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Exhibit 10.4

AMENDMENT NO. 1 TO THE
ENSCO
2005
NON-EMPLOYEE DIRECTOR DEFERRED COMPENSATION PLAN

       THIS AMENDMENT No. 1, executed this 11th day of March, 2008, and
effective as of the dates specified herein, by ENSCO International Incorporated,
having its principal office in Dallas, Texas (hereinafter referred to as the
"Company").

W I T N E S S E T H:

       WHEREAS, the Company adopted the ENSCO 2005 Non-Employee Director
Deferred Compensation Plan (the "2005 Plan), effective January 1, 2005;

       WHEREAS, the Board of Directors of the Company, upon recommendation of
its Nominating, Governance and Compensation Committee, has approved this
Amendment No. 1 to the 2005 Plan during a regular meeting held on March 10,
2008; and

       WHEREAS, the Company now desires to adopt this Amendment No. 1 to the
2005 Plan in order to amend Section 7.2 of the 2005 Plan to (i) revise,
effective as of January 1, 2008, the investment funds available for election by
a participant for investment of his account consistent with the simultaneous
revision to the registered mutual funds offered to the participants in the ENSCO
Savings Plan, (ii) expand, effective June 1, 2008, the permissible investment
options of a participant's account to provide that a participant may direct that
up to 100 percent of the balance of his account may be invested pursuant to the
terms, conditions and limitations of the agreements governing the T. Rowe Price
TradeLink+ self-directed brokerage investment program, and (iii) provide,
effective June 1, 2008, a limitation on the portion of a participant's account
that may be invested in the Company stock fund;

       NOW, THEREFORE, in consideration of the premises and the covenants herein
contained, the Company hereby adopts the following Amendment No. 1 to the 2005
Plan:

       Section 7.2 of the 2005 Plan is hereby amended to read as follows:

       7.2  Investments.  If a trust is established as provided for in Section
7.1, earnings and/or losses of the trust attributable to amounts credited to a
Participant's Account shall increase or, if applicable, decrease such
Participant's Account for purposes of determining the Participant's Benefits
payable hereunder. The Committee may determine from time to time to direct the
investment manager appointed pursuant to any such trust to invest the balance of
a Participant's Account in accordance with the wishes and written directions of
that Participant from among the registered mutual funds and the Company stock
fund offered to the participants in the ENSCO Savings Plan (which have been
revised effective as of January 1, 2008) from time to time under the terms of
the ENSCO Savings Plan. If the Committee determines for any reason that a
particular registered mutual fund available under the ENSCO Savings Plan cannot
be made available under the Plan, a comparable fund will be substituted in its
place.

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       Up to 100 percent of the balance of a Participant's Account attributable
to Deferred Retainer and Company Discretionary Contributions, if any, credited
to his Account on or before May 31, 2008 may be invested in the Company stock
fund. Effective June 1, 2008, a Participant may not direct that more than 50
percent of the balance of his Account attributable to Deferred Retainer and
Company Discretionary Contributions, if any, credited to his Account after May
31, 2008 may be invested in the Company stock fund. If the investment election
of any Participant in effect on June 1, 2008 provides for an election in excess
of 50 percent to the Company stock fund, that investment election shall be
automatically revised, effective June 1, 2008, with respect to the specific
election to the Company stock fund to provide for an election of 50 percent to
the Company stock fund and the percentage elected in excess of 50 percent shall
be deemed to be an election of that excess percentage to the particular T. Rowe
Price target date retirement fund offered to participants in the ENSCO Savings
Plan determined by the age of the Participant. Notwithstanding that the balance
of a Participant's Account that is invested in the Company stock fund on June 1,
2008 is 50 percent or more of the total balance of his Account on that date, the
Participant's Account may continue to hold that investment interest in the
Company stock fund after May 31, 2008 and the investment election in the Company
stock fund permitted by the two preceding sentences with respect to
contributions credited to his Account after May 31, 2008 shall not be affected.
A Participant shall not be permitted, however, to direct the investment manager
after May 31, 2008 to change the investment of the then balance of his Account
if (i) that investment election requires reinvestment of any portion of his
Account into the Company stock fund and the balance of his Account that is
invested in the Company stock fund on that date is 50 percent or more of the
total balance of his Account on that date, or (ii) the effect of that investment
election would result in more than 50 percent of the total balance of his
Account on that date being invested in the Company stock fund.

       Effective June 1, 2008, the Committee has also determined that it will
direct the investment manager appointed pursuant to any such trust to invest up
to 100 percent of the balance of a Participant's Account in accordance with the
wishes and written directions of that Participant pursuant to the terms,
conditions and limitations of the agreements governing the T. Rowe Price
TradeLink+ self-directed brokerage investment program, as amended from time to
time.

       IN WITNESS WHEREOF, the Company, acting by and through its duly
authorized officer, has caused this Amendment No. 1 to be executed on the date
first above written.
 

ENSCO INTERNATIONAL INCORPORATED

  /s/ Charles A. Mills                                                         
By:  Charles A. Mills, Vice President - Human Resources and Security

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