<PAGE>
                                                                   EXHIBIT 10.20

                                 AMENDMENT NO. 2
                                     TO THE
                                NOBLE CORPORATION
                            EQUITY COMPENSATION PLAN
                           FOR NON-EMPLOYEE DIRECTORS

         WHEREAS, Noble Corporation, a Cayman Islands exempted company limited
by shares (the "Company"), has previously adopted the Noble Corporation Equity
Compensation Plan for Non-Employee Directors (the "Plan");

         WHEREAS, the Board of Directors of the Company (the "Board") has
determined that certain amendments to the Plan are appropriate and in the best
interests of the Company and its members; and

         WHEREAS, pursuant to the provisions of Section 6 of the Plan and the
rules of the New York Stock Exchange (which are applicable to the Company), the
Board of Directors has determined to submit such amendments to members for their
approval;

         NOW THEREFORE, the Company does hereby amend the Plan, subject to
member approval, as follows:

         1. The first sentence of Section 4(a) of the Plan is amended by
deleting "Seventy-five thousand (75,000)" in such section and replacing it with
"One hundred twenty-five thousand (125,000)".

         2. Section 5(a) of the Plan is deleted in its entirety and the
following is substituted in its place:

                  "Quarterly Amounts; Required Share Amount. Subject to the
         provisions of the Plan, each Outside Director shall be paid an annual
         retainer for serving as a director of the Company (the "Annual
         Retainer"). The amount of the Annual Retainer to be paid to each
         Outside Director for each Plan Year shall be $50,000. Of this amount,
         (i) $40,000 shall be the cash component of the Annual Retainer, payable
         in cash in quarterly installments of $10,000 each at the end of each
         Plan Quarter of the Plan Year (each such quarterly installment being
         herein referred to as a "Quarterly Amount"), and (ii) $10,000 shall be
         the equity component of the Annual Retainer, payable in Ordinary Shares
         in one installment at the end of the Plan Year (the "Required Share
         Amount"). An Outside Director who serves in such capacity for less than
         an entire Plan Quarter shall have his Quarterly Amount for such Plan
         Quarter pro-rated based on his number of days of service as an Outside
         Director during such Plan Quarter. An Outside Director who serves in
         such capacity for less than an entire Plan Year shall have his Required
         Share Amount for such Plan Year pro-rated based on his number of days
         of service as an Outside Director during such Plan Year."

         3. This Amendment No. 2 shall amend only those provisions of the Plan
set forth herein, and those Sections, paragraphs and sentences not expressly
amended hereby shall remain in full force and effect.

         4. This Amendment No. 2 shall become effective as of August 1, 2004,
subject to and upon the receipt of member approval by the affirmative votes of
the holders of a majority of the Ordinary Shares present, or represented, and
entitled to vote at a meeting of members duly held in accordance with the
applicable laws of the Cayman Islands.

         IN WITNESS WHEREOF, the undersigned has executed this Amendment No. 2
as of February 4, 2005.

                                   NOBLE CORPORATION


                                   By: /s/ JAMES C. DAY
                                       ------------------------------------
                                       James C. Day
                                       Chairman of the Board and
                                       Chief Executive Officer