2012 AMENDMENT TO THE PRIDE INTERNATIONAL, INC. 1998 LONG-TERM INCENTIVE PLAN (As Amended and Restated Effective February 17, 2005 and As Assumedby Ensco plc as of May 31, 2011)

Exhibit 10.4

2012 AMENDMENT TO THE

PRIDE INTERNATIONAL, INC.

1998 LONG-TERM INCENTIVE PLAN

(As Amended and Restated Effective February 17, 2005 and

As Assumed by Ensco plc as of May 31, 2011)

THIS AMENDMENT is effective the 14^th of May 2012, by Ensco plc, having its principal office in London, England (hereinafter referred to as the “Company”).

WITNESSETH:

WHEREAS, the board of directors of Pride International, Inc., a Delaware corporation (“Pride”), adopted the Pride International, Inc. 1998 Long-Term Incentive Plan which became effective as of the date of its approval by the stockholders of Pride on May 12, 1998, and was subsequently amended and restated effective February 17, 2005 (the “Plan”);

WHEREAS, the Plan was subsequently amended and assumed by the Company in its merger with Pride, effective as of May 31, 2011;

WHEREAS, the Board of Directors of the Company (the “Board”) has authorized and approved this 2012 Amendment to the Plan by unanimous written consent on May 8, 2012; and

WHEREAS, the Company now desires to adopt this 2012 Amendment to Plan for the purpose of (i) deleting the definition of “ADS” in Section 2 of the Plan, (ii) amending the definition of “Common Stock” in Section 2 of the Plan, and (iii) amending Section 4 of the Plan to remove references to ADSs held in reserve by a subsidiary of the Company;

NOW, THEREFORE, in consideration of the premises and covenants herein contained, the Company hereby adopts the following 2012 Amendment to the Plan:

1. Section 2 of the Plan is hereby amended by deleting the definition “ADS.”

2. The definition of “Common Stock” in Section 2 of the Plan is hereby amended in its entirety to read as follows:

“Common Stock” means Class A ordinary shares of the Company, nominal value US$0.10 per share. All references in the Plan to ADSs shall be read and considered to be references to shares of Common Stock, unless the context otherwise requires, and all references (specific or otherwise) to “stockholders of the Company” shall be read and considered to be references to holders of shares of Common Stock, unless the context otherwise requires, and all provisions of the Plan shall be consistently interpreted and applied.

3. Section 4 of the Plan is hereby amended to read as follows:

4. Common Stock Available for Awards. There shall be available for Awards granted wholly or partly in Common Stock (including rights or options which may be exercised for or settled in Common Stock) under this Plan ten percent (10%) of the total shares of Common Stock outstanding from time to time. Notwithstanding the foregoing, however, the maximum number of shares of Common Stock that may be issued pursuant to ISOs shall be 1,000,000 shares. The Board and the appropriate officers of the Company shall from time to time take whatever actions

are necessary to file required documents with governmental authorities and stock exchanges and transaction reporting systems to make shares of Common Stock available for issuance pursuant to Awards. Common Stock related to Awards that are forfeited or terminated, expire unexercised, are settled in cash in lieu of Common Stock or in a manner such that all or some of the shares covered by an Award are not issued to a Participant or are exchanged for Awards that do not involve Common Stock, shall immediately become available for Awards hereunder. Shares of Common Stock used to satisfy the exercise of Nonqualified Options that are assumed by the Company in connection with the merger between Pride International, Inc. and the Company may be authorized but unissued shares of Common Stock or, if the Committee so determines, shares of Common Stock that have been acquired by the trustees of any employee benefit trust established in connection with the Company’s equity incentive plans.

[signatures on next page]

IN WITNESS WHEREOF, the Company has caused this 2012 Amendment to the Pride International, Inc. 1998 Long-Term Incentive Plan to be signed on its behalf by and a its duly authorized officer, effective as first above written.