Filed Pursuant to Rule 424(b)(3)
                                                    Registration No. 333-110348


PROSPECTUS SUPPLEMENT NO. 13
(TO PROSPECTUS DATED DECEMBER 4, 2003)

                            (CENTERPOINT ENERGY LOGO)

                                  $575,000,000
                     3.75% Convertible Senior Notes due 2023
                                       and
               Common Stock Issuable Upon Conversion of the Notes

         This document supplements our prospectus dated December 4, 2003,
relating to $575,000,000 aggregate principal amount of our 3.75% Convertible
Senior Notes Due 2023 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)
                       ----                        -------------------    -------------  ----------------   ---------------
                                                                                                
ING Convertible Fund ............................     $ 1,000,000               *              86,356                *
ING VP Convertible Fund .........................     $    15,000               *               1,295                *


- ----------

*        Less than 1%

(1)      Calculated using 306,077,942 shares of common stock outstanding as of
         November 3, 2003. 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.

         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 3, 2004.