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                                                                    Exhibit 10.4

                TEXAS GENCO HOLDINGS, INC. PERFORMANCE UNIT PLAN

                        (Effective as of January 1, 2003)

                                 First Amendment

            Texas Genco Holdings, Inc., a Texas corporation, having established
the Texas Genco Holdings, Inc. Performance Unit Plan, effective as of January 1,
2003 (the "Plan"), and having reserved the right under Section 10 thereof to
amend the Plan, does hereby amend the Plan, effective as of October 1, 2004, to
read as follows:

            1. The Plan is hereby renamed the "Texas Genco Performance Unit
Plan" and all references in the Plan are amended accordingly.

            2. The Plan is hereby amended to provide that, except as provided in
Paragraph 4 herein, all references to "Texas Genco Holdings, Inc." are hereby
deleted and replaced in lieu thereof with "Texas Genco, LP" and the definition
of "Company" in Section 3 of the Plan is hereby amended to read as follows:

            "`COMPANY' means Texas Genco, LP, a Texas limited partnership, or
its successors."

            3. Section 3 of the Plan is hereby amended to add the following new
definitions thereto:

            "`GENERAL PARTNER' means the general partner of the Company.

            `SCHEDULED EMPLOYEE' means an Employee who is a Scheduled Employee
      on Section 6.8(a) of the Companies Disclosure Letter as defined in Section
      4.3(a) of the Transaction Agreement.

            `TRANSACTION AGREEMENT' means that certain Transaction Agreement
      among CenterPoint Energy, Inc., Utility Holding, LLC, NN Houston Sub,
      Inc., Texas Genco Holdings, Inc., HPC Merger Sub, Inc. and GC Power
      Acquisition LLC, dated as of July 21, 2004."

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            4. The definitions of "Authorized Officer," "Committee," "Employee"
and "Subsidiary" in Section 3 of the Plan are hereby amended to read as follows:

            "`AUTHORIZED OFFICER' means the Chairman of the Board of Directors
      of the General Partner or the Chief Executive Officer of the General
      Partner or the Company (or any other senior officer of the General Partner
      or the Company to whom either of them shall delegate the authority to
      execute any Award Agreement, where applicable).

            `COMMITTEE' means the Board of Directors of the General Partner
      until such time as there is established a Compensation Committee of the
      Board of Directors of the General Partner, and thereafter the Compensation
      Committee.

            `EMPLOYEE' means (i) an employee of the Company or any of its
      Subsidiaries or (ii) a Scheduled Employee who, immediately prior to the
      execution date of the Transaction Agreement, was a Participant in the
      Plan.

            `SUBSIDIARY' means (a) in the case of a corporation, any corporation
      of which the Company directly or indirectly owns shares representing 50%
      or more of the combined voting power of the shares of all classes or
      series of capital stock of such corporation which have the right to vote
      generally on matters submitted to a vote of the stockholders of such
      corporation and (b) in the case of a partnership or other business entity
      not organized as a corporation, any such business entity of which the
      Company directly or indirectly owns 50% or more of the voting, capital or
      profits interests (whether in the form of partnership interests,
      membership interests or otherwise); provided, however, that, regardless of
      whether or not the foregoing clause (a) or clause (b) is satisfied, for
      purposes of this Plan, Texas Genco Holdings, Inc. and its direct and
      indirect affiliates and subsidiaries shall be deemed to be Subsidiaries
      during the period commencing on the `Non-STP Acquisition Closing Date'
      under the Transaction Agreement and ending on the `STP Acquisition Closing
      Date' under the Transaction Agreement."

            5. Section 3 of the Plan is hereby amended to delete the definition
of "Board" and all references in the Plan to "Board" are hereby deleted and
replaced in lieu thereof with "General Partner."

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            IN WITNESS WHEREOF, Texas Genco Holdings, Inc. and Texas Genco, LP,
have caused these presents to be executed by their duly authorized officers in a
number of copies, all of which shall constitute one and the same instrument,
which may be sufficiently evidenced by any executed copy hereof, on this 22nd
day of September, 2004, but effective as of the date specified herein.

                                       TEXAS GENCO HOLDINGS, INC.

                                       By /s/ DAVID G. TEES
                                          --------------------------------------
                                          David G. Tees
                                          Chief Executive Officer
ATTEST:

/s/ RICHARD DAUPHIN
--------------------------

                                       TEXAS GENCO, LP

                                       BY:  TEXAS GENCO GP, LLC
                                       ITS GENERAL PARTNER

                                       By /s/ DAVID G. TEES
                                          --------------------------------------
                                          David G. Tees
                                          President and Chief Executive Officer
ATTEST:

/s/ RICHARD DAUPHIN
--------------------------

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