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


PROSPECTUS SUPPLEMENT NO. 4
(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)
                      ----                        -------------------   -------------   ----------------   ---------------
                                                                                               
Aviator Master Fund ...........................             $5,000             *                 390            *
J.P. Morgan Securities Inc.(2) ................           $225,000             *              17,564            *
Whitebox Diversified Convertible Arbitrage
  Partners L.P. ...............................         $4,000,000             *             312,256            *



- -------------------------
*        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)      J.P. Morgan Securities Inc. was one of the initial purchasers in
         connection with the private placement of the notes in December 2003.
         J.P. Morgan Securities Inc. also beneficially owns 7,943 shares of
         our common stock.

         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 July 6, 2004.