Document:

<PAGE>

                                                                     EXHIBIT 4.5

                       AMENDMENT NO. 2 TO RIGHTS AGREEMENT

         THIS AMENDMENT NO. 2 TO RIGHTS AGREEMENT (this "Amendment"), dated as
of February 5, 2002, is between NOBLE DRILLING CORPORATION, a Delaware
corporation (the "Company"), and BANK ONE TRUST COMPANY, N.A., AS SUCCESSOR
TO LIBERTY BANK AND TRUST COMPANY OF OKLAHOMA CITY, N.A., a national banking
association, as rights agent (the "Rights Agent");

                                   WITNESSETH:

         WHEREAS, the Company and the Rights Agent are parties to a Rights
Agreement, dated as of June 28, 1995, as amended (the "Agreement"); and

         WHEREAS, the Board of Directors of the Company deems it desirable to
amend the Agreement pursuant to the provisions of Section 27 of the Agreement to
make certain modifications to the Agreement upon the terms and conditions
hereinafter set forth, such modifications to be effective on the date
hereinafter set forth;

         NOW, THEREFORE, in consideration of the premises and the mutual
agreements herein set forth, the parties hereby agree as follows:

         1. Defined Terms. Capitalized terms used but not otherwise defined
herein shall have the respective meanings ascribed to such terms in the
Agreement.

         2. Amendment of Section 1. Section 1 of the Agreement is hereby amended
in the following respects:

                  (a) by adding thereto a new defined term "Merger Agreement"
which shall read in its entirety as follows:

                           "'Merger' shall mean the merger of the Company with
                  any of its subsidiaries, where the purpose of such merger is
                  to cause the Company to become a direct or indirect, wholly
                  owned subsidiary of a Person that prior to the effective time
                  of such merger had been a direct or indirect, wholly owned
                  subsidiary of the Company (the 'New Parent')."

                  (b) by adding thereto a new defined term "New Parent" which
shall read in its entirety as follows:

                           "'New Parent' shall have the meaning set forth in the
                  definition of Merger."

                  (c) by adding thereto a new defined term "Merger Agreement"
which shall read in its entirety as follows:

                                       1
<PAGE>

                           "'Merger Agreement' shall have the meaning set forth
                  in Section 34 hereof."

         3. Amendment of Section 7. Paragraphs (a) and (b) of Section 7 of the
Agreement are each amended by (i) deleting the word "and" immediately preceding
clause (iii) thereof and inserting a "," in lieu thereof, and (ii) adding a new
clause (iv) immediately following clause (iii) thereof which shall read in its
entirety as follows: "and (iv) immediately prior to the effective time of a
Merger."

         4. Addition of New Section 34. The Agreement is amended by adding a new
Section 34 thereof which shall read in its entirety as follows:

                           "Section 34. Exception For Merger. Notwithstanding
                  any provision of this Agreement to the contrary, neither a
                  Distribution Date, Flip-In Event, Flip-In Trigger Date,
                  Flip-Over Event, nor a Shares Acquisition Date shall be deemed
                  to have occurred, none of the New Parent, or any of its
                  Affiliates or Associates shall be deemed to have become an
                  Acquiring Person, and no holder of any Rights shall be
                  entitled to exercise such Rights under, or be entitled to any
                  rights pursuant to, any of Sections 3, 7, 11 or 13 of this
                  Agreement, in any such case by reason of (a) the approval,
                  execution or delivery of a merger agreement providing for a
                  Merger, or any amendments thereof, approved in advance by the
                  Board of Directors of the Company (each, a 'Merger Agreement')
                  or (b) the commencement or, prior to termination of a Merger
                  Agreement, the consummation of any of the transactions
                  contemplated by such Merger Agreement in accordance with the
                  provisions thereof, including the Merger provided for in such
                  Merger Agreement."

         5. Effectiveness. This Amendment shall be deemed effective as of
January 31, 2002, as if executed by both parties hereto on such date. Except as
amended hereby, the Agreement shall remain in full force and effect and shall be
otherwise unaffected hereby.

         6. Miscellaneous. This Amendment shall be deemed to be a contract made
under the laws of the State of Delaware and for all purposes shall be governed
by and construed in accordance with the laws of such state applicable to
contracts to be made and performed entirely within such state. This Amendment
may be executed in any number of counterparts, each of such counterparts shall
for all purposes be deemed to be an original, and all such counterparts shall
together constitute but one and the same instrument. If any term, provision,
covenant or restriction of this Amendment is held by a court of competent
jurisdiction or other authority to be invalid, illegal, or unenforceable, the
remainder of the terms, provisions, covenants and restrictions of this Amendment
shall remain in full force and effect and shall in no way be affected, impaired
or invalidated.

                                       2
<PAGE>

         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed as of the date set forth above.

                                            NOBLE DRILLING CORPORATION

                                            By: /s/ ROBERT D. CAMPBELL
                                                --------------------------------
                                            Name:   Robert D. Campbell
                                                 -------------------------------
                                            Title:  President
                                                  ------------------------------

                                            BANK ONE TRUST COMPANY, N.A., AS
                                            SUCCESSOR TO LIBERTY BANK AND TRUST
                                            COMPANY OF OKLAHOMA CITY, N.A.

                                            By: /s/ JAKE L. RILEY
                                                --------------------------------
                                            Name:   Jake L. Riley
                                                 -------------------------------
                                            Title:  Senior Vice President
                                                  ------------------------------

                                       3<PAGE>

                                                                     EXHIBIT 4.6

                              CONSENT AND AGREEMENT

         THIS CONSENT AND AGREEMENT (this "Consent") dated December 20, 2001 by
and among NOBLE DRILLING (PAUL ROMANO) INC., a Delaware corporation ("NDPRI"),
NOBLE DRILLING CORPORATION, a Delaware corporation ("Noble"), and the
Noteholders a party hereto.

                                   WITNESSETH

         WHEREAS, NDPRI executed and delivered that certain Trust Indenture and
Security Agreement dated as of November 24, 1998 (the "Indenture") between NDPRI
and JPMorgan Chase Bank (as successor to Chase Bank of Texas, National
Association), a New York State banking corporation, as Trustee (the "Trustee");
and

         WHEREAS, NDPRI issued its Series A and Series B Senior Secured Notes to
Noteholders pursuant to the Indenture; and

         WHEREAS, in connection therewith, NDPRI executed and delivered that
certain First Naval Mortgage dated November 24, 1998 (the "Mortgage") in favor
of Trustee, covering Noble Paul Romano (the "Vessel"), securing the obligations
and indebtedness under the Indenture and the Series A and Series B Senior
Secured Notes; and

         WHEREAS, the Vessel is contracted to Shell Deepwater Development Inc.
("SDDI") for a period of five years pursuant to the Shell Contract, which
currently provides for a termination date of December 31, 2003; and

         WHEREAS, in order to facilitate its business activities and align the
cost structure under its drilling programs, SDDI has requested that NDPRI reduce
the Vessel day rate to $95,000 and change the existing December 31, 2003
termination date of the Shell Contract to December 31, 2002, with an option for
SDDI to extend such termination date to December 31, 2003, with no other
material terms or conditions of the Shell Contract to be affected; and

         WHEREAS, SDDI and Shell Oil Company are important and valued clients of
NDPRI and its parent, Noble, and as there is no negative economic or financial
implications to Noble, as a whole, resulting from the aforementioned changes to
the Shell Contract, Noble fully supports the day rate and contract term
amendments; and

         WHEREAS, Section 2.13(a) of the Mortgage provides that NDPRI insure the
Vessel and keep her insured, or cause the Vessel to be insured, with respect to
Hull and Machinery, including War Risks for an amount never less than the
aggregate principal amount of the Notes outstanding from time to time, plus
$250,000, with a deductible amount not greater than U.S. $250,000 per
occurrence; and

         WHEREAS, Noble has reviewed with its insurance broker the Hull and
Machinery insurance coverage with respect to the Vessel, as the current policy's
3 year term expires at the end of 2001, and due to significant losses suffered
by the insurance industry as a whole in 2001, the insurance market does not
offer Hull and Machinery insurance with deductibles approximating the current
policy, and as a result Noble and its affiliates are compelled to increase the
deductible under the new policy to U.S. $3,700,000 per occurrence for all of
their respective rigs, including the Vessel; and

         WHEREAS, Section 7.3(d)(ii) of the Indenture requires the approval of
the Required Holders upon the amendment or modification of the Shell Contract,
and the increase in Hull and Machinery deductible also requires the approval of
the Required Holders, and NDPRI has requested that each

                                        1
<PAGE>

Noteholder consent to such amendment and modification of the Shell Contract and
such increased deductible;

         NOW, THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which is hereby acknowledged, NDPRI, Noble and each undersigned
Noteholder hereby agree as follows:

CONSENT TO SHELL CONTRACT AMENDMENT AND MODIFICATION

         Each undersigned Noteholder hereby consents to the reduction of the
contractual term and day rate under the Shell Contract with respect to the
Vessel as set forth above, such consent to be effective upon the satisfaction of
each of the following conditions precedent:

         1. Noble, NDPRI and Required Holders shall have executed this Consent.

         2. Noble shall have delivered to Trustee, as collateral security for
the payments of principal, interest and Make-Whole Amount under the Series A
Notes and interest under the Series B Notes scheduled to come due after December
31, 2002, a letter of credit substantially in the form of Exhibit A attached
hereto (the "Letter of Credit") and issued by Nordea Bank Norge ASA, New York
Branch.

         3. Noble shall have paid to each Noteholder a work fee of 10 basis
points, calculated on such Noteholder's pro rata share of the aggregate
principal amount of the Notes that is scheduled to come due after December 31,
2002 (the "Consent Fee"), as set forth on Exhibit B attached hereto.

         The Trustee, NDPRI and the Noteholders hereby agree that (a) prior to
the Full Payment Date (as such term is hereinafter defined), in the event funds
on deposit in the Collection Account shall be insufficient to satisfy any
regularly scheduled required prepayment of principal and interest on the Series
A Notes or any regularly scheduled payment of the interest on the Series B Notes
due and payable on any Payment Date after December 31, 2002, the Trustee shall
make a drawing under Annex A to the Letter of Credit to satisfy such obligations
in lieu of and in substitution for a withdrawal of a like amount of funds from
the Debt Service Reserve Fund, and (b) after the Full Payment Date (as such term
is hereinafter defined), the Trustee shall make a drawing under Annex A to the
Letter of Credit to pay any principal or accrued interest or Make-Whole Amount
due and payable on the Series A Notes or any accrued interest due and payable on
the Series B Notes. As used herein, the term "Full Payment Date" shall mean the
date on which the Series A Notes and the Series B Notes become due and payable
in their entirety (whether as a result of an acceleration or otherwise).

         The Trustee hereby agrees that in the event the issuer of the Letter of
Credit shall deliver a notice to the Trustee under Section 4(b) of the Letter of
Credit that the Letter of Credit will not be extended pursuant to the terms
thereof, the Trustee shall promptly forward a copy of such notice to each
Noteholder. NDPRI hereby agrees that if (i) the Letter of Credit shall for any
reason cease to be in full force and effect or shall not be valid, binding and
enforceable in accordance with its terms, (ii) the issuer thereof shall refuse
to honor any drawing request made by Trustee thereunder pursuant to the terms
thereof, or (iii) a bankruptcy, insolvency, reorganization, winding-up or
liquidation proceeding shall be commenced with respect to the issuer thereof,
such cessation, refusal or commencement shall constitute an automatic Indenture
Event of Default under the Indenture, and the Trustee and NDPRI, by its
acceptance hereof, and the Noteholders, by their execution hereof, agree that
the Indenture is hereby amended accordingly.

         The Trustee and the Noteholders further agree that in the event the
Trustee shall draw the entire amount available for drawing under the Letter of
Credit pursuant to a Ratings Downgrade Drawing or LC Expiration Drawing as
provided therein (a "Full Drawing"), the Trustee shall deposit such amount in a

                                        2
<PAGE>

separate account (the "LC Proceeds Account") to be held as collateral for the
Notes and shall invest such funds as set forth in Section 4.4 of the Indenture.
Following any Full Drawing and prior to the Full Payment Date, in the event
funds on deposit in the Collection Account shall be insufficient to satisfy any
regularly scheduled required prepayment of principal and interest on the Series
A Notes or any regularly scheduled payment of the interest on the Series B Notes
due and payable on any Payment Date after December 31, 2002, the Trustee shall
apply funds from the LC Proceeds Account to satisfy such obligations in lieu of
and in substitution for a withdrawal of a like amount of funds from the Debt
Service Reserve Fund. Following any Full Drawing and following the Full Payment
Date, the Trustee shall apply all funds in the LC Proceeds Account to principal
and accrued interest and Make-Whole Amount then due on the Series A Notes and
accrued interest then due on the Series B Notes.

CONSENT TO INCREASED HULL AND MACHINERY INSURANCE DEDUCTIBLE

         Each undersigned Noteholder hereby consents to the increased Hull and
Machinery Insurance deductible with respect to the Vessel as set forth above,
and authorizes NDPRI and Trustee to enter into such amendment to the Mortgage as
they may deem necessary to evidence such change in such required insurance
coverage, such consent and authorization to be effective upon the execution of
this Consent by NDPRI and Required Holders. With respect to hull and
machinery/increased value insurance, including war risk, NDPRI hereby covenants
that it shall insure the Vessel at all times for an amount which is at least
equal to the Obligations (as such term is defined in the Mortgage) plus
$3,700,000, such obligation not to be in derogation of any other obligation set
forth in Section 2.13(a) of the Mortgage.

MISCELLANEOUS

         This Consent shall be governed by, and construed in accordance with,
the laws of the State of New York, other than the conflict of laws rules thereof
that would require the application of the laws of a jurisdiction other than such
state. For the avoidance of doubt, the parties hereto agree that this Consent
shall constitute a "Credit Document" for purposes of the Indenture. Capitalized
terms used and not defined herein shall have the meanings given such terms in
the Indenture. This Consent may be executed in any number of counterparts, each
counterpart constituting an original, but all together one agreement.

                                NOBLE DRILLING (PAUL ROMANO), INC.

                                By:   /s/ MARK L. MEY
                                   --------------------------------------
                                   Name:  Mark L. Mey
                                   Title: Treasurer

                                NOBLE DRILLING CORPORATION

                                By:   /s/ JULIE J. ROBERTSON
                                   --------------------------------------
                                   Name:  Julie J. Robertson
                                   Title: Secretary

ACKNOWLEDGED AND AGREED
this 20th day of December

NOBLE DRILLING (U.S.) INC.

By:   /s/ JULIE J. ROBERTSON
   --------------------------------------
   Name:  Julie J. Robertson
   Title: Secretary

                                        3
<PAGE>

SERIES A NOTEHOLDERS:  FIRST PENN-PACIFIC LIFE INSURANCE COMPANY

                       By:  Delaware Lincoln Investment Advisers, a series of
                            Delaware Management Business Trust, Attorney-In-Fact

                       By:   /s/ CHUCK DEVEREUX
                          ------------------------------------------------------
                          Name:  Chuck Devereux
                          Title: Vice President

                       LINCOLN NATIONAL HEALTH & CASUALTY INSURANCE COMPANY

                       By:  Delaware Lincoln Investment Advisers, a series of
                            Delaware Management Business Trust, Attorney-In-Fact

                       By:   /s/ CHUCK DEVEREUX
                          ------------------------------------------------------
                          Name:  Chuck Devereux
                          Title: Vice President

                       LINCOLN LIFE & ANNUITY COMPANY OF NEW YORK

                       By:  Delaware Lincoln Investment Advisers, a series of
                            Delaware Management Business Trust, Attorney-In-Fact

                       By:   /s/ CHUCK DEVEREUX
                          ------------------------------------------------------
                          Name:  Chuck Devereux
                          Title: Vice President

                       THE LINCOLN NATIONAL LIFE INSURANCE COMPANY

                       By:  Delaware Lincoln Investment Advisers, a series of
                            Delaware Management Business Trust, Attorney-In-Fact

                       By:   /s/ CHUCK DEVEREUX
                          ------------------------------------------------------
                          Name:  Chuck Devereux
                          Title: Vice President

                                        4
<PAGE>

                       NATIONWIDE LIFE & ANNUITY INSURANCE COMPANY

                       By:   /s/ MARK W. POEPPELMAN
                          ------------------------------------------------------
                          Name:  Mark W. Poeppelman
                          Title: Associate Vice President

                       NATIONWIDE LIFE INSURANCE COMPANY

                       By:   /s/ MARK W. POEPPELMAN
                          ------------------------------------------------------
                          Name:  Mark W. Poeppelman
                          Title: Associate Vice President

                       PRINCIPAL LIFE INSURANCE COMPANY

                       By:  Principal Capital Management, LLC, a Delaware
                            limited liability company, its authorized signatory

                       By:   /s/ [AUTHORIZED SIGNATOR]
                          ------------------------------------------------------

                       PROVIDENT LIFE & ANNUITY COMPANY OF AMERICA

                       By:   /s/ [AUTHORIZED SIGNATOR]
                          ------------------------------------------------------

                       PROVIDENT MUTUAL LIFE INSURANCE COMPANY

                       By:   /s/ [AUTHORIZED SIGNATOR]
                          ------------------------------------------------------

                                        5
<PAGE>

                       SUNAMERICA LIFE INSURANCE COMPANY

                       By:   /s/ GREG HAMMER
                          ------------------------------------------------------
                          Name:  Greg Hammer
                          Title: Authorized Agent

                       TEACHERS INSURANCE & ANNUITY ASSOCIATION OF
                       AMERICA

                       By:   /s/ [AUTHORIZED SIGNATOR]
                          ------------------------------------------------------

SERIES B NOTEHOLDER:   VICTORY RECEIVABLES CORPORATION

                       By:   /s/ KAREN A. GRANQUIST
                          ------------------------------------------------------
                          Name:  Karen A. Granquist
                          Title: Secretary

ACKNOWLEDGED, ACCEPTED AND AGREED
this 20th day of December, 2001

JPMORGAN CHASE BANK, as Trustee

By:   /s/ MAURI J. COWEN
   ---------------------------------------
   Name:  Mauri J. Cowen
   Title: Vice President and Trust Officer

                                        6
<PAGE>

                                                                       EXHIBIT B

             PRINCIPAL BALANCE OF SERIES A NOTES AND SERIES B NOTES
                             AS OF DECEMBER 31, 2002

<Table>
<Caption>
                                                  Series A Note Principal
Series A Noteholder                               Balance as of 12/31/02     Consent Fee
-------------------                               -----------------------    -----------
<S>                                               <C>                        <C>

First Penn-Pacific Life Insurance Company           $   904,060.76           $   904.06
Lincoln Nat'l Health & Casualty Insurance Co.       $   432,254.05           $   432.25
Lincoln Life & Annuity Co. of New York              $   113,007.60           $   113.01
The Lincoln National Life Insurance Company         $ 5,424,364.56           $ 5,424.36
Nationwide Life & Annuity Insurance Co.             $ 1,130,075.95           $ 1,130.08
Nationwide Life Insurance Company                   $ 2,260,151.90           $ 2,260.15
Principal Life Insurance Company                    $ 3,390,227.85           $ 3,390.23
Provident Life & Annuity Company of America         $   452,030.38           $   452.03
Provident Mutual Life Insurance Company             $   678,045.57           $   678.05
SunAmerica Life Insurance Company                   $ 2,260,151.90           $ 2,260.15
Teachers Insurance & Annuity Assn. of America       $ 4,520,303.80           $ 4,520.30
                                                    ==============           ==========

TOTAL                                               $21,564,674.33           $21,564.67
</Table>

<Table>
<Caption>
                                                  Series B Note Principal
Series B Noteholder                               Balance as of 12/31/02     Consent Fee
-------------------                               -----------------------    -----------
<S>                                               <C>                        <C>

Victory Receivables Corporation                     $16,837,500.00           $16,837.50
</Table>

                                        7

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00033-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00033-of-00352.parquet"}]]