Exhibit 10.5

SCHLUMBERGER LIMITED SUPPLEMENTARY BENEFITS PLAN

(As Established Effective June 1, 1995)

First Amendment

Schlumberger Limited, a Netherlands Antilles corporation (the “Company”), having reserved the right under Section 7.2 of the Schlumberger Limited Supplementary Benefit Plan, as established effective June 1, 1995, to amend the Plan, does hereby amend the Plan, effective as of January 1, 2004, as follows:

1. Section 3.3(a) of the Plan is hereby amended by deleting the phrase:

“provided, however, that such a Defined Benefit Restoration Benefit shall only be paid to or in respect of a Participant who terminates Active Service after attaining age 55,”

and replacing it with:

“provided, however, that such a Defined Benefit Restoration Benefit shall only be paid to or in respect of a Participant who terminates Active Service after attaining age 50,”

each time such phrase appears in this Section.

2. Section 4.3(a) of the Plan is hereby amended by deleting the phrase “after attaining age 55” and replacing it with the phrase “after attaining age 50” each time it appears therein.

3. Section 5.1 of the Plan is hereby amended by deleting the first sentence thereof and replacing it with the following:

“Vesting: A Participant shall become vested in the benefits payable under Sections 3.3 and 4.3 hereof at the same time that he becomes vested under the applicable Qualified Plan; provided however, that in order to become vested in the Defined Benefit Restoration Benefit and the Section 415 Defined Benefit Restoration Benefit, the Participant must attain age 50 before he terminates Active Service.”

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