<PAGE>

                                                                   EXHIBIT 10(x)

                    [LETTERHEAD OF CENTERPOINT ENERGY, INC.]

                                                 November 27, 2002

Mr. Milton Carroll
7114 Belfort
Houston, Texas 77087

Dear Milton:

         As authorized by CenterPoint's Board of Directors at its November 6,
2002 meeting, we wish to set forth what your supplemental compensation and
related perquisites will be for your service as non-executive Chairman of the
Board of Directors of CenterPoint Energy, Inc., which the Board envisions will
require a substantial amount of your time and attention over the next two years:

         1.       Effective October 1, 2002 and continuing until September 30,
2004 (which will be the term of this letter agreement for all purposes), in
addition to the normal retainer paid to all members of the CenterPoint Board
(which you shall continue to receive while a member of the Board), CenterPoint
will pay you an annual supplemental retainer of $300,000, payable in equal
monthly amounts of $25,000 on the last day of each month, commencing on November
30, 2002 (with the first such payment to include the October and November 2002
monthly payments); and continuing each month thereafter until September 30,
2004. This supplemental retainer shall not be included for purposes of
calculating any benefits under the Board members' retirement programs.

         2.       You will be provided an office commensurate with your position
as Chairman of the Board at CenterPoint's Houston headquarters. In addition,
CenterPoint will employ for you a full-time executive assistant, acceptable to
you, who will be an employee of CenterPoint with full participation in
CenterPoint's employee benefit plans, programs and practices. The duties of your
executive assistant will be determined by you consistent with the overall
employment practices, guidelines and policies of CenterPoint. You and your
executive assistant will also be provided parking spaces acceptable to you at
CenterPoint's Houston headquarters.

         3.       You will be reimbursed by CenterPoint, promptly upon
submission of appropriate written requests, for all reasonable and necessary
expenses incurred by you in furtherance of CenterPoint business.

         4.       In addition to shares of CenterPoint common stock to be
received by you under its stock plan for outside directors, you will be issued
(1) 10,000 shares of CenterPoint common stock immediately and (2) an additional
10,000 shares of CenterPoint common stock on October 1, 2003. The shares will be
fully vested when issued, but will be subject to the holding period and resale
restrictions contained in Rule 144 under the Securities Act of 1933.

<PAGE>

         If this letter is consistent with your prior understandings, then
please so indicate by signing below and returning a counterpart copy to
CenterPoint's General Counsel. You understand, of course, that your rights to
the supplemental compensation and perquisites described above are personal to
you and may not be assigned to any other person.

                                         Very truly yours,

                                         /s/ DAVID M. MCCLANAHAN
                                         ---------------------------------------
                                         David M. McClanahan
                                         President and Chief Executive Officer

                                         /s/ ROBERT J. CRUIKSHANK
                                         ---------------------------------------
                                         Robert J. Cruikshank
                                         Director
AGREED TO AND ACCEPTED
AS OF November 27, 2002

/s/ MILTON CARROLL
----------------------------
Milton Carroll