Filed Pursuant to Rule 424(b)(3)
                                                     Registration No. 333-114440


PROSPECTUS SUPPLEMENT NO. 1
(TO PROSPECTUS DATED APRIL 30, 2004)

                            (CENTERPOINT ENERGY LOGO)

                                  $255,000,000
                    2.875% Convertible Senior Notes due 2024
                                       and
               Common Stock Issuable Upon Conversion of the Notes

         This document supplements our prospectus dated April 30, 2004, relating
to $255,000,000 aggregate principal amount of our 2.875% Convertible Senior
Notes Due 2024 and the common stock issuable upon conversion of the notes. You
should read this prospectus supplement in conjunction with the accompanying
prospectus, which is to be delivered by selling securityholders to prospective
purchasers along with this prospectus supplement. The information in the
following table supplements the information set forth under the caption "Selling
Security Holders" in the prospectus.



                                                  PRINCIPAL AMOUNT OF                   NUMBER OF SHARES
                                                   NOTES BENEFICIALLY   PERCENTAGE OF    OF COMMON STOCK   PERCENTAGE OF
                                                     OWNED THAT MAY         NOTES             THAT          COMMON STOCK
                      NAME                              BE SOLD          OUTSTANDING       MAY BE SOLD     OUTSTANDING (1)
                      ----                        -------------------   -------------   ----------------   ---------------
                                                                                               
Canadian Imperial Holdings Inc.................        $2,500,000             *              195,160              *
Citigroup Global Markets Inc. (2)..............        $2,000,000             *              156,128              *
Triborough Partners International Ltd. (3).....        $5,040,000           1.98%            393,443              *
Triborough Partners LLC (4)....................        $1,960,000             *              153,005              *


- -------------------------
*        Less than 1%

(1)      Calculated using 307,072,860 shares of common stock outstanding as of
         March 31, 2004. In calculating this amount for each holder, we treated
         as outstanding the number of shares of common stock issuable upon
         conversion of all of that holder's notes, but we did not assume
         conversion of any other holder's notes.

(2)      Represents the aggregate principal amount of transfer restricted notes
         held by Citigroup Global Markets Inc. as of the date of this prospectus
         supplement. Citigroup Global Markets Inc. was one of the initial
         purchasers in connection with the private placement of the notes in
         December 2003. In addition, Citigroup Global Markets Inc. was one of
         the initial purchasers in connection with the private placement of our
         3.75% Convertible Senior Notes due 2023 in May 2003, and also
         beneficially owns $2,804,000 principal amount of our 3.75% Convertible
         Senior Notes due 2023.

(3)      Represents the aggregate principal amount of transfer restricted notes
         held by Triborough Partners International Ltd. as of the date of this
         prospectus supplement.

(4)      Represents the aggregate principal amount of transfer restricted notes
         held by Triborough Partners LLC as of the date of this prospectus
         supplement.


         INVESTING IN THE NOTES INVOLVES RISKS. SEE "RISK FACTORS" BEGINNING ON
PAGE 10 OF THE ACCOMPANYING PROSPECTUS.

         NEITHER THE SECURITIES AND EXCHANGE COMMISSION NOR ANY STATE SECURITIES
COMMISSION HAS APPROVED OR DISAPPROVED OF THESE SECURITIES OR PASSED UPON THE
ADEQUACY OR ACCURACY OF THIS PROSPECTUS SUPPLEMENT OR THE ACCOMPANYING
PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A CRIMINAL OFFENSE.

             The date of this prospectus supplement is May 18, 2004.