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                                                                    EXHIBIT 4(g)

                          SUPPLEMENTAL INDENTURE NO. 3

     This Supplemental Indenture No. 3, effective as of August 31, 2002 (this
"Supplemental Indenture"), among CenterPoint Energy, Inc., a Texas corporation
("CNP"), Reliant Energy, Incorporated, a Texas corporation (formerly Houston
Lighting & Power Company) (the "Company"), and The Bank of New York, as Trustee
(the "Trustee"), supplements the Junior Subordinated Indenture dated as of
February 1, 1997, between the Company and the Trustee, as supplemented by
Supplemental Indenture No. 1 dated as of February 1, 1997 between the Company
and the Trustee and Supplemental Indenture No. 2 dated as of February 1, 1997
between the Company and the Trustee (the "Indenture") under which the Company's
Junior Subordinated Debentures related to $250,000,000 of 8.125% trust preferred
securities issued by HL&P Capital Trust I and $100,000,000 of 8.257% capital
securities issued by HL&P Capital Trust II (the "Securities") were issued and
remain outstanding.

                                    RECITALS

     WHEREAS, pursuant to an Agreement and Plan of Merger dated as of October
19, 2001, among the Company, CNP and Reliant Energy MergerCo, Inc., a Texas
corporation and an indirect wholly-owned subsidiary of CNP ("MergerCo"),
MergerCo will be merged with and into the Company (the "Merger"), with the
Company to be the surviving corporation, as a result of which, at the effective
time of the Merger, each share of common stock, without par value, of the
Company will be converted into one share of common stock, par value $0.01 per
share, of CNP and the Company will become a wholly-owned subsidiary of CNP;

     WHEREAS, concurrently with the Merger, the Company will (i) distribute the
capital stock of all of its subsidiaries, other than certain financing
subsidiaries, to CNP (the "Stock Distribution") and (ii) convey its Texas
electric generation assets and certain buildings and related assets to indirect
wholly-owned subsidiaries of CNP (the "Asset Conveyance," and together with the
Merger and the Stock Distribution, the "Restructuring");

     WHEREAS, the Restructuring is a transfer of the Company's properties and
assets substantially as an entirety;

     WHEREAS, pursuant to Section 8.1 of the Indenture, CNP, as the transferee
of the Company's properties and assets substantially as an entirety, is required
to expressly assume, by an indenture supplemental to the Indenture, the due and
punctual payment of the principal of (and premium, if any) and interest
(including any Additional Interest) on all the Securities and the performance of
every covenant of the Indenture on the part of the Company to be performed or
observed;

     WHEREAS, Section 9.1 of the Indenture provides that under certain
conditions the Company and the Trustee, without the consent of the Holders of
Securities, at any time and from time to time, may enter into an indenture
supplemental to the Indenture for the purposes

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inter alia, to evidence the succession of another corporation to the Company and
the assumption by any such successor of the covenants of the Company under the
Indenture and in the Securities;

                   NOW, THEREFORE, THIS SUPPLEMENTAL INDENTURE
                                   WITNESSETH:

     In consideration of the premises and other good and valuable consideration,
the receipt and sufficiency of which are hereby acknowledged, and to comply with
Sections 8.1 and 9.1 of the Indenture, the parties hereto hereby agree, for the
equal and proportionate benefit of the respective Holders from time to time of
the Securities, as follows:

     Section 1. Defined Terms. Capitalized terms used and not otherwise defined
herein shall have the respective meanings assigned to such terms in the
Indenture.

     Section 2. Succession by Transfer of Properties and Assets Substantially as
an Entirety.

     (1) Upon consummation of the Restructuring, CNP shall become the successor
to the Company for all purposes of the Indenture and CNP hereby expressly
assumes the due and punctual payment of the principal of (and premium, if any)
and interest (including any Additional Interest) on all the Securities and the
performance of every covenant of the Indenture, as supplemented by this
Supplemental Indenture, on the part of the Company to be performed or observed.

     (2) Concurrently with the execution and delivery of this Supplemental
Indenture, the Company has delivered to the Trustee an Officers' Certificate and
an Opinion of Counsel as required by Section 8.1(4) of the Indenture.

     (3) Pursuant to Section 8.2 of the Indenture, concurrently with the
execution and delivery of this Supplemental Indenture, (i) CNP shall succeed to,
and be substituted for, and may exercise every right and power of, the Company
under the Indenture with the same effect as if CNP had been named as the Company
in the Indenture and (ii) the Company shall be discharged from all obligations
and covenants under the Indenture and the Securities.

     Section 3. Ratification. The Indenture as hereby supplemented is in all
respects ratified and confirmed by each of the parties hereto, and all of the
rights and powers created thereby or thereunder shall be and remain in full
force and effect.

     Section 4. Governing Law. The laws of the State of New York shall govern
this Supplemental Indenture without regard to principles of conflicts of laws.

     Section 5. Successors. All agreements of the parties hereto in this
Supplemental Indenture shall bind their respective successors.

     Section 6. Multiple Counterparts. The parties hereto may sign multiple
counterparts of this Supplemental Indenture. Each signed counterpart shall be
deemed an original, but all of them together represent the same agreement.

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     Section 7. Trustee's Disclaimer. The recitals contained herein shall be
taken as the statements of the Company and CNP, and the Trustee assumes no
responsibility for their correctness. The Trustee makes no representations as to
the validity or sufficiency of this Supplemental Indenture.

     IN WITNESS WHEREOF, the undersigned have caused this Supplemental Indenture
to be executed by its duly authorized officer as of the date first above
written.

                                      CENTERPOINT ENERGY, INC.

                                      By:          /s/ Rufus Scott
                                         ---------------------------------------
Attest:                                  Name: Rufus Scott
                                         Title: Vice President

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

                                      RELIANT ENERGY, INCORPORATED

                                      By:         /s/ Marc Kilbride
                                         ---------------------------------------
Attest:                                  Name: Marc Kilbride
                                         Title: Treasurer

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

                                      THE BANK OF NEW YORK,
                                      Trustee

                                      By:       /s/ Barbara A. Bevelaqua
                                         ---------------------------------------
Attest:                                  Name: Barbara A. Bevelaqua
                                         Title: Vice President

By:     /s/ Beata Hryniewicka
   ----------------------------------
   Name: Beata Hryniewicka
   Title: Assistant Treasurer

                                       3<PAGE>

                                                                    EXHIBIT 4(h)

                          THIRD SUPPLEMENTAL INDENTURE

     This Third Supplemental Indenture, effective as of August 31, 2002 (this
"Third Supplemental Indenture"), among CenterPoint Energy, Inc., a Texas
corporation ("CNP"), Reliant Energy, Incorporated (formerly Houston Lighting &
Power Company), a Texas corporation ("REI"), Reliant Energy Resources Corp.
(formerly NorAm Energy Corp.), a Delaware corporation ("RERC"), and The Bank of
New York, as Trustee (the "Trustee"), supplements the Indenture dated as of June
15, 1996 between NorAm Energy Corp., a Delaware corporation ("NorAm"), and the
Trustee, as supplemented by the First Supplemental Indenture, dated as of June
15, 1996 (the "First Supplemental Indenture") between NorAm and the Trustee and
the Second Supplemental Indenture dated as of August 6, 1997 (the "Second
Supplemental Indenture") among Houston Lighting & Power Company, HI Merger,
Inc., a Delaware corporation, NorAm, and the Trustee (as supplemented by the
First Supplemental Indenture and the Second Supplemental Indenture, the
"Indenture"), under which RERC's 6 1/4% Convertible Junior Subordinated
Debentures (the "Debentures") were issued and are outstanding.

                                    RECITALS

     WHEREAS, pursuant to the terms of the Indenture, each $50 principal amount
of the Debentures is currently convertible into $33.62 of cash (the "Cash
Consideration") and 1.55 shares of common stock, without par value, of REI ("REI
Common Stock");

     WHEREAS, pursuant to the Agreement and Plan of Merger dated as of October
19, 2001 (the "Merger Agreement") among REI, Reliant Energy MergerCo, Inc., a
Texas corporation and indirect subsidiary of CNP ("MergerCo"), and CNP, REI will
be merged with and into MergerCo, with REI to be the surviving corporation (the
"Merger");

     WHEREAS, at the effective time of the Merger (the "Effective Time"), each
outstanding share of REI Common Stock will be converted into one share of common
stock, par value $0.01 per share, of CNP ("CNP Common Stock");

     WHEREAS, in connection with the Merger, CNP, REI and RERC have duly
determined to make, execute and deliver to the Trustee this Third Supplemental
Indenture in order to reflect the results of the Merger as required by Section
7.4 of the First Supplemental Indenture;

     WHEREAS, Section 7.4 of the First Supplemental Indenture requires that, as
a result of the Merger, each Holder of a Debenture shall have the right to
convert the Debenture into the consideration receivable upon the Merger by a
holder of the number of shares of REI Common Stock into which the Debenture
could have been converted immediately prior to the Merger;

     WHEREAS, Section 9.1 of the Indenture provides that under certain
conditions RERC and the Trustee, without the consent of the Holders of
Debentures, from time to time and at any time, may enter into an indenture
supplemental to the Indenture, inter alia, to evidence the assumption by any
successor of the covenants under the Indenture and in the Debentures and to add
to such covenants for the benefit of the Holders of Debentures;

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                NOW, THEREFORE, THIS THIRD SUPPLEMENTAL INDENTURE
                                  WITNESSETH:

     In consideration of the premises and other good and valuable consideration,
the receipt and sufficiency of which are hereby acknowledged, and to comply with
Section 9.1 of the Indenture and Section 7.4 of the First Supplemental
Indenture, the parties hereto hereby agree, for the equal and proportionate
benefit of the respective Holders from time to time of the Debentures, as
follows:

     Section 1. Defined Terms. Capitalized terms used and not otherwise defined
herein have the respective meanings assigned to such terms in the Indenture.

     Section 2. Conversion Privilege. The Holder of each Debenture outstanding
as of the Effective Time (and each subsequent Holder) shall have the right from
and after the Effective Time to convert such Debenture only into (i) 1.55 shares
of CNP Common Stock (the "Stock Consideration"), subject to the adjustments
provided for in Article Seven of the First Supplemental Indenture, (and cash in
lieu of fractional shares of CNP Common Stock) and (ii) the Cash Consideration.

     Section 3. Additional Covenants of CNP. CNP hereby (i) agrees to (A)
reserve and keep available out of its authorized but unissued capital stock,
solely for the purpose of issuance upon the conversion of Debentures as provided
in this Third Supplemental Indenture and the First Supplemental Indenture, a
number of shares of CNP Common Stock sufficient to issue the Stock Consideration
upon the conversion of all outstanding Debentures and (B) issue and cause to be
delivered in accordance with this Third Supplemental Indenture, the First
Supplemental Indenture and the Company's instructions, the Stock Consideration
and the Cash Consideration upon conversion of any Debenture and (ii) warrants
that all shares of CNP Common Stock that may be issued upon the conversion of
any Debenture, when so issued, shall be duly authorized, validly issued, fully
paid and nonassessable.

     Section 4. Ratification. The Indenture as hereby supplemented is in all
respects ratified and confirmed by each of the parties hereto, and all of the
rights and powers created thereby or thereunder shall be and remain in full
force and effect.

     Section 5. Governing Law. The laws of the State of New York shall govern
this Third Supplemental Indenture without regard to principles of conflicts of
laws.

     Section 6. Successors. All agreements of the parties hereto in this Third
Supplemental Indenture shall bind their respective successors.

     Section 7. Multiple Counterparts. The parties hereto may sign multiple
counterparts of this Third Supplemental Indenture. Each signed counterpart shall
be deemed an original, but all of them together represent the same agreement.

     Section 8. Trustee's Disclaimer. The recitals contained herein shall be
taken as the statements of REI, CNP and RERC, and the Trustee assumes no
responsibility for their correctness. The Trustee makes no representations as to
the validity or sufficiency of this Third Supplemental Indenture.

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     IN WITNESS WHEREOF, the undersigned have caused this Third Supplemental
Indenture to be executed by its duly authorized officer as of the date first
above written.

                                       CENTERPOINT ENERGY, INC.

                                       By:           /s/ Rufus Scott
                                          --------------------------------------
Attest:                                   Name: Rufus Scott
                                          Title: Vice President

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

                                       RELIANT ENERGY, INCORPORATED

                                       By:         /s/ Marc Kilbride
                                          --------------------------------------
Attest:                                   Name: Marc Kilbride
                                          Title: Treasurer

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

                                       RELIANT ENERGY RESOURCES CORP.

                                       By:          /s/ Rufus Scott
                                          --------------------------------------
Attest:                                   Name: Rufus Scott
                                          Title: Vice President

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

                                       THE BANK OF NEW YORK, Trustee

                                       By:      /s/ Barbara A. Bevelaqua
                                          --------------------------------------
Attest:                                   Name: Barbara A. Bevelaqua
                                          Title: Vice President

By:       /s/ Beata Hryniewicka
   -----------------------------------
   Name: Beata Hryniewicka
   Title: Assistant Treasurer

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