EXHIBIT 4(h)(4)

                            CENTERPOINT ENERGY, INC.
                   (Successor to Reliant Energy, Incorporated)

                                       To

                    JPMORGAN CHASE BANK, NATIONAL ASSOCIATION
            (Successor to Chase Bank of Texas, National Association)

                                     Trustee

                                   ----------

                          SUPPLEMENTAL INDENTURE No. 3

                          Dated as of December 28, 2005

                                   ----------

      2.0% Zero-Premium Exchangeable Subordinated Notes due 2029 (ZENS(SM))

- --------
(SM) Service Mark of Goldman, Sachs & Co.



                            CENTERPOINT ENERGY, INC.

                          SUPPLEMENTAL INDENTURE NO. 3

      2.0% Zero-Premium Exchangeable Subordinated Notes due 2029 (ZENS(SM))

     SUPPLEMENTAL INDENTURE No. 3, dated as of December 28, 2005, between
CENTERPOINT ENERGY, INC. (successor to Reliant Energy, Incorporated), a Texas
corporation (the "Company"), and JPMORGAN CHASE BANK, NATIONAL ASSOCIATION
(successor to Chase Bank of Texas, National Association), a national banking
association, as Trustee (the "Trustee").

                                    RECITALS

     The Company has heretofore executed and delivered to the Trustee a
Subordinated Indenture, dated as of September 1, 1999 (the "Original Indenture"
and, as previously and hereby supplemented and amended, the "Indenture"),
providing for the issuance from time to time of one or more series of the
Company's Securities.

     Pursuant to the terms of the Indenture, the Company provided for the
establishment of a series of Securities designated as the "2% Zero-Premium
Exchangeable Subordinated Notes due 2029" (the "ZENS"), the form and substance
of the ZENS and the terms, provisions and conditions thereof in Supplemental
Indenture No. 1, dated as of September 1, 1999, between the Company and the
Trustee.

     Section 307 of the Indenture provides that the Company may at any time
designate additional Paying Agents or rescind the designation of any Paying
Agent.

     Subparagraph (5) of Section 901 of the Indenture provides that the Company
and the Trustee may enter into an indenture supplemental to the Indenture to add
to, change or eliminate any of the provisions of the Indenture if such action
does not adversely affect the interests of any Holders.

     For and in consideration of the premises and the issuance of the series of
Securities provided for herein, it is mutually covenanted and agreed, for the
equal and proportionate benefit of the Holders of the Securities of such series,
as follows:



                                   ARTICLE ONE

                            Relation to the Indenture

     Section 101. Relation to the Indenture. This Supplemental Indenture No. 3
constitutes an integral part of the Indenture.

                                   ARTICLE TWO

                           Designation of Paying Agent

     Section 201. Designation of Paying Agent. JPMorgan Chase Bank, National
Association is hereby designated as the Paying Agent on the ZENS. The
designation of CenterPoint Energy, Inc. as the Paying Agent on the ZENS is
hereby rescinded.

                                  ARTICLE THREE

                            Miscellaneous Provisions

     Section 301. The Indenture, as supplemented and amended by this
Supplemental Indenture No. 3, is in all respects hereby adopted, ratified and
confirmed.

     Section 302. This Supplemental Indenture No. 3 may be executed in any
number of counterparts, each of which shall be an original, but such
counterparts shall together constitute but one and the same instrument. This
Supplemental Indenture No. 3 shall be deemed part of the Indenture in the manner
and to the extent herein and therein provided.

     Section 303. THIS SUPPLEMENTAL INDENTURE NO. 3 AND EACH ZENS SHALL BE
DEEMED TO BE A CONTRACT MADE UNDER THE LAWS OF THE STATE OF NEW YORK AND SHALL
BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW
YORK WITHOUT REGARD TO CONFLICTS OF LAWS PRINCIPLES THEREOF.



     IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture No. 3 to be duly executed, as of the day and year first written above.

                                        CENTERPOINT ENERGY, INC.


                                        By: /s/ Marc Kilbride
                                            ------------------------------------
                                        Name: Marc Kilbride
                                        Title: Vice President and Treasurer


Attest: /s/ Richard B. Dauphin
        -----------------------------
Name: Richard B. Dauphin
Title: Assistant Corporate Secretary

(SEAL)


                                        JPMORGAN CHASE BANK, NATIONAL
                                        ASSOCIATION, as Trustee


                                        By: /s/ Carol Logan
                                            ------------------------------------
                                        Name: Carol Logan
                                        Title: Vice President

(SEAL)