement and the Merger.
 
     3.4  No Solicitation. From and after the date of this Agreement, neither
Cliffs nor any Cliffs Subsidiary shall, directly or indirectly, through any
officer, director, employee, representative or agent of Cliffs or any of the
Cliffs Subsidiaries, (i) solicit or knowingly encourage, including by way of
furnishing information, the initiation of any inquiries or proposals regarding
(A) any merger, tender offer, sale of shares of capital stock or similar
business combination transactions involving Cliffs or the Cliffs Subsidiaries
(other than (1) a merger of one or more wholly owned Cliffs Subsidiaries with or
into another wholly owned Cliffs Subsidiary or Cliffs, (2) an issuance of Cliffs
Common Stock in exchange for assets of another entity, or (3) a merger of a
wholly owned Cliffs Subsidiary with or into another entity in which the
surviving entity is a wholly owned Cliffs Subsidiary and the securities of such
entity outstanding prior to such merger are converted into shares of Cliffs
Common Stock; provided that the aggregate number of shares of Cliffs Common
Stock issued in connection with any and all transactions effected in reliance
upon clause (2) or (3) do not exceed 15% of the outstanding shares of Cliffs
Common Stock as of the date hereof), or (B) any sale of 15% or more of the
assets of Cliffs and the Cliffs Subsidiaries, taken as a whole (any of the
foregoing transactions being referred to herein as a "Cliffs Acquisition
Transaction"), (ii) negotiate, explore or otherwise engage in discussions with
any person (other than R&B Falcon, Sub or their respective directors, officers,
employees, agents and representatives) with respect to any Cliffs Acquisition
Transaction, or (iii) enter into any agreement, arrangement or understanding
requiring it to abandon, terminate or fail to consummate the Merger or any other
transactions contemplated by this Agreement; provided, however, that nothing in
this Section 3.4 or elsewhere in this Agreement shall prevent the members of the
Board of Directors of Cliffs from (i) furnishing information to (but only
pursuant to a confidentiality agreement substantially similar to the
Confidentiality Agreement between Cliffs and R&B Falcon dated August 7, 1998
(the "Confidentiality Agreement")) or entering into discussions or negotiations
with any person or group that makes an unsolicited bona fide written proposal
for a Cliffs Acquisition Transaction (an "Alternative Proposal"), if, and only
to the extent that, (A) the Board of Directors of Cliffs, based on the written
opinion of outside counsel, determines in good faith that such action is
required for the Board of Directors of Cliffs to comply with its fiduciary
duties to stockholders imposed by law, and (B) prior to furnishing such
information to, or entering into discussions or negotiations with, such person
or entity, Cliffs provides written notice to R&B Falcon to the effect that it is
furnishing information to, or entering into negotiations with, such person or
group; (ii) failing to make or withdrawing or modifying its recommendation
referred to in Section 3.3 if (A) there exists an Alternative Proposal and the
Board of Directors of Cliffs, based on the written opinion of outside counsel,
determines in good faith that such action is required for the Board of Directors
of Cliffs to comply with its fiduciary duties to stockholders imposed by law,
(B) either such Alternative Proposal is not conditioned on the receipt of
financing or the Board of Directors of Cliffs has reasonably concluded in good
faith that the person or group making such Alternative Proposal will have
adequate sources of financing to consummate such Alternative Proposal, (C) the
Board of Directors of Cliffs has reasonably determined in good faith that such
Alternative Proposal is more favorable to the stockholders of Cliffs than the
Merger, and (D) the Board of Directors of Cliffs has received a written opinion
from a nationally-recognized investment banking firm to the effect that the
consideration to be received by
                                      A-17
<PAGE>   80
 
stockholders of Cliffs in connection with such Alternative Proposal is superior,
from a financial point of view, to the consideration to be received by them in
the Merger; or (iii) to the extent applicable, complying with Rule 14e-2
promulgated under the Exchange Act with regard to an Alternative Proposal.
 
     3.5  Affiliate Letters. At least 30 days prior to the Closing Date, Cliffs
shall deliver to R&B Falcon a list, which shall be reasonably acceptable to R&B
Falcon, identifying all persons whom it believes are, at the time this Agreement
is submitted for approval to the stockholders of Cliffs, "affiliates" of Cliffs
for purposes of Rule 145 under the Securities Act. Cliffs shall deliver or cause
to be delivered to R&B Falcon on or prior to the Closing Date a duly executed
affiliate letter in the form of Exhibit A for each such "affiliate" of Cliffs.
R&B Falcon shall be entitled to place legends as specified in such affiliate
letters on the certificates evidencing any R&B Falcon Common Stock to be
received by such "affiliates" pursuant to the terms of this Agreement and to
issue appropriate stop transfer instructions to the transfer agent for R&B
Falcon Common Stock consistent with the terms of such affiliate letters.
 
     3.6  Waivers and Releases. Immediately prior to the Effective Time, Cliffs
shall pay to each executive officer identified on Schedule 3.6 hereto a cash
payment equal to the amount listed beside such executive officer's name on
Schedule 3.6 hereto as consideration for such executive officer's execution of a
waiver and release in a form to be mutually agreed by Cliffs and R&B Falcon (the
"Waiver and Release"). In the event it is determined that such payment to any
executive officer would be subject to the excise tax imposed by Section 4999 of
the Code, or any interest or penalties are incurred by the executive officer
with respect to such excise tax (such excise tax, together with any interest and
penalties, being referred to as the "Excise Tax"), then Cliffs shall pay to such
executive officer an additional payment (a "Gross-Up Payment") in an amount such
that after payment by the executive officer of all taxes, including without
limitation, any income taxes and Excise Tax imposed upon the Gross-Up Payment,
the executive officer retains an amount of the Gross-Up Payment equal to the
Excise Tax on such payment. Cliffs shall deliver or cause to be delivered on or
prior to the Closing Date a duly executed Waiver and Release for each such
executive officer identified on Schedule 3.6.
 
     3.7  Obtain Tax Opinion. Cliffs shall use its best efforts to obtain the
tax opinion referred to in Section 6.3(e) hereof.
 
                                   ARTICLE IV
 
              COVENANTS OF R&B FALCON PRIOR TO THE EFFECTIVE TIME
 
     R&B Falcon covenants and agrees as follows:
 
     4.1  Conduct of Business by R&B Falcon Pending the Merger. From the date of
this Agreement until the Effective Time, unless Cliffs shall otherwise agree in
writing or as otherwise expressly contemplated by this Agreement, the business
of R&B Falcon and the R&B Falcon Subsidiaries shall be conducted only in the
ordinary course of business consistent with past practice, and R&B Falcon shall
not, and shall not permit any of the R&B Falcon Subsidiaries to, take any action
(i) other than in the ordinary course of business consistent with past practice
or (ii) that would, or that reasonably could be expected to, result in any of
the representations and warranties set forth in this Agreement becoming untrue
or any of the conditions to the Merger set forth in Article VI not being
satisfied. For purposes hereof, acquisitions by R&B Falcon or any R&B Falcon
Subsidiary of entities or assets relating to or involved in the energy service
business shall be considered to be in the ordinary course of R&B Falcon's
business consistent with past practice. R&B Falcon promptly shall advise Cliffs
orally and in writing of any change or event having, or which, insofar as
reasonably can be foreseen, would have, a R&B Falcon MAE. R&B Falcon shall, and
shall cause the R&B Falcon Subsidiaries to, make available to Cliffs and its
representatives such information with respect to the business and affairs of R&B
Falcon and the R&B Falcon Subsidiaries as Cliffs shall reasonably request, and
shall confer at all times as Cliffs may reasonably request with one or more
representatives of Cliffs with respect to R&B Falcon's material operational
matters and the general status of its operations.
 
     4.2  Registration Statement. Promptly after the date of this Agreement, R&B
Falcon will file a registration statement (the "Registration Statement") on Form
S-4 with the Commission under the Securities
                                      A-18
<PAGE>   81
 
Act with respect to the offering, sale and delivery of the shares of R&B Falcon
Common Stock to be issued pursuant to the Merger, and R&B Falcon shall cooperate
with Cliffs in preparing the Proxy Statement. R&B Falcon will use its reasonable
efforts to cause such Registration Statement to become effective as soon as
practicable after filing. R&B Falcon shall cause (i) the Registration Statement
to comply as to form in all material respects with the requirements of the
Securities Act and the Exchange Act and the respective rules and regulations
adopted thereunder, and (ii) the Registration Statement (except with respect to
information concerning Cliffs and the Cliffs Subsidiaries furnished in writing
by or on behalf of Cliffs specifically for use therein, for which information
Cliffs shall be responsible) and the Proxy Statement (but only with respect to
information concerning R&B Falcon and the R&B Falcon Subsidiaries furnished in
writing by or on behalf of R&B Falcon specifically for use therein, for which
information R&B Falcon shall be responsible) to not contain any untrue statement
of any material fact or omit to state any material fact required to be stated
therein or necessary to make the statements made therein not misleading. R&B
Falcon will advise Cliffs in writing if prior to the Effective Time it shall
obtain knowledge of any fact that would, in its opinion, make it necessary to
amend or supplement the Registration Statement in order to make the statements
therein not misleading or to comply with applicable law.
 
     4.3  Adequate R&B Falcon Common Stock. R&B Falcon shall ensure that it has
adequate authorized and unissued shares of R&B Falcon Common Stock as of the
Effective Time to issue the required number of shares of R&B Falcon Common Stock
issuable pursuant to the Merger.
 
     4.4  Stock Exchange Listing. R&B Falcon shall use all reasonable efforts to
cause the shares of R&B Falcon Common Stock to be issued in the Merger and the
shares of R&B Falcon Common Stock to be reserved for issuance upon the exercise
of Cliffs Options to be assumed by R&B Falcon in the Merger, if any, to be
approved for listing on the New York Stock Exchange, subject to official notice
of issuance, prior to the Closing Date.
 
                                   ARTICLE V
 
                             ADDITIONAL AGREEMENTS
 
     5.1  Accountants Letters.
 
          (a) Cliffs shall use its reasonable efforts to cause Ernst & Young LLP
     to deliver a letter dated as of the date of the Proxy Statement, and
     addressed to Cliffs and R&B Falcon, in form and substance reasonably
     satisfactory to R&B Falcon and customary in scope and substance for agreed
     upon procedures letters delivered by independent public accountants in
     connection with registration statements and proxy statements similar to the
     Registration Statement and Proxy Statement.
 
          (b) R&B Falcon shall use its reasonable efforts to cause Arthur
     Andersen LLP to deliver a letter dated as of the date of the Registration
     Statement, and addressed to R&B Falcon and Cliffs, in form and substance
     reasonably satisfactory to Cliffs and customary in scope and substance for
     agreed upon procedures letters delivered by independent public accountants
     in connection with registration statements and proxy statements similar to
     the Registration Statement and Proxy Statement.
 
     5.2  Filings; Consents; Reasonable Efforts. Subject to the terms and
conditions of this Agreement, Cliffs and R&B Falcon shall (i) make all necessary
filings with respect to the Merger and this Agreement under the HSR Act, the
Securities Act, the Exchange Act and applicable blue sky or similar securities
laws and shall use all reasonable efforts to obtain required approvals and
clearances with respect thereto; (ii) obtain all consents, waivers, approvals,
authorizations and orders required in connection with the authorization,
execution and delivery of this Agreement and the consummation of the Merger; and
(iii) take, or cause to be taken, all appropriate action, and do, or cause to be
done, all things necessary, proper or advisable to consummate and make effective
as promptly as practicable the transactions contemplated by this Agreement.
 
     5.3  Notification of Certain Matters. Cliffs shall give prompt notice to
R&B Falcon, and R&B Falcon shall give prompt notice to Cliffs, orally and in
writing, of (i) the occurrence, or failure to occur, of any event which
occurrence or failure would be likely to cause any of its representations or
warranties contained in this
                                      A-19
<PAGE>   82
 
Agreement to be untrue or inaccurate at any time from the date hereof to the
Effective Time, and (ii) any material failure by it or any of its officers,
directors, employees or agents to comply with or satisfy any covenant, condition
or agreement to be complied with or satisfied by it hereunder.
 
     5.4  Agreement to Defend. If any claim, action, suit, investigation or
other proceeding by any governmental body or other person or other legal or
administrative proceeding is commenced that questions the validity or legality
of the transactions contemplated hereby or seeks damages in connection
therewith, the parties hereto agree to cooperate and use their reasonable
efforts to defend against and respond thereto.
 
     5.5  Expenses. Whether or not the Merger is consummated, all costs and
expenses incurred in connection with this Agreement and the transactions
contemplated hereby shall be paid by the party incurring such expense, except
that expenses incurred in connection with printing and mailing the Registration
Statement and the Proxy Statement shall be shared equally by R&B Falcon and
Cliffs.
 
     5.6  R&B Falcon's Board of Directors. R&B Falcon's Board of Directors will
take action to increase the number of directors comprising the full Board of
Directors of R&B Falcon at the Effective Time to eleven persons, and the
directors of R&B Falcon shall elect Douglas E. Swanson as a Class I director to
fill the vacancy created by the increase in the number of directors at or prior
to the Effective Time. If, prior to the Effective Time, Douglas E. Swanson shall
decline or be unable to serve, Cliffs shall designate another person to serve in
his stead, which designee shall be reasonably acceptable to R&B Falcon.
 
     5.7  Employment Agreements. As of the Effective Time, the Surviving
Corporation will enter into employment agreements with the executive officers of
Cliffs listed on Schedule 5.7 hereto in a form to be mutually agreed by Cliffs
and R&B Falcon providing for a salary and term equal to the salary and term
listed beside such employee's name under the columns headed "Salary" and "Term"
on Schedule 5.7 hereto. Cliffs shall use its reasonable efforts to cause each
such executive officer to deliver to R&B Falcon on or prior to the Closing Date
such an employment agreement.
 
     5.8  Cliffs Employee Benefits.
 
          (a) The amounts of target bonuses to employees of Cliffs and the
     Cliffs Subsidiaries under the Cliffs Incentive Bonus Plan have previously
     been determined by the Board of Directors of Cliffs. Final bonuses shall be
     awarded based upon Cliffs' achievement of certain financial and other
     targets for Cliffs for the fiscal year ending December 31, 1998, in a
     manner consistent with the Cliffs Incentive Bonus Plan and with the
     administration of the Cliffs Incentive Bonus Plan in prior years. The final
     amount of bonuses shall be determined by the Board of Directors of the
     Surviving Corporation and the Chief Executive Officer of the Surviving
     Corporation as provided in the Cliffs Incentive Bonus Plan. Bonuses under
     the Cliffs Incentive Bonus Plan will be paid not later than February 28,
     1999. Any employee of Cliffs or a Cliffs Subsidiary who is terminated after
     the Closing Date shall receive the full amount of any bonus to which such
     employee would have been entitled under the Cliffs Incentive Bonus Plan but
     for the termination of employment.
 
          (b) As soon as practicable after the Effective Time, those employees
     of Cliffs and the Cliffs Subsidiaries who become employees of the Surviving
     Corporation or a subsidiary of the Surviving Corporation or R&B Falcon or
     an R&B Falcon Subsidiary (the "Cliffs Employees") shall be entitled to
     participate in the R&B Falcon 401(k) savings and defined benefit pension
     plans in respect of their service after the Effective Time to the same
     extent that employees of R&B Falcon who are employed in comparable
     positions are entitled to participate. R&B Falcon and Cliffs further agree
     that any such employees shall be credited with their Cliffs service for
     purposes of eligibility and vesting in such plans provided by R&B Falcon
     (but not for purposes of benefit accruals under the defined benefit pension
     plan). Notwithstanding the preceding provisions of this Section 5.8(b), the
     Cliffs Employees shall be permitted to continue their active participation
     in the Cliffs Savings Plan until such time as such employees are entitled
     to participate in the R&B Falcon 401(k) and defined benefit pension plans.
 
          (c) Cliffs shall, and shall cause the Cliffs Subsidiaries to, if and
     to the extent requested by R&B Falcon prior to the Effective Time, take all
     actions necessary (i) to amend or terminate the Cliffs Executive Split
     Dollar Life Insurance Plan as so requested by R&B Falcon, and (ii) to amend
     the Cliffs
                                      A-20
<PAGE>   83
 
     Compensation Deferral Plan to provide that no further amounts may be
     deferred thereunder after the Effective Time and that such plan shall
     terminate five years after the Effective Time.
 
          (d) As soon as practicable after the Effective Time, the Cliffs
     Employees shall be entitled to participate in all other R&B Falcon welfare
     plans (health, disability and life insurance, etc.) in respect of their
     service after the Effective Time to the same extent that employees of R&B
     Falcon who are employed in comparable positions are entitled to
     participate; provided that life insurance benefits will not be so provided
     to any person who continues to receive company funded life insurance under
     the Cliffs Executive Split Dollar Life Insurance Plan. R&B Falcon and
     Cliffs further agree that the Cliffs Employees shall be credited for their
     service with Cliffs for purposes of eligibility in such plans provided by
     R&B Falcon. The Cliffs Employees' benefits under R&B Falcon's medical
     benefit plan shall not be subject to any exclusions for any pre-existing
     conditions, and credit shall be received for any deductibles or
     out-of-pocket amounts previously paid by the Cliffs Employees.
 
          (e) At the Effective Time, the obligation of Cliffs to issue shares of
     Cliffs Common Stock pursuant to the Cliffs Compensation Deferral Plan shall
     be assumed by R&B Falcon and shall thereafter constitute an obligation of
     R&B Falcon to issue, on the same terms and conditions as were applicable
     under the Cliffs Compensation Deferral Plan, 1.7 shares of R&B Falcon
     Common Stock (rounded downward to the nearest whole number) for each share
     of Cliffs Common Stock to be issued thereunder. R&B Falcon shall ensure at
     all times that it has sufficient authorized and unissued shares of R&B
     Falcon Common Stock to issue in satisfaction of such obligation.
 
     5.9  Cliffs Stock Options.
 
          (a) At the Effective Time, each outstanding Cliffs Option under either
     of the Cliffs Stock Option Plans, whether vested or unvested, shall be
     deemed to constitute an option to acquire, on the same terms and conditions
     as were applicable under the applicable Cliffs Stock Option Plan and such
     Cliffs Option, 1.7 shares of R&B Falcon Common Stock (rounded downward to
     the nearest whole number), at a price per share (rounded upward to the
     nearest whole cent) equal to (y) the exercise price per share for the
     shares of Cliffs Common Stock purchasable pursuant to such Cliffs Option
     immediately prior to the Effective Time divided by (z) 1.7.
 
          (b) Upon proper exercise after the Effective Time of any Cliffs Option
     that has become, pursuant to this Section 5.9, an option to acquire R&B
     Falcon Common Stock, R&B Falcon shall issue such shares of R&B Falcon
     Common Stock to the holder exercising such option. R&B Falcon shall ensure
     at all times that it has sufficient authorized and unissued shares of R&B
     Falcon Common Stock to issue such shares upon proper exercise of such
     options.
 
          (c) As soon as practicable after the Effective Time, R&B Falcon shall
     deliver to the participants in Cliffs Stock Option Plans appropriate notice
     setting forth such participants' rights pursuant thereto, and the grants
     pursuant to the Cliffs Stock Option Plans shall continue in effect on the
     same terms and conditions (subject to the adjustments required by this
     Section 5.9 after giving effect to the Merger).
 
          (d) As soon as practicable after the Effective Time, R&B Falcon shall
     file a registration statement on Form S-8 (or any successor or other
     appropriate forms), or another appropriate form with respect to the shares
     of R&B Falcon Common Stock subject to such options and shall use its
     reasonable efforts to maintain the effectiveness of such registration
     statement or registration statements (and maintain the current status of
     the prospectus or prospectuses contained therein) for so long as such
     options remain outstanding.
 
          (e) The Board of Directors of Cliffs shall, prior to or as of the
     Effective Time, take all necessary actions, pursuant to and in accordance
     with the terms of the Cliffs Stock Option Plans and the instruments
     evidencing the Cliffs Options, to provide for the conversion of the Cliffs
     Options into options to acquire R&B Falcon Common Stock in accordance with
     this Section 5.9, and to ensure that no consent of the holders of the
     Cliffs Options is required in connection with such conversion.
 
                                      A-21
<PAGE>   84
 
     5.10  New R&B Falcon Option Grants. As of the Effective Time, R&B Falcon
shall grant options to purchase R&B Falcon Common Stock under the R&B Falcon
1998 Employee Long-Term Incentive Plan to each of the Cliffs employees listed on
Schedule 5.10 hereto in an amount equal to the number of options listed beside
each such employee's name under the column headed "New Option Award" on Schedule
5.10 hereto. The exercise price of such options shall be equal to the closing
sales price of R&B Falcon Common Stock, as reported on the New York Stock
Exchange, on the date on which the Effective Time occurs. Such options shall
have a term of ten years and shall vest as to 50% of such options on the first
anniversary of the grant date, as to an additional 25% on the second anniversary
of the grant date, and as to the remaining 25% on the third anniversary of the
grant date. Such options shall otherwise be on terms and conditions consistent
with employee stock options granted by R&B Falcon prior to the Effective Time.
 
     5.11  Post-Effective Time Mailing. As soon as practicable following the
Effective Time, R&B Falcon shall cause to be mailed to each holder of
certificates that represented shares of Cliffs Common Stock immediately prior to
the Effective Time, at such holder's address as it appears on Cliffs's stock
transfer records, a letter of transmittal and other information advising such
holder of the consummation of the Merger along with information and instructions
to enable such holder to effect the exchange of stock certificates as
contemplated by Article I of this Agreement.
 
     5.12  Tax-Free Reorganization.
 
          (a) R&B Falcon and Cliffs shall each use its reasonable efforts to
     cause the Merger to be treated as a reorganization within the meaning of
     Section 368(a) of the Code.
 
          (b) To the extent permitted under applicable tax laws, the Merger
     shall be reported as a reorganization within the meaning of Section
     368(a)(1)(A) and Section 368(a)(2)(E) of the Code in all federal, state and
     local Tax Returns after the Effective Time.
 
          (c) R&B Falcon will cause the Surviving Corporation to hold following
     the Merger at least 90% of the fair market value of its net assets and at
     least 70% of the fair market value of its gross assets, and at least 90% of
     the fair market value of Sub's net assets and 70% of the fair market value
     of Sub's gross assets, held immediately prior to the Merger. For purposes
     of the preceding sentence, amounts paid by Cliffs to its stockholders who
     receive cash or other property, to pay reorganization expenses, and in
     connection with redemptions and distributions (except for regular, normal
     distributions), will be treated as assets of Cliffs immediately prior to
     the Merger.
 
     5.13  Indemnification.
 
          (a) From and after the Effective Time, R&B Falcon and the Surviving
     Corporation shall, subject to the proviso at the end of this Section
     5.13(a), indemnify, defend and hold harmless each person who is now, or has
     been at any time prior to the date hereof or who becomes prior to the
     Effective Time, an officer, director or employee of Cliffs or any of the
     Cliffs Subsidiaries (the "Indemnified Parties") against losses, claims,
     damages, costs, expenses, liabilities or judgments or amounts that are paid
     in settlement with the approval of the indemnifying party (which approval
     shall not be unreasonably withheld) of or in connection with a claim,
     action, suit, proceeding or investigation based in whole or in part on or
     arising in whole or in part out of the fact that such person is or was a
     director, officer or employee of Cliffs or any of the Cliffs Subsidiaries,
     whether pertaining to any matter existing or occurring at or prior to the
     Effective Time and whether reasserted or claimed prior to, or at or after,
     the Effective Time ("Indemnified Liabilities"), including without
     limitation, all Indemnified Liabilities based in whole or in part on, or
     arising in whole or in part out of, or pertaining to this Agreement, the
     Merger or the transactions contemplated hereby, AND SPECIFICALLY INCLUDING
     ANY INDEMNIFIED LIABILITY THAT MAY BE BASED ON THE SOLE OR CONTRIBUTORY
     NEGLIGENCE (WHETHER ACTIVE, PASSIVE OR GROSS) OF ANY INDEMNIFIED PARTY, and
     R&B Falcon and the Surviving Corporation shall, subject to the proviso at
     the end of this Section 5.13(a), pay expenses in advance of the final
     disposition of any such action or proceeding to each Indemnified Party;
     provided, however, that in no event shall R&B Falcon or the Surviving
     Corporation be required to indemnify any Indemnified Party or advance any
     expenses on behalf of any Indemnified Party pursuant to this
                                      A-22
<PAGE>   85
 
     Section 5.13 to any greater extent than Cliffs would have been required to
     so indemnify or advance expenses pursuant to the certificate of
     incorporation or bylaws of Cliffs or contractual indemnification agreements
     binding on Cliffs, each as in existence on August 11, 1998.
 
          (b) The defense of any such claim, action, suit, proceeding or
     investigation shall be conducted by R&B Falcon and the Surviving
     Corporation. If R&B Falcon or the Surviving Corporation has failed to
     conduct such defense or counsel for the Indemnified Parties has advised the
     Indemnified Parties that there are substantive issues that raise conflicts
     of interest between R&B Falcon or the Surviving Corporation and the
     Indemnified Parties, the Indemnified Parties may retain counsel
     satisfactory to them and, subject to Section 5.13(a), R&B Falcon and the
     Surviving Corporation shall pay all reasonable fees and expenses of such
     counsel for the Indemnified Parties promptly as statements therefor are
     received. The party not conducting the defense will use reasonable efforts
     to assist in the vigorous defense of any such matter, provided that such
     party shall not be liable for any settlement of any claim effected without
     its written consent, which consent, however, shall not be unreasonably
     withheld. Any Indemnified Party wishing to claim indemnification under this
     Section 5.13, upon learning of any such claim, action, suit, proceeding or
     investigation, shall notify R&B Falcon and the Surviving Corporation (but
     the failure so to notify shall not relieve them from any liability which
     they may have under this Section 5.13 except to the extent such failure
     materially prejudices them). If R&B Falcon and the Surviving Corporation
     are responsible for the attorneys' fees of the Indemnified Parties, then
     the Indemnified Parties as a group may retain only one law firm to
     represent them with respect to each such matter unless there is, under
     applicable standards of professional conduct, a conflict on any significant
     issue between the positions of any two or more Indemnified Parties.
 
          (c) The Surviving Corporation shall purchase and maintain for a period
     of six years after the Effective Time continuation coverage for runoff
     liability with respect to Cliffs' (i) directors' and officers' liability
     insurance policy as in effect on August 11, 1998 (or obtain a directors'
     and officers' liability insurance policy for the benefit of those persons
     covered by Cliffs' current directors' and officers' liability insurance
     policy with comparable coverage) and (ii) fiduciary liability policy,
     commercial crime policy and special crime policy as in effect on August 11,
     1998 (or obtain similar policies for those persons currently covered
     thereby with comparable coverage). R&B Falcon will cause its fiduciary
     liability policy to be endorsed to cover the individuals acting as
     fiduciaries for Cliffs subsequent to the Effective Date.
 
     5.14  Cliffs Rights Plan. Cliffs shall take or cause to be taken all
further action reasonably necessary pursuant to the Cliffs Rights Plan in order
to prevent the rights issuable thereunder from becoming exercisable as a result
of the execution of this Agreement, the Merger or the consummation of any of the
transactions contemplated hereby.
 
                                   ARTICLE VI
 
                                   CONDITIONS
 
     6.1  Conditions to Obligation of Each Party to Effect the Merger. The
respective obligations of each party to effect the Merger shall be subject to
the fulfillment at or prior to the Closing Date of the following conditions:
 
          (a) This Agreement shall have been approved and adopted by the
     requisite vote of the stockholders of Cliffs, as may be required by law,
     and by the rules of the New York Stock Exchange, respectively, and by any
     applicable provisions of Cliffs' certificate of incorporation or bylaws;
 
          (b) The waiting period (and any extension thereof) applicable to the
     consummation of the Merger under the HSR Act shall have expired or been
     terminated;
 
          (c) No order shall have been entered and remain in effect in any
     action or proceeding before any foreign, federal or state court or
     governmental agency or other foreign, federal or state regulatory or
     administrative agency or commission that would prevent or make illegal the
     consummation of the Merger;
                                      A-23
<PAGE>   86
 
          (d) The Registration Statement shall be effective (and remain
     effective on the Closing Date), and all post-effective amendments filed
     shall have been declared effective or shall have been withdrawn; and no
     stop-order suspending the effectiveness thereof shall have been issued and
     no proceedings for that purpose shall have been initiated or, to the
     knowledge of the parties, threatened by the Commission;
 
          (e) There shall have been obtained any and all material permits,
     approvals and consents of securities or blue sky commissions of any
     jurisdiction, and of any other governmental body or agency, that reasonably
     may be deemed necessary so that the consummation of the Merger and the
     transactions contemplated thereby will be in compliance with applicable
     laws, the failure to comply with which would have a material adverse effect
     on the business, financial condition or results of operations of the
     Surviving Corporation and its subsidiaries, taken as a whole, after
     consummation of the Merger;
 
          (f) The shares of R&B Falcon Common Stock issuable upon consummation
     of the Merger and the shares of R&B Falcon Common Stock issuable upon
     exercise of any Cliffs Options that are to become options to purchase R&B
     Falcon Common Stock pursuant to Section 5.9 shall have been approved for
     listing on the New York Stock Exchange, subject to official notice of
     issuance; and
 
          (g) All approvals of private persons or corporations, (i) the granting
     of which is necessary for the consummation of the Merger or the
     transactions contemplated in connection therewith and (ii) the non-receipt
     of which would have a material adverse effect on the business, financial
     condition or results of operations of the Surviving Corporation and its
     subsidiaries, taken as a whole after the consummation of the Merger, shall
     have been obtained.
 
     6.2  Additional Conditions to Obligations of R&B Falcon. The obligation of
R&B Falcon to effect the Merger is, at the option of R&B Falcon, also subject to
the fulfillment at or prior to the Closing Date of the following conditions:
 
          (a) The representations and warranties of Cliffs contained in Section
     2.2 shall be accurate as of the date of this Agreement and (except to the
     extent such representations and warranties speak specifically as of an
     earlier date) as of the Closing Date as though such representations and
     warranties had been made at and as of that time; all of the terms,
     covenants and conditions of this Agreement to be complied with and
     performed by Cliffs on or before the Closing Date shall have been duly
     complied with and performed in all material respects; and a certificate to
     the foregoing effect dated the Closing Date and signed by the chief
     executive officer of Cliffs shall have been delivered to R&B Falcon;
 
          (b) Since the date of this Agreement, no material adverse change in
     the financial condition, results of operations or business of Cliffs and
     the Cliffs Subsidiaries, taken as a whole, shall have occurred (other than
     as a result of material adverse changes affecting the contract drilling
     industry generally or the U.S. economy generally), and no Cliffs MAE shall
     have occurred, and R&B Falcon shall have received a certificate signed by
     the chief executive officer of Cliffs dated the Closing Date to such
     effect;
 
          (c) The Board of Directors of R&B Falcon shall have received from
     Donaldson, Lufkin & Jenrette Securities Corporation, financial advisor to
     R&B Falcon, a written opinion, dated as of the date of this Agreement,
     satisfactory in form and substance to the Board of Directors of R&B Falcon,
     to the effect that the conversion ratio of 1.7 shares of R&B Falcon Common
     Stock to be issued for each share of Cliffs Common Stock pursuant to the
     Merger is fair to the stockholders of R&B Falcon from a financial point of
     view, which opinion shall have been confirmed in writing to such Board as
     of the date the Proxy Statement is first mailed to the stockholders of
     Cliffs and shall not have been subsequently withdrawn;
 
          (d) Cliffs shall have received, and furnished written copies to R&B
     Falcon of, each of the Cliffs affiliate letters required pursuant to
     Section 3.5;
 
          (e) Cliffs shall have received, and furnished written copies to R&B
     Falcon of, each Waiver and Release required pursuant to Section 3.6; and
 
                                      A-24
<PAGE>   87
 
          (f) R&B Falcon shall have received from Griggs & Harrison, P.C.,
     counsel to Cliffs, an opinion dated the Closing Date in form and substance
     reasonably acceptable to R&B Falcon covering such matters as are customary
     in similar transactions.
 
     6.3  Additional Conditions to Obligations of Cliffs. The obligation of
Cliffs to effect the Merger is, at the option of Cliffs, also subject to the
fulfillment at or prior to the Closing Date of the following conditions:
 
          (a) The representations and warranties of R&B Falcon and Sub contained
     in Section 2.1 shall be accurate as of the date of this Agreement and
     (except to the extent such representations and warranties speak
     specifically as of an earlier date) as of the Closing Date as though such
     representations and warranties had been made at and as of that time; all
     the terms, covenants and conditions of this Agreement to be complied with
     and performed by R&B Falcon or Sub on or before the Closing Date shall have
     been duly complied with and performed in all material respects; and a
     certificate to the foregoing effect dated the Closing Date and signed by
     the chief executive officer of R&B Falcon shall have been delivered to
     Cliffs;
 
          (b) Since the date of this Agreement, no material adverse change in
     the financial condition, results of operations or business of R&B Falcon
     and the R&B Falcon Subsidiaries, taken as a whole, shall have occurred
     (other than as a result of material adverse changes affecting the contract
     drilling industry generally or the U.S. economy generally), and no R&B
     Falcon MAE shall have occurred, and Cliffs shall have received a
     certificate signed by the chief executive officer of R&B Falcon dated the
     Closing Date to such effect;
 
          (c) The Board of Directors of Cliffs shall have received from
     Jefferies & Company, Inc., financial advisor to Cliffs, a written opinion,
     dated as of the date of this Agreement, satisfactory in form and substance
     to the Board of Directors of Cliffs, to the effect that the conversion
     ratio of 1.7 shares of R&B Falcon Common Stock to be issued for each share
     of Cliffs Common Stock pursuant to the Merger is fair to the stockholders
     of Cliffs from a financial point of view, which opinion shall have been
     confirmed in writing to such Board as of the date the Proxy Statement is
     first mailed to the stockholders of Cliffs and shall not have been
     subsequently withdrawn;
 
          (d) Cliffs shall have received from Gardere Wynne Sewell & Riggs,
     L.L.P., counsel to R&B Falcon, an opinion dated the Closing Date in form
     and substance reasonably acceptable to Cliffs covering such matters as are
     customary in similar transactions; and
 
          (e) Cliffs shall have received a written opinion dated as of the
     Closing Date to the effect that for U.S. federal income tax purposes (i)
     the Merger will be treated as a reorganization within the meaning of
     Section 368(a) of the Code, (ii) R&B Falcon, Sub and Cliffs will each be a
     party to that reorganization within the meaning of Section 368(b) of the
     Code, and (iii) Cliffs and the stockholders of Cliffs will not recognize
     any gain or loss as a result of the Merger, other than to the extent such
     stockholders receive cash in lieu of fractional shares. In rendering such
     opinion, counsel may require and rely upon (and may incorporate by
     reference) representations and covenants to the extent reasonable,
     including those contained in certificates of officers and/or directors of
     R&B Falcon, Cliffs and Sub and others. Cliffs shall have received executed
     copies of the certificates of officers and directors of Cliffs, R&B Falcon,
     Sub and others that may reasonably be required by counsel in connection
     with the tax opinions referred to in this Section 6.3(e).
 
                                      A-25
<PAGE>   88
 
                                  ARTICLE VII
 
                                 MISCELLANEOUS
 
     7.1  Termination. This Agreement may be terminated and the Merger and the
other transactions contemplated herein may be abandoned at any time prior to the
Effective Time, whether prior to or after approval by the stockholders of
Cliffs:
 
          (a) by mutual consent of R&B Falcon and Cliffs;
 
          (b) by either R&B Falcon or Cliffs if the Merger has not been effected
     on or before February 28, 1999; provided, however, that the right to
     terminate this Agreement under this Section 7.1(b) shall not be available
     to a party whose failure to fulfill any obligation under this Agreement has
     been the cause of or resulted in the failure of the Merger to occur on or
     before such date;
 
          (c) by R&B Falcon if the condition set forth in Section 6.2(c) is not
     satisfied;
 
          (d) by Cliffs if the condition set forth in Section 6.3(c) is not
     satisfied;
 
          (e) by either R&B Falcon or Cliffs if a final, unappealable order of a
     judicial or administrative authority of competent jurisdiction to restrain,
     enjoin or otherwise prevent a consummation of this Agreement or the
     transactions contemplated in connection herewith shall have been entered;
 
          (f) by either R&B Falcon or Cliffs if the required approval of the
     stockholders of Cliffs provided for in Section 3.3 is not received in a
     vote duly taken at the Cliffs stockholders' meeting;
 
          (g) by R&B Falcon if (i) since the date of this Agreement there has
     been a material adverse change in the results of operations, financial
     condition or business of Cliffs and the Cliffs Subsidiaries, taken as a
     whole (other than as a result of material adverse changes affecting the
     contract drilling industry generally or the U.S. economy generally), or
     (ii) there has been a breach of any representation or warranty or covenant
     set forth in this Agreement by Cliffs which breach has not been cured
     within 30 days following receipt by Cliffs of notice of such breach;
 
          (h) by Cliffs if (i) since the date of this Agreement there has been a
     material adverse change in the results of operations, financial condition
     or business of R&B Falcon and the R&B Falcon Subsidiaries, taken as a whole
     (other than as a result of material adverse changes affecting the contract
     drilling industry generally or the U.S. economy generally), or (ii) there
     has been a breach of any representation or warranty or covenant set forth
     in this Agreement by R&B Falcon which breach has not been cured within 30
     days following receipt by R&B Falcon of notice of such breach; or
 
          (i) by R&B Falcon if the Board of Directors of Cliffs exercises its
     right pursuant to Section 3.4 not to convene a meeting of the Cliffs
     stockholders to approve the Merger or to withdraw or otherwise change its
     recommendation that the Cliffs stockholders approve the Merger.
 
     7.2  Effect of Termination.
 
          (a) In the event of any termination of this Agreement pursuant to
     Section 7.1, (i) the provisions of the Confidentiality Agreement and the
     provisions of Section 5.5 shall survive any such termination, and (ii) such
     termination shall not relieve any party from liability for any breach of
     this Agreement, provided that a party's liability for any such breach shall
     be limited to that set forth in the provisions of this Section 7.2.
 
          (b) If this Agreement is terminated (i) pursuant to Section 7.1(d) and
     Cliffs is not entitled to terminate this Agreement pursuant to Section
     7.1(h)(i), or (ii) pursuant to Section 7.1(f), 7.1(g)(ii) or 7.1(i), then
     Cliffs shall promptly, but in no event later than five business days after
     written request by R&B Falcon, pay to R&B Falcon an amount equal to
     $15,000,000 as liquidated damages.
 
          (c) If this Agreement is terminated (i) pursuant to Section 7.1(c) and
     R&B Falcon is not entitled to terminate this Agreement pursuant to Section
     7.1(g)(i), or (ii) pursuant to Section 7.1(h)(ii), then
 
                                      A-26
<PAGE>   89
 
     R&B Falcon shall promptly, but in no event later than five business days
     after written request by Cliffs, pay to Cliffs an amount equal to
     $15,000,000 as liquidated damages.
 
          (d) If this Agreement is terminated (i) pursuant to Section 7.1(d) and
     Cliffs is not entitled to terminate this Agreement pursuant to Section
     7.1(h)(i), or (ii) pursuant to Section 7.1(f), 7.1(g)(ii) or 7.1(i), or if
     Cliffs terminates this Agreement pursuant to Section 7.1(b), and (A) after
     the date of this Agreement but at or before the time this Agreement is
     terminated a Cliffs Acquisition Transaction shall have been made known to
     Cliffs or shall have been made directly to Cliffs stockholders or any
     person shall have publicly announced an intention to effect a Cliffs
     Acquisition Transaction, and (B) any Cliffs Acquisition Transaction
     (whether the same or different from the one referenced in clause (A)) is
     consummated at any time within one year after the date of termination of
     this Agreement, then Cliffs shall promptly pay to R&B Falcon the sum of
     $30,000,000, less any amounts previously paid by Cliffs to R&B Falcon
     pursuant to Section 7.2(b).
 
     7.3  Waiver and Amendment. Any provision of this Agreement may be waived at
any time by the party that is, or whose stockholders are, entitled to the
benefits thereof. This Agreement may not be amended or supplemented at any time,
except by an instrument in writing signed on behalf of each party hereto,
provided that after this Agreement has been approved and adopted by the
stockholders of Cliffs, this Agreement may be amended only as may be permitted
by applicable provisions of the DGCL. The waiver by any party hereto of any
condition or of a breach of another provision of this Agreement shall not
operate or be construed as a waiver of any other condition or subsequent breach.
The waiver by any party hereto of any of the conditions precedent to its
obligations under this Agreement shall not preclude it from seeking redress for
breach of this Agreement other than with respect to the condition so waived.
 
     7.4  Nonsurvival of Representations, Warranties and Agreements. None of the
representations, warranties, covenants or agreements in this Agreement shall
survive the Effective Time, except for the terms of Article I, Section 2.1(h),
Sections 5.8, 5.9, 5.11, 5.12 and 5.13, and Article VII.
 
     7.5  Public Statements. Cliffs and R&B Falcon agree to consult with each
other prior to issuing any press release or otherwise making any public
statement with respect to the transactions contemplated hereby, and shall not
issue any such press release or make any such public statement without the
consent of the other, except as may be required by law or applicable stock
exchange rules.
 
     7.6  Assignment. This Agreement shall inure to the benefit of and will be
binding upon the parties hereto and their respective legal representatives,
successors and permitted assigns. Except as set forth in this Agreement, this
Agreement shall not be assignable by the parties hereto.
 
     7.7  Notices. All notices, requests, demands, claims and other
communications which are required to be or may be given under this Agreement
shall be in writing and shall be deemed to have been duly given if (i) delivered
in person or by courier, (ii) sent by confirmed telecopy or facsimile
transmission, or (iii) mailed, certified first class mail, postage prepaid,
return receipt requested, to the parties hereto at the following addresses:
 
          if to Cliffs:       Cliffs Drilling Company
                              300 Citicorp Center
                              1200 Smith Street
                              Houston, Texas 77002
                              Attention: Douglas E. Swanson
 
          with a copy to:     Griggs & Harrison, P.C.
                              1301 McKinney, Suite 3200
                              Houston, Texas 77010
                              Attention: W. Garney Griggs
 
                                      A-27
<PAGE>   90
 
          if to R&B Falcon or Sub:
                              R&B Falcon Drilling Corporation
                              901 Threadneedle
                              Houston, Texas 77079
                              Attention: Steven A. Webster
 
          with a copy to:     Gardere Wynne Sewell & Riggs, L.L.P.
                              333 Clay, Suite 800
                              Houston, Texas 77002
                              Attention: Frank M. Putman
 
or to such other address as any party shall have furnished to the other by
notice given in accordance with this Section 7.7. Such notices shall be
effective, (i) if delivered in person or by courier, upon actual receipt by the
intended recipient, (ii) if sent by telecopy or facsimile transmission, on the
date indicated by the confirmation, or (iii) if mailed, upon the earlier of five
days after deposit in the mail and the date of delivery as shown by the return
receipt therefor.
 
     7.8  Governing Law. This Agreement shall be governed by and construed in
accordance with the substantive law of the State of Delaware without giving
effect to the principles of conflicts of law thereof.
 
     7.9  Severability. If any term, provision, covenant or restriction of this
Agreement is held by a court of competent jurisdiction to be invalid, void or
unenforceable, the remainder of the terms, provision, covenants and restrictions
of this Agreement shall continue in full force and effect and shall in no way be
affected, impaired or invalidated.
 
     7.10  Counterparts. This Agreement may be executed in counterparts, each of
which shall be an original, but all of which together shall constitute one and
the same agreement.
 
     7.11  Headings. The Section headings herein are for convenience only and
shall not affect the construction hereof.
 
     7.12  Entire Agreement; Third Party Beneficiaries. This Agreement and the
Confidentiality Agreement constitute the entire agreement and supersede all
other prior agreements and understandings, both oral and written, among the
parties or any of them, with respect to the subject matter hereof and neither
this nor any document delivered in connection with this Agreement confers upon
any person not a party hereto any rights or remedies hereunder except as
provided in Sections 5.7, 5.8, 5.9, 5.10 and 5.13, which are intended for the
benefit of, and shall be enforceable by, the Indemnified Parties and their heirs
or representatives or the employees described therein, as applicable.
 
     7.13  Disclosure Letters.
 
          (a) The Cliffs Disclosure Letter, executed by Cliffs as of the date
     hereof, and delivered to R&B Falcon on the date hereof, contains all
     disclosure required to be made by Cliffs under the various terms and
     provisions of this Agreement. Each item of disclosure set forth in the
     Cliffs Disclosure Letter specifically refers to the Article and Section of
     the Agreement to which such disclosure responds, and shall not be deemed to
     be disclosed with respect to any other Article or Section of the Agreement.
 
          (b) The R&B Falcon Disclosure Letter, executed by R&B Falcon as of the
     date hereof, and delivered to Cliffs on the date hereof, contains all
     disclosure required to be made by R&B Falcon under the various terms and
     provisions of this Agreement. Each item of disclosure set forth in the R&B
     Falcon Disclosure Letter specifically refers to the Article and Section of
     the Agreement to which such disclosure responds, and shall not be deemed to
     be disclosed with respect to any other Article or Section of the Agreement.
 
                    [REMAINDER OF PAGE INTENTIONALLY BLANK.
                     THE NEXT PAGE IS THE SIGNATURE PAGE.]
 
                                      A-28
<PAGE>   91
 
     IN WITNESS WHEREOF, each of the parties has caused this Agreement to be
executed on its behalf by its officers thereunto duly authorized, all as of the
date first above written.
 
                                            CLIFFS DRILLING COMPANY
 
                                            BY:   /s/ DOUGLAS E. SWANSON
 
                                              ----------------------------------
                                                Douglas E. Swanson, President
 
                                            R&B FALCON CORPORATION
 
                                            BY:    /s/ STEVEN A. WEBSTER
 
                                              ----------------------------------
                                                 Steven A. Webster, President
 
                                            RBF CLIFFS ACQUISITION CORP.
 
                                            BY:    /s/ STEVEN A. WEBSTER
 
                                              ----------------------------------
                                                 Steven A. Webster, President
 
                                      A-29
<PAGE>   92
 
                                                                       EXHIBIT A
 
                            FORM OF AFFILIATE LETTER
 
                                           , 1998
 
R&B Falcon Corporation
901 Threadneedle
Houston, Texas 77079
Attention: Leighton E. Moss
 
Ladies and Gentlemen:
 
     I have been advised that as of the date of this letter I may be deemed to
be an "affiliate" of Cliff Drilling Company, a Delaware corporation ("Cliffs"),
as the term "affiliate" is defined for purposes of paragraphs (c) and (d) of
Rule 145 of the rules and regulations (the "Rules and Regulations") of the
Securities and Exchange Commission (the "SEC") under the Securities Act of 1933,
as amended (the "Securities Act"). Pursuant to the terms of the Agreement and
Plan of Merger, dated as of August   , 1998 (the "Merger Agreement"), among
Cliffs, R&B Falcon Corporation, a Delaware corporation ("R&B Falcon") and RBF
Cliffs Acquisition Corp., a Delaware corporation and wholly owned subsidiary of
R&B Falcon ("Sub"), Sub will be merged with and into Cliffs (the "Merger"), with
Cliffs as the surviving corporation.
 
     As a result of the Merger, I may receive shares of common stock, $0.01 par
value per share, of R&B Falcon ("R&B Falcon Common Stock") or options to
purchase shares of R&B Falcon Common Stock (the "R&B Falcon Options") (the R&B
Falcon Common Stock, the R&B Falcon Options and any R&B Falcon Common Stock
issued upon exercise of the R&B Falcon Options are collectively referred to
hereinafter as the "R&B Falcon Securities") in exchange for shares of the common
stock, $0.01 par value per share, of Cliffs (the "Cliffs Common Stock") or
options to purchase Cliffs Common Stock, as the case may be.
 
     I represent, warrant and covenant to R&B Falcon that if I receive any R&B
Falcon Securities as a result of the Merger:
 
          a. I shall not make any sale, transfer or other disposition of the R&B
     Falcon Securities in violation of the Securities Act or the Rules and
     Regulations.
 
          b. I have carefully read this letter and the Merger Agreement and, to
     the extent I felt it necessary, discussed the requirements of such
     documents and other applicable limitations upon my ability to sell,
     transfer or otherwise dispose of the R&B Falcon Securities with my counsel
     or counsel for Cliffs.
 
          c. I have been advised that the issuance of R&B Falcon Common Stock to
     me pursuant to the Merger has been registered with the SEC under the
     Securities Act on a Registration Statement on Form S-4. However, I have
     also been advised that, since at the time the Merger was submitted for a
     vote of the stockholders of Cliffs, I may be deemed to have been an
     affiliate of Cliffs and the distribution by me of the R&B Falcon Securities
     has not been registered under the Act, I may not sell, transfer or
     otherwise dispose of the R&B Falcon Securities issued to me in the Merger
     unless (i) such sale, transfer or other disposition has been registered
     under the Securities Act, (ii) such sale, transfer or other disposition is
     made in conformity with Rule 145 promulgated by the SEC under the
     Securities Act, or (iii) in the opinion of counsel reasonably acceptable to
     R&B Falcon, or a "no-action" letter obtained by me from the staff of the
     SEC, such sale, transfer or other disposition is otherwise exempt from
     registration under the Securities Act. Pursuant to the regulations of the
     SEC as currently in effect, I may make bona fide gifts or distributions
     without consideration so long as the recipients thereof agree not to sell,
     transfer or otherwise dispose of the R&B Falcon Common Stock except as
     provided herein. With respect to a transfer under clause (ii) above, I
     understand that unless you have a reasonable basis for believing to the
     contrary, such transfer will be viewed by you as in conformity with Rule
     145 upon my delivery to you or your transfer agent of a broker's letter in
     customary form stating that the requirements of Rule 145(d)(1) have been
     met.
 
                                      A-30
<PAGE>   93
 
          d. I understand that R&B Falcon is under no obligation to register the
     sale, transfer or other disposition of the R&B Falcon Securities by me or
     on my behalf under the Securities Act or to take any other action necessary
     in order to make compliance with an exemption from such registration
     available other than to timely file all reports as required under the
     Securities Exchange Act of 1934, as amended, and the rules and regulations
     of the SEC thereunder.
 
          e. I also understand that stop transfer instructions will be given to
     R&B Falcon's transfer agent with respect to the R&B Falcon Common Stock and
     that there will be placed on the certificates for the R&B Falcon Common
     Stock issued to me in the Merger or the R&B Falcon Common Stock issued to
     me upon exercise of the R&B Falcon Options, or any substitutions therefor,
     a legend stating in substance:
 
        "THE SHARES REPRESENTED BY THIS CERTIFICATE WERE ISSUED IN A TRANSACTION
        TO WHICH RULE 145 PROMULGATED UNDER THE SECURITIES ACT OF 1933 APPLIES.
        THE SHARES REPRESENTED BY THIS CERTIFICATE MAY BE TRANSFERRED ONLY IN
        ACCORDANCE WITH THE TERMS OF AN AGREEMENT DATED             , 1998
        BETWEEN THE REGISTERED HOLDER HEREOF AND R&B FALCON CORPORATION, A COPY
        OF WHICH AGREEMENT IS ON FILE AT THE PRINCIPAL OFFICES OF R&B FALCON
        CORPORATION."
 
          f. I also understand that unless the transfer by me of my R&B Falcon
     Securities has been registered under the Securities Act or is made in a
     sale in conformity with the provisions of Rule 145, R&B Falcon reserves the
     right to put the following legend on the certificates issued to my
     transferee:
 
        "THE SHARES REPRESENTED BY THIS CERTIFICATE WERE ACQUIRED FROM A PERSON
        WHO RECEIVED SUCH SHARES IN A TRANSACTION TO WHICH RULE 145 PROMULGATED
        UNDER THE SECURITIES ACT OF 1933 APPLIES. THE SHARES HAVE BEEN ACQUIRED
        BY THE HOLDER NOT WITH A VIEW TO, OR FOR RESALE IN CONNECTION WITH, ANY
        DISTRIBUTION THEREOF WITHIN THE MEANING OF THE SECURITIES ACT OF 1933
        AND MAY NOT BE SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT PURSUANT TO
        AN EFFECTIVE REGISTRATION STATEMENT OR IN ACCORDANCE WITH AN EXEMPTION
        FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT OF 1933."
 
     The legend(s) set forth in paragraphs "e" and, if applicable, "f" above
shall be removed by delivery of substitute certificates without such legend if
such legend is not required for purposes of the Securities Act or this letter.
Such legend(s) and the stop transfer orders referred to above will be removed if
(i) one year shall have elapsed from the date the undersigned acquired the R&B
Falcon Securities received in the Merger and the provisions of Rule 145(d)(2)
are then available to the undersigned, (ii) two years shall have elapsed from
the date the undersigned acquired the R&B Falcon Securities received in the
Merger and the provisions of Rule 145(d)(3) are then applicable to the
undersigned, or (iii) R&B Falcon has received either an opinion of counsel,
which opinion and counsel shall be reasonably satisfactory to R&B Falcon, or a
"no-action" letter obtained by the undersigned from the staff of the SEC, to the
effect that the restrictions imposed by Rule 145 under the Securities Act no
longer apply to the undersigned.
 
                                      A-31
<PAGE>   94
 
     Execution of this letter should not be considered an admission on my part
that I am an "affiliate" of Cliffs as described in the first paragraph of this
letter, or as a waiver of any rights I may have to object to any claim that I am
such an affiliate on or after the date of this letter.
 
                                            Very truly yours,
 
                                            ------------------------------------
 
Accepted this     day of
            , 1998 by
 
R&B FALCON CORPORATION
 
By: ________________________________

Name: ______________________________

Title: _____________________________
 
                                      A-32
<PAGE>   95
 
                                                                      APPENDIX B
 
                                August 20, 1998
 
The Board of Directors
Cliffs Drilling Company
2 Allen Center
1200 Smith Street
Suite 300
Houston, TX 77002
 
Members of the Board:
 
     You have advised us that Cliffs Drilling Company ("Cliffs" or the
"Company") proposes to be acquired by R&B Falcon Corporation ("R&B") through a
business combination (the "Combination Transaction") in which outstanding shares
of Cliffs will be exchanged for or converted into shares of common stock (the
"Purchase Consideration") of R&B (the "R&B Shares"). You have further advised us
that the Combination Transaction will be effected pursuant to a Definitive
Merger Agreement to be dated and signed August 21, 1998 (which, with the
exhibits thereto, is defined herein as the "Agreement") to which each of Cliffs
and R&B is a party. The parties have entered into a Letter of Intent ("LOI")
with respect to the Combination Transaction dated August 10, 1998. You have
requested our opinion as to the fairness, from a financial point of view, to the
holders of Cliffs Common Stock (as defined below), of the consideration to be
received by such holders pursuant to the Combination Transaction (the
"Opinion").
 
     As more specifically set forth in the Agreement, and subject to the terms
and conditions thereof, upon consummation of the Combination Transaction, each
outstanding share of Cliffs common stock, US$ 0.01 par value ("Cliffs Common
Stock"), will be exchanged for or converted into, on a per share basis, 1.7 R&B
Shares, US$ 0.01 par value ("R&B Common Stock"). We understand that the
Combination Transaction will be accounted for as a purchase transaction in
accordance with generally accepted accounting principles more fully described in
Accounting Principles Board Opinion Number 16.
 
     Jefferies & Company, Inc. ("Jefferies") has acted as financial advisor to
Cliffs in connection with the Combination Transaction and will receive (i) a
fee, payable in cash at the closing of the Combination Transaction, equal to
0.4% of the Aggregate Consideration for the Combination Transaction, estimated
to be $2.2 million and (ii) a cash fee of $350,000 upon rendering of the
Opinion.
 
     Jefferies has previously rendered certain investment banking and financial
advisory services to Cliffs for which it has received customary compensation.
Recently, Jefferies acted as a lead underwriter for the $150,000,000 Senior
Notes Offering by Cliffs in May 1996 and the $50,000,000 Add-on Notes Offering
in July 1997. In addition, in the ordinary course of Jefferies' business, it
actively trades the securities of Cliffs and R&B for its own account and for the
accounts of its customers, and, accordingly, may at any time hold a long or
short position in such securities. Jefferies has not rendered any investment
banking or financial advisory services to R&B in connection with the Combination
Transaction. Jefferies has recently been engaged to provide financial advisory
services to R&B in connection with certain strategic combination opportunities
that R&B is currently evaluating.
 
     In our review and analysis and in rendering the Opinion, we have with your
permission assumed and relied upon the accuracy and completeness of all the
financial and other information provided to us by Cliffs' and R&B's management,
as well as publicly available information, and have not verified such
information. We have not conducted a physical inspection of any of the
properties or facilities of Cliffs or R&B, nor have we made, been provided or
considered any independent evaluations or appraisals of any of such properties
or facilities. The Purchase Consideration was based on negotiations between
Cliffs and R&B during which Jefferies provided investment banking services to
Cliffs.
 
     In conducting our analysis and rendering our opinion as expressed herein,
we have reviewed and considered such financial and other factors as we have
deemed appropriate under the circumstances including,
 
                                       B-1
<PAGE>   96
 
among others, the following: (i) the Agreement; (ii) the historical and current
financial condition and results of operations of Cliffs and R&B, including (a)
the Annual Reports on Form 10-K of Cliffs for the years ended December 31, 1995,
1996 and 1997, and (b) the Quarterly Report on Form 10-Q of Cliffs for the
quarter ended March 31, 1998; (iii) certain non-public financial and
non-financial information prepared by the management of Cliffs and R&B, which
data was made available to us in our role as financial advisor to Cliffs; (iv)
published information regarding the financial performance and operating
characteristics of a selected group of companies which we deemed comparable; (v)
business prospects of Cliffs and R&B when taking into consideration the impact
of the Combination Transaction; (vi) the historical and current market prices
for Cliffs Common Stock and R&B Common Stock and for the equity securities of
certain other companies with businesses that we consider relevant to our
inquiry; (vii) publicly available information, including research reports on
companies we considered relevant to our inquiry; and (viii) the nature and terms
of other recent acquisition transactions in the offshore drilling industry. We
have met with certain officers and employees of Cliffs and R&B to discuss the
foregoing as well as other matters we believed relevant to our opinion. We have
also taken into account general economic, monetary, political, market and other
conditions as well as our experience in connection with similar transactions and
securities valuation generally. Our opinion is based upon all of such conditions
as they exist currently and can be evaluated on the date hereof. Existing
conditions are subject to rapid and unpredictable changes and such changes could
impact Jefferies' opinion. Our opinion does not constitute a recommendation of
the Combination Transaction over any alternative transactions which may be
available to Cliffs and does not address Cliffs' underlying business decision to
effect the Combination Transaction. Finally, we are not opining as to the market
value of the consideration to be received by Cliffs or the prices at which any
of the securities of R&B may trade following the consummation of the Combination
Transaction.
 
     Based upon and subject to the foregoing, and upon such other matters as we
consider relevant, we are of the opinion as investment bankers that the
consideration to be received by the holders of Cliffs Common Stock pursuant to
the Combination Transaction is fair, from a financial point of view, to such
holders.
 
     It is understood and agreed that this opinion is provided solely for the
use of the Board of Directors of Cliffs as one element in the Board's
consideration of the Combination Transaction and may not be used for any other
purpose, or otherwise referred to, relied upon or circulated without our prior
written consent. Without limiting the foregoing, this opinion does not
constitute a recommendation to any shareholder (or any other person) as to how
such person should vote with respect to the Combination Transaction.
 
                                            Very truly yours,
 
                                            /s/ JEFFRIES & COMPANY, INC.
                                            Jefferies & Company, Inc.
 
                                       B-2
<PAGE>   97
 
                                    PART II
                     INFORMATION NOT REQUIRED IN PROSPECTUS
 
ITEM 20. INDEMNIFICATION OF DIRECTORS AND OFFICERS.
 
     The Amended and Restated Certificate of Incorporation and Bylaws of R&B
Falcon Corporation require the indemnification of directors and officers to the
fullest extent permitted by law.
 
     Section 145 of the Delaware General Corporation Law authorizes and empowers
R&B Falcon Corporation to indemnify the directors, officers, employees and
agents of R&B Falcon Corporation against liabilities incurred in connection
with, and related expenses resulting from, any claim, action or suit brought
against any such person as a result of his relationship with R&B Falcon
Corporation, provided that such person acted in good faith and in a manner such
person reasonably believed to be in, and not opposed to, the best interests of
R&B Falcon Corporation in connection with the acts or events on which such
claim, action or suit is based. The finding of either civil or criminal
liability on the part of such persons in connection with such acts or events is
not necessarily determinative of the question of whether such persons have met
the required standard of conduct and are, accordingly, entitled to be
indemnified. The foregoing statements are subject to the detailed provisions of
Section 145 of the General Corporation law of the State of Delaware.
 
     Article 6.1 of the Bylaws of R&B Falcon Corporation provides that R&B
Falcon Corporation shall indemnify to the fullest extent authorized or permitted
by law, any person made, or threatened to be made, a party to or otherwise
involved in any action or proceeding by reason of the fact that he or she is or
was a director or officer of R&B Falcon Corporation, at the request of R&B
Falcon Corporation or by reason of the fact that such director or officer at the
request of R&B Falcon Corporation, is or was serving any other corporation,
partnership, joint venture, trust, employee benefit plan or other enterprise, in
any capacity.
 
ITEM 21. EXHIBITS AND FINANCIAL STATEMENT SCHEDULES.
 
<TABLE>
<C>                      <S>
          2              -- Agreement and Plan of Merger dated August 21, 1998 by and
                            among Cliffs Drilling Company, R&B Falcon Corporation and
                            RBF Cliffs Acquisition Corp. (included in Prospectus as
                            Exhibit A).
          3.1            -- Amended and Restated Certificate of Incorporation of the
                            Registrant (incorporated by reference to Exhibit 3.1 to
                            the Registrant's Annual Report on Form 10-K for the year
                            ended December 31, 1997 ("1997 10-K")).
          3.2            -- Amended and Restated Bylaws of the Registrant
                            (incorporated by reference to Exhibit 3.2 to the
                            Registrant's 1997 10-K).
          4.1            -- Rights Agreement, dated as of December 23, 1997, between
                            the Registrant and American Stock Transfer & Trust
                            Company, as Rights Agent (incorporated by reference to
                            Exhibit 4.2 to the Registrant's 1997 10-K).
          5.1*           -- Opinion of Gardere Wynne Sewell & Riggs, L.L.P.,
                            regarding legality of securities.
          8.1*           -- Opinion of Griggs & Harrison, P.C. regarding certain tax
                            matters.
         15.1*           -- Letter regarding Unaudited Interim Financial Information.
         23.1            -- Consent of Gardere Wynne Sewell & Riggs, L.L.P. (included
                            in Exhibit 5.1).
         23.2            -- Consent of Griggs & Harrison, P.C. (included in Exhibit
                            8.1).
         23.3*           -- Consent of Arthur Andersen LLP with respect to the
                            financial statements of R&B Falcon Corporation.
         23.4*           -- Consent of Ernst & Young LLP with respect to the
                            financial statements of Cliffs Drilling Company.
 
         24.1            -- Powers of Attorney (contained on page II-3).
</TABLE>
 
- ---------------
 
* Filed herewith
 
                                      II-1
<PAGE>   98
 
ITEM 22. UNDERTAKINGS.
 
     (a) The undersigned Registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of the
Registrant's annual report pursuant to Section 13(a) of 15(d) of the Securities
Exchange Act of 1934 (and, where applicable, each filing of an employee benefit
plan's annual report pursuant to Section 15(d) of the Securities Exchange Act of
1934) that is incorporated by reference in the registration statement shall be
deemed to be a new registration statement relating to the securities offered
therein, and the offering of such securities at that time shall be deemed to be
the initial bona fide offering thereof.
 
     (b) The undersigned registrant hereby undertakes as follows: that prior to
any public reoffering of the securities registered hereunder through use of a
prospectus which is a part of this registration statement, by any person or
party who is deemed to be an underwriter within the meaning of Rule 145(c), the
issuer undertakes that such reoffering prospectus will contain the information
called for by the applicable registration form with respect to reofferings by
persons who may be deemed underwriters, in addition to the information called
for by the other Items of the applicable form.
 
     (c) The registrant undertakes that every prospectus (i) that is filed
pursuant to paragraph (1) immediately preceding, or (ii) that purports to meet
the requirements of section 10(a)(3) of the Act and is used in connection with
an offering of securities subject to Rule 415, will be filed as a part of an
amendment to the registration statement and will not be used until such
amendment is effective, and that, for purposes of determining any liability
under the Securities Act of 1933, each such post-effective amendment shall be
deemed to be a new registration statement relating to the securities offered
therein, and the offering of such securities at that time shall be deemed to be
the initial bona fide offering thereof.
 
     (d) Insofar as indemnification for liabilities arising under the Securities
Act of 1933 may be permitted to directors, officers and controlling persons of
the Registrant pursuant to the foregoing provisions, or otherwise, the
Registrant has been advised that in the opinion of the Securities and Exchange
Commission such indemnification is against public policy as expressed in the Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the Registrant of expenses
incurred or paid by a director, officer or controlling person of the Registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the Registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Act and will be governed by the final adjudication of
such issue.
 
     (e) The undersigned Registrant hereby undertakes to respond to requests for
information that is incorporated by reference into the prospectus pursuant to
Item 4, 10(b), 11, or 13 of this Form, within one business day of receipt of
such request, and to send the incorporated documents by first class mail or
other equally prompt means. This includes information contained in documents
filed subsequent to the effective date of the registration statement through the
date of responding to the request.
 
     (f) The undersigned Registrant hereby undertakes to supply by means of a
post-effective amendment all information concerning a transaction, and the
company being acquired involved therein, that was not the subject of and
included in the registration statement when it became effective.
 
                                      II-2
<PAGE>   99
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Act, the registrant has duly
caused this Registration Statement to be signed on its behalf by the
undersigned, thereunto duly authorized, in the City of Houston, State of Texas,
on September 15, 1998.
 
                                            R&B FALCON CORPORATION
 
                                            By:    /s/ STEVEN A. WEBSTER
                                              ----------------------------------
                                                      Steven A. Webster
                                                 Chief Executive Officer and
                                                           President
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that each person whose signature appears
below constitutes and appoints Steven A. Webster, Robert F. Fulton and Leighton
E. Moss, and each of them, each of whom may act without joinder of the other,
his or her true and lawful attorneys and agents, with full power of substitution
and resubstitution, for him or her and in his or her name, place and stead, in
any and all capacities, to sign any or all pre- and post-effective amendments to
this Registration Statement, and to file the same, with all exhibits thereto and
other documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorney-in-fact and agents, and each of them,
full power and authority to do and perform each and every act and thing
requisite and necessary to be done in and about the premises, as fully as to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents, and each of them, or
the substitute or substitutes of any or all of them, may lawfully do or cause to
be done by virtue hereof.
 
     Pursuant to the requirements of the Securities Act, this Registration
Statement has been signed by the following persons in the capacities and on the
dates indicated.
 
<TABLE>
<CAPTION>
                      SIGNATURE                                   TITLE                     DATE
                      ---------                                   -----                     ----
<C>                                                    <S>                           <C>
                /s/ STEVEN A. WEBSTER                  Chief Executive Officer,      September 15, 1998
- -----------------------------------------------------    President and Director
                  Steven A. Webster                      (Principal Executive
                                                         Officer)
 
                  /s/ PAUL B. LOYD                     Chairman of the Board and     September 15, 1998
- -----------------------------------------------------    Director
                    Paul B. Loyd
 
                /s/ ROBERT F. FULTON                   Executive Vice President      September 15, 1998
- -----------------------------------------------------    (Principal Financial
                  Robert F. Fulton                       Officer)
 
                  /s/ TIM W. NAGLE                     Executive Vice President      September 15, 1998
- -----------------------------------------------------    (Principal Accounting
                    Tim W. Nagle                         Officer)
 
               /s/ PURNENDU CHATTERJEE                 Director                      September 15, 1998
- -----------------------------------------------------
                 Purnendu Chatterjee
 
                /s/ ARNOLD L. CHAVKIN                  Director                      September 15, 1998
- -----------------------------------------------------
                  Arnold L. Chavkin
</TABLE>
 
                                      II-3
<PAGE>   100
 
<TABLE>
<CAPTION>
                      SIGNATURE                                   TITLE                     DATE
                      ---------                                   -----                     ----
<C>                                                    <S>                           <C>
              /s/ CHARLES A. DONABEDIAN                Director                      September 15, 1998
- -----------------------------------------------------
                Charles A. Donabedian
 
                                                       Director                            , 1998
- -----------------------------------------------------
                Douglas A.P. Hamilton
 
                                                       Director                            , 1998
- -----------------------------------------------------
                 Macko A.E. Laqueur
 
                /s/ MICHAEL E. PORTER                  Director                      September 15, 1998
- -----------------------------------------------------
                  Michael E. Porter
 
               /s/ ROBERT L. SANDMEYER                 Director                      September 15, 1998
- -----------------------------------------------------
                 Robert L. Sandmeyer
 
                                                       Director                            , 1998
- -----------------------------------------------------
                 William R. Ziegler
</TABLE>
 
                                      II-4
<PAGE>   101
 
- --------------------------------------------------------------------------------
 
                            CLIFFS DRILLING COMPANY
 
                   PROXY FOR SPECIAL MEETING OF STOCKHOLDERS
                                           , 1998
 
          THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS
 
         The undersigned stockholder hereby appoints Michael M. Cone and
     Robert M. McInnes or either of them, proxies, each with power to act
     without the other and with full power of substitution, to vote all
     shares of Common Stock that the undersigned would be entitled to vote
     if personally present at the Special Meeting of Stockholders of Cliffs
     Drilling Company ("Cliffs Drilling") to be held on             , 1998
     at 10:00 a.m., Houston time, at the Doubletree Hotel at Allen Center,
     400 Dallas Street at Bagby, Houston, Texas, and at any adjournment or
     postponement thereof, on the following matters that are more
     particularly described in the Proxy Statement/Prospectus dated
                 , 1998:
 
     (1) Proposal to adopt and approve the Agreement and Plan of Merger
         dated August 21, 1998 among Cliffs Drilling, R&B Falcon
         Corporation ("R&B Falcon"), and RBF Cliffs Acquisition Corp., a
         wholly owned subsidiary of R&B Falcon ("Sub"), pursuant to which
         Sub will merge with and into Cliffs Drilling and each outstanding
         share of common stock, par value $0.01 per share, of Cliffs
         Drilling will be converted into the right to receive 1.7 shares of
         common stock, par value $0.01 per share, of R&B Falcon.
 
           [ ] FOR                [ ] AGAINST                [ ] ABSTAIN
 
     (2) To consider and take action upon any other matter which may
         properly come before the meeting or any adjournment or
         postponement thereof.
 
                   (Continued and to be signed on other side)
 
- --------------------------------------------------------------------------------
<PAGE>   102
 
- --------------------------------------------------------------------------------
 
     You are encouraged to specify your choices by marking the appropriate
     boxes, SEE REVERSE SIDE, but if no choice is indicated, your shares
     will be voted FOR each proposal in accordance with the Board of
     Directors' recommendations. The Proxies cannot vote your shares unless
     you sign and return the Card.
 
                                              Dated   , 1998
 
                                              -----------------------------
                                                Signature of Stockholder
 
                                              -----------------------------
                                                Signature of Stockholder
 
                                              Note: Please sign exactly as
                                                    name appears hereon.
                                                    Joint owners should
                                                    each sign. When signing
                                                    as attorney, executor,
                                                    administrator, trustee
                                                    or guardian, please
                                                    give full title as
                                                    such. If signer is a
                                                    corporation, please
                                                    sign with the full
                                                    corporate name by duly
                                                    authorized officer or
                                                    officers. A partnership
                                                    should sign in the
                                                    partnership name by a
                                                    partner.
 
- --------------------------------------------------------------------------------
<PAGE>   103
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
        EXHIBIT
          NO.                                    DESCRIPTION
        -------                                  -----------
<C>                      <S>
          2              -- Agreement and Plan of Merger dated August 21, 1998 by and
                            among Cliffs Drilling Company, R&B Falcon Corporation and
                            RBF Cliffs Acquisition Corp. (included in Prospectus as
                            Exhibit A).
          3.1            -- Amended and Restated Certificate of Incorporation of the
                            Registrant (incorporated by reference to Exhibit 3.1 to
                            the Registrant's Annual Report on Form 10-K for the year
                            ended December 31, 1997 ("1997 10-K")).
          3.2            -- Amended and Restated Bylaws of the Registrant
                            (incorporated by reference to Exhibit 3.2 to the
                            Registrant's 1997 10-K).
          4.1            -- Rights Agreement, dated as of December 23, 1997, between
                            the Registrant and American Stock Transfer & Trust
                            Company, as Rights Agent (incorporated by reference to
                            Exhibit 4.2 to the Registrant's 1997 10-K).
          5.1*           -- Opinion of Gardere Wynne Sewell & Riggs, L.L.P.,
                            regarding legality of securities.
          8.1*           -- Opinion of Griggs & Harrison, P.C. regarding certain tax
                            matters.
         15.1*           -- Letter regarding Unaudited Interim Financial Information.
         23.1            -- Consent of Gardere Wynne Sewell & Riggs, L.L.P. (included
                            in Exhibit 5.1).
         23.2            -- Consent of Griggs & Harrison, P.C. (included in Exhibit
                            8.1).
         23.3*           -- Consent of Arthur Andersen LLP with respect to the
                            financial statements of R&B Falcon Corporation.
         23.4*           -- Consent of Ernst & Young LLP with respect to the
                            financial statements of Cliffs Drilling Company.
         24.1            -- Powers of Attorney (contained on page II-3).
</TABLE>
 
- ---------------
 
* Filed herewith

<PAGE>   1
                                                                     EXHIBIT 5.1





713-308-5864



September 15, 1998


R&B Falcon Corporation
901 Threadneedle
Houston, Texas 77079

Gentlemen:

As set forth in the Registration Statement (the "Registration Statement") on
Form S-4 to be filed by R&B Falcon Corporation, a Delaware corporation (the
"Company"), with the Securities and Exchange Commission (the "Commission") under
the Securities Act of 1933, as amended (the "Act"), relating to the proposed
issuance of up to 28,212,564 shares (the "Shares") of the Company's common
stock, par value $0.01 per share ("Common Stock"), certain legal matters in
connection with the Common Stock are being passed upon for the Company by us.
The Shares are to be issued pursuant to the terms and provisions of an Agreement
and Plan of Merger dated as of August 21, 1998 among the Company, RBF Cliffs
Acquisition Corp., a Delaware corporation and a wholly owned subsidiary of the
Company, and Cliffs Drilling Company, a Delaware corporation (the "Merger
Agreement"). At your request, this opinion is being furnished to you for filing
as Exhibit 5.1 to the Registration Statement.

In our capacity as your counsel in the connection referred to above, we have
examined the Amended and Restated Certificate of Incorporation and the Amended
and Restated Bylaws of the Company and the originals, or copies certified or
otherwise identified, of corporate records of the Company, including minute
books of the Company as furnished to us by the Company, certificates of public
officials and of representatives of the Company, statutes and other instruments
and documents as a basis for the opinions hereinafter expressed. In giving such
opinions, we have relied upon certificates of officers of the Company with
respect to the accuracy of the material factual matters contained in such
certificates.

We have assumed the authenticity and completeness of all records, certificates
and other instruments submitted to us as originals, the conformity to original
documents of all records, certificates and other instruments submitted to us as
copies, the authenticity and completeness of the originals of those records,
certificates and other instruments submitted to us as copies and the correctness
of all statements of fact contained in all records, certificates and other
instruments that we have examined.



<PAGE>   2


R&B Falcon Corporation
Page 2

Based on the foregoing, and having regard for such legal considerations as we
have deemed relevant, we are of the opinion that upon the issuance by the
Company of the Shares upon consummation of the Merger (as defined in the Merger
Agreement) pursuant to the Merger Agreement, such Shares will be duly
authorized, validly issued, fully paid and nonassessable.

The foregoing opinion is limited to the federal laws of the United States of
America and the General Corporation Law of the State of Delaware, and we are
expressing no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion with the Commission as an
exhibit to the Registration Statement and to the references to our Firm under
the caption "Legal Matters" in the Proxy Statement/Prospectus included in the
Registration Statement.

Very truly yours,

GARDERE WYNNE SEWELL & RIGGS, L.L.P.



By: /s/      WILLIAM MARK YOUNG
   ---------------------------------------------  
             William Mark Young, Partner


<PAGE>   1
                                                                     EXHIBIT 8.1




                               September 15, 1998


Cliffs Drilling Company
1200 Smith, Suite 300
Houston, Texas 77002



Gentlemen:

         You have requested our opinion regarding certain federal income tax
consequences of the acquisition of Cliffs Drilling Company ("Cliffs Drilling")
by R&B Falcon Corporation ("R&B Falcon").  We understand that the acquisition
will be accomplished by a merger of RBF Cliffs Drilling Acquisition Corp.
("Sub"), a wholly owned subsidiary of R&B Falcon, with and into Cliffs
Drilling.  Thereafter, Cliffs Drilling will continue as a wholly owned
subsidiary of R&B Falcon.

         In rendering this opinion we have relied upon the facts as presented
to us in originals or copies of pertinent documents, including, among others,
(i) the Agreement and Plan of Merger dated August 21, 1998,  among Cliffs
Drilling, R&B Falcon and Sub (the "Merger Agreement"), (ii) R&B Falcon's
Registration Statement on Form S-4 filed with the Securities and Exchange
Commission (the "SEC") on September 15, 1998 (the "Registration Statement"),
and (iii) representations made by Cliffs Drilling, R&B Falcon and Sub in the
Certificates of Representation dated September 14, 1998.  In addition, we have
obtained other relevant information through consultation with various officers
and representatives of such companies. We have not investigated or made any
independent determination regarding such facts and circumstances and,
therefore, have relied upon the information set forth in the pertinent
documents for the purposes of this opinion.  Any changes to the pertinent
documents may adversely affect the conclusions stated herein.

         Based upon the facts presented to us in the documents described above
and the representations made by Cliffs Drilling, R&B Falcon and Sub, we are of
the opinion that the following federal income tax consequences will result:

         1.               The merger of Sub with and into Cliffs Drilling in
                          accordance with the terms of the Merger Agreement
                          will constitute a reorganization within the meaning
                          of Section 368(a) of the Internal Revenue Code of
                          1986, as amended (the "Code").  Cliffs
<PAGE>   2
Cliffs Drilling Company
September 15, 1998
Page 2


                          Drilling, R&B Falcon and Sub will each be a party to
                          the reorganization within the meaning of Section
                          368(b) of the Code.

         2.               No gain or loss will be recognized by R&B Falcon upon
                          the receipt of the common stock, par value $0.01 per
                          share, of Cliffs Drilling ("Cliffs Drilling Common
                          Stock") solely in exchange for Sub common stock, par
                          value $0.01 per share (Section 354(a)(1) of the
                          Code).

         3.               No gain or loss will be recognized by Sub upon the
                          transfer of its assets, if any, to Cliffs Drilling in
                          exchange for Cliffs Drilling Common Stock (Section
                          361 of the Code).

         4.               No gain or loss will be recognized by Cliffs Drilling
                          on the merger of Sub with and into Cliffs Drilling.

         5.               No gain or loss will be recognized by the Cliffs
                          Drilling stockholders upon the receipt of R&B Falcon
                          voting common stock, par value $0.01 per share ("R&B
                          Falcon Voting Common Stock") solely in exchange for
                          Cliffs Drilling Common Stock (Section 354(a)(1) of
                          the Code).

         6.               Cash received by a holder of Cliffs Drilling Common
                          Stock in lieu of fractional shares of R&B Falcon
                          Voting Common Stock will be treated as received in
                          exchange for such fractional share interests.  These
                          cash payments will be treated as having been received
                          as distributions in full payment in exchange for the
                          stock redeemed as provided in Section 302(a) of the
                          Code. Gain or loss will be recognized for federal
                          income tax purposes, measured by the difference
                          between the amount of cash received and the portion of
                          the basis of the Cliffs Drilling Common Stock
                          allocable to such fractional share interests.
                          Provided that the Cliffs Drilling Common Stock is a
                          capital asset in the hands of the holder of such
                          stock, the gain, if any, will constitute capital gain
                          subject to the conditions and limitations of
                          Subchapter P of Chapter 1 of the Code.

         7.               The basis of the R&B Falcon Voting Common Stock
                          (including fractional share interests, if any) to be
                          received by the Cliffs Drilling stockholders will, in
                          each instance, be the same as the basis of the Cliffs
                          Drilling Common Stock surrendered in exchange
                          therefor (Section 358(a)(1) of the Code).
<PAGE>   3
Cliffs Drilling Company
September 15, 1998
Page 3



         8.               The holding period of the R&B Falcon Voting Common
                          Stock (including fractional share interests, if any)
                          to be received by the Cliffs Drilling stockholders
                          will include the period during which the Cliffs
                          Drilling Common Stock surrendered in exchange
                          therefor was held, provided that the Cliffs Drilling
                          Common Stock was a capital asset within the meaning
                          of Section 1221 of the Code on the date of the
                          exchange (Section 1223 of the Code).

         We express no opinion concerning any tax consequences of the
transaction other than those specifically addressed above in this opinion.  No
opinion has been requested and none is provided with respect to any other
issues arising from the transaction, including but not limited to, consolidated
return consequences, if any; alternative minimum tax consequences, if any;
state, local, and/or foreign tax consequences, if any; and employee benefit tax
consequences, if any.

         Our opinion, as set forth above, is based upon our analysis of the
Code, the Treasury Regulations, current case law and published pronouncements
of the Internal Revenue Service.  The foregoing are subject to change, and such
change may be retroactively effective.  If so, our views, as set forth above,
may be affected and may not be relied upon.  In addition our opinion is based
on the information contained in the above described documents.  Any variation
or differences in documents may affect our opinion, perhaps in an adverse
manner.  We have undertaken no obligation to update this opinion for changes in
facts or law occurring subsequent to the date thereof.

         Our opinion is rendered only to Cliffs Drilling in connection with the
proposed acquisition and is solely for its benefit.  Our opinion may not be
relied upon by any other person or persons, or used for any other purposes,
including, but not necessarily limited to, filings with the SEC or other
governmental agencies, without our prior written consent.

         We hereby consent to the filing of this opinion as an exhibit to the
Registration Statement and to the reference to our firm under the caption
"Legal Matters" in the Proxy Statement/Prospectus contained in the Registration
Statement.
<PAGE>   4
Cliffs Drilling Company
September 15, 1998
Page 4



         This letter is the opinion of Griggs & Harrison P.C. as to the
interpretation of existing tax law and, as such, is not binding on the Internal
Revenue Service or the courts.

                                        Very truly yours,

                                        /s/ GRIGGS & HARRISON, P.C.

                                        GRIGGS & HARRISON, P.C.





<PAGE>   1
 
                                                                    EXHIBIT 15.1
 
            LETTER REGARDING UNAUDITED INTERIM FINANCIAL INFORMATION
 
R&B Falcon Corporation:
 
     We are aware that R&B Falcon Corporation has incorporated by reference in
this registration statement on Form S-4 its Form 10-Q for the quarters ended
June 30, 1998 and March 31, 1998, which include our reports dated July 28, 1998
and April 28, 1998, respectively, covering the unaudited interim financial
information contained therein. Pursuant to Regulation C of the Securities Act of
1933, these reports are not considered a part of the registration statement
prepared or certified by our firm within the meaning of Sections 7 and 11 of the
Act.
 
/s/ ARTHUR ANDERSEN LLP
 
Houston, Texas
September 14, 1998

<PAGE>   1
 
                                                                    EXHIBIT 23.3
 
                   CONSENT OF INDEPENDENT PUBLIC ACCOUNTANTS
 
     As independent public accountants, we hereby consent to the incorporation
by reference in this registration statement on Form S-4 of our report dated
March 24, 1998 included in R&B Falcon Corporation's Form 10-K for the year ended
December 31, 1997 and to all references to our Firm in this registration
statement.
 
/s/ ARTHUR ANDERSEN LLP
 
Houston, Texas
September 14, 1998

<PAGE>   1
 
                                                                    EXHIBIT 23.4
 
                        CONSENT OF INDEPENDENT AUDITORS
 
     We consent to the reference to our firm under the caption "Experts" and to
the use of our report dated February 13, 1998, incorporated by reference in the
Proxy Statement of Cliffs Drilling Company and made a part of the Registration
Statement (Form S-4 No. 333-       ) and related Prospectus of R&B Falcon
Corporation for the registration of 28,212,564 shares of its common stock, filed
with the Securities and Exchange Commission.
 
/s/ ERNST & YOUNG LLP
 
Houston, Texas
September 14, 1998


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