Document:

<PAGE>

                                                                    EXHIBIT 4(e)

                          SUPPLEMENTAL INDENTURE NO. 2

     This Supplemental Indenture No. 2, effective as of August 31, 2002 (this
"Supplemental Indenture"), among CenterPoint Energy, Inc., a Texas corporation
("CNP"), Reliant Energy, Incorporated, a Texas corporation (the "Company"), and
JPMorgan Chase Bank, formerly Chase Bank of Texas, National Association, as
Trustee (the "Trustee"), supplements the Subordinated Indenture dated as of
September 1, 1999 (the "Indenture") between the Company and the Trustee, and
Supplemental Indenture No. 1 dated as of September 1, 1999 between the Company
and the Trustee, under which 17,166,571 of the Company's 2.0% Zero-Premium
Exchangeable Subordinated Notes due 2029 (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 801 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 any premium and interest on all the
Securities and the performance or observance of every covenant of the Indenture
on the part of the Company to be performed or observed;

     WHEREAS, Section 901 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 inter alia, to evidence the
succession of another corporation to the Company and the assumption by the
successor corporation of the covenants, agreements and obligations of the
Company under the Indenture and in the Securities;

<PAGE>

                   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 801 and 901 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 any premium and
interest on all the Securities and the performance or observance of every
covenant, obligation and agreement 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 801(3) of the Indenture.

     (3) Pursuant to Section 802 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.

                                       2
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     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

                                      JPMORGAN CHASE BANK,
                                      Trustee

Attest:                               By:         /s/ Carol Logan
                                         ---------------------------------------
                                         Name: Carol Logan
                                         Title: Vice President and Trust Officer
By:       /s/ Donna Edmundson
   -----------------------------------
   Name: Donna Edmundson
   Title: Vice President and Trust
          Officer

                                       3<PAGE>

                                                                    EXHIBIT 4(f)

                          SUPPLEMENTAL INDENTURE NO. 2

     This Supplemental Indenture No. 2, effective as of August 31, 2002 (this
"Supplemental Indenture"), among CenterPoint Energy, Inc., a Texas corporation
("CNP"), Reliant Energy, Incorporated, a Texas corporation (the "Company"), and
The Bank of New York, as Trustee (the "Trustee"), supplements the Junior
Subordinated Indenture dated as of February 15, 1999, between the Company and
the Trustee, as supplemented by Supplemental Indenture No. 1 dated as of
February 15, 1999, between the Company and the Trustee (the "Indenture") under
which the Company's Junior Subordinated Debentures related to $375,000,000 of
7.20% trust originated preferred securities issued by REI Trust I (the
"Debentures") 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 10.01 of the Indenture, CNP, as transferee of
the Company's properties and assets substantially as an entirety, is required to
expressly assume, by an indenture supplemental to the Indenture, all the
obligations of the Company under the Debentures and the Indenture;

     WHEREAS, Section 9.01 of the Indenture provides that under certain
conditions the Company and the Trustee, without the consent of the
Debentureholders, from time to time and at any time, may enter into an indenture
supplemental to the Indenture for the purposes inter alia, to evidence the
succession of another corporation to the Company and the assumption by any such
successor of the obligations of the Company contained in the Indenture or
otherwise established with respect to the Debentures;

<PAGE>

                   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 9.01 and 10.01 of the 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 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 all the obligations of the Company under the Debentures and the
Indenture.

     (2) Concurrently with the execution and delivery of this Supplemental
Indenture, the Company has delivered to the Trustee an Opinion of Counsel as
allowed by Sections 9.05 and 10.03 of the Indenture.

     (3) Pursuant to Section 10.02 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 relieved of all obligations and
covenants under the Indenture and the Debentures.

     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.

     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.

                                       2

<PAGE>

     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

Attest:                                By:      /s/ Barbara A. Bevelaqua
                                          --------------------------------------
                                          Name: Barbara A. Bevelaqua
                                          Title: Vice President
By:    /s/ Beata Hryniewicka
   -----------------------------------
   Name: Beata Hryniewicka
   Title: Assistant Treasurer

                                       3

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