<PAGE>

                                                                 EXHIBIT 4(a)(3)

                                CLECO POWER LLC

                    [Successor to Cleco Utility Group Inc.,
              formerly Central Louisiana Electric Company, Inc.]

                                      TO

                             THE BANK OF NEW YORK

                     [Successor to Bankers Trust Company],
                                                        as Trustee

                                ______________


                         SECOND SUPPLEMENTAL INDENTURE

                          DATED AS OF JANUARY 1, 2001

                                ______________



                   Assumption of and Supplement to Indenture
                          dated as of October 1, 1988
<PAGE>

     SECOND SUPPLEMENTAL INDENTURE, dated as of January 1, 2001, between CLECO
POWER LLC [successor to Cleco Utility Group Inc., formerly Central Louisiana
Electric Company, Inc.], a Louisiana limited liability company (the "Company"),
                                                                     -------
having its principal office at 2030 Donahue Ferry Road, Pineville, Louisiana
71360-5226, and The Bank of New York [successor to Bankers Trust Company], a
banking corporation duly organized and existing under the laws of the State of
New York, as Trustee (the "Trustee"), having its principal Corporate Trust
                           -------
Office at 101 Barclay Street, Floor 21W, New York, New York 10286.

                            RECITALS OF THE COMPANY

     Central Louisiana Electric Company, Inc., a Louisiana corporation, executed
and delivered its Indenture dated as of October 1, 1988 to Bankers Trust
Company, as Trustee (the "Original Indenture"), to provide for the issuance from
                          ------------------
time to time of its unsecured debentures, notes or other evidences of
indebtedness, in the manner and subject to the conditions set forth in the
Indenture.

     The Original Indenture was amended and modified by the First Supplemental
Indenture dated as of December 1, 2000 between Cleco Utility Group Inc. (f/k/a
Central Louisiana Electric Company, Inc.) and the Trustee, which together with
the Original Indenture is hereinafter referred to as the "Indenture".
                                                          ---------

     Terms used herein without definition that are defined in the Indenture
shall have the respective meanings given them in the Indenture.

     Cleco Utility Group Inc. merged with and into the Company (the "Merger")
                                                                     ------
pursuant to the Joint Agreement of Merger dated December 15, 2000 and effective
December 31, 2000 at 11:59 p.m. (Baton Rouge, La. time) between Cleco Utility
Group Inc. and the Company, and in connection therewith the Company desires to
supplement the Indenture as required under Section 801 of the Indenture.

     Section 901(1) of the Indenture provides that without the consent of any
Holders of Securities or coupons, the Company, when authorized by a Board
Resolution, and the Trustee may enter into a supplemental indenture to, among
other things, evidence the succession of another corporation (including without
limitation a limited liability company) to the "Company," as defined therein,
and the assumption by any such successor of the covenants of the "Company," as
defined therein, in the Indenture and in the Securities contained.

     The Company has duly authorized the execution and delivery of this Second
Supplemental Indenture.

     All things necessary to make this Second Supplemental Indenture a valid
agreement of the Company have been done.

     NOW, THEREFORE, THIS SECOND SUPPLEMENTAL INDENTURE WITNESSETH:
<PAGE>

     For and in consideration of the premises, the sum of one Dollar duly paid
by the Company to the Trustee, the receipt of which is hereby acknowledged, it
is mutually covenanted and agreed, for the equal and proportionate benefit of
all the Holders of the Securities or of series thereof, as follows:

                                  ARTICLE ONE

                         ASSUMPTION BY CLECO POWER LLC

     Section 1.  Immediately upon consummation of the Merger, (i) the Company
hereby assumes the due and punctual payment of the principal of (and premium, if
any), any interest on, and any Additional Amounts payable pursuant to Section
1004 of the Indenture with respect to, all the Securities, according to their
tenor, and the due and punctual performance and observance of all of the
covenants and conditions of the Indenture to be performed by the "Company" under
and as defined in the Indenture, and (ii) the Company hereby represents and
warrants to the Trustee that immediately after the Merger, the Company is not in
default under any such covenant or condition.

     Section 2.  The Indenture shall be deemed supplemented to the extent
necessary to give effect to the foregoing.  Except as supplemented hereby, the
Indenture shall remain in full force and effect.


                                  ARTICLE TWO

                                 MISCELLANEOUS

     Section 1.  As supplemented by this Second Supplemental Indenture, the
Indenture shall be read, taken and construed as one and the same instrument.

     Section 2.  The Trustee assumes no duties, responsibilities or liabilities
by reason of this Second Supplemental Indenture, other than as set forth in the
Indenture, as fully as if said terms and conditions were herein set forth at
length.

     Section 3.  This Second Supplemental Indenture may be executed in any
number of counterparts, each of which, when so executed and delivered, shall be
an original; but such counterparts shall together constitute one and the same
instrument.

     Section 4.  This Second Supplemental Indenture shall be governed by and
construed in accordance with the laws of the State of New York applicable to
agreements made and to be performed in such state.

     Section 5.  The dating of this Second Supplemental Indenture as of January
1, 2001, is intended as and for the convenient identification of the Second
Supplemental Indenture and is not
<PAGE>

intended to indicate that this Second Supplemental Indenture was executed and
delivered on said date, this Second Supplemental Indenture being executed and
effective on the dates of the respective acknowledgments hereto attached.
<PAGE>

     IN WITNESS WHEREOF, the Company has caused this Second Supplemental
Indenture to be executed in its limited liability company name and its limited
liability company seal to be hereunto affixed and attested by its duly
authorized officers, all as of the date first above written.


                                               CLECO POWER LLC

[SEAL]
                                               By: /s/ THOMAS J. HOWLIN
                                                   --------------------------
                                                   Name:  Thomas J. Howlin
                                                   Title: Sr. Vice President
ATTEST:


/s/ MICHAEL P. PRUDHOMME
-------------------------------
Name:  Michael P. Prudhomme
Title: Secretary

Signed, sealed, acknowledged and delivered
by CLECO POWER LLC, in the presence of:


/s/ SHANNON HARVEY
-------------------------------
Name:  Shannon Harvey


/s/ K. MICHAEL SAWRIE
-------------------------------
Name:  K. Michael Sawrie


                     [Signatures continued on next page.]
<PAGE>

     IN WITNESS WHEREOF, the Trustee has caused this Second Supplemental
Indenture to be executed in its corporate name and its corporate seal to be
hereunto affixed and attested by its duly authorized officers, all as of the
date first above written.


                                             THE BANK OF NEW YORK, as Trustee

[SEAL]
                                             By: /s/ ROBERT A. MASSIMILLO
                                                 ---------------------------
                                                 Name:  Robert A. Massimillo
                                                 Title: Assistant Vice President
ATTEST:


/s/ MARYBETH LEWICKI
-------------------------------------------
Name:  MaryBeth Lewicki
Title:  Vice President

Signed, sealed, acknowledged and delivered
by THE BANK OF NEW YORK
in the presence of:


/s/ ADA L. LI
-------------------------------------------
Name:



/s/ [Illegible]
-------------------------------------------
Name:
<PAGE>

STATE OF LOUISIANA

PARISH OF RAPIDES


     BE IT KNOWN, that on this 3rd day of January, 2001, before me, the
undersigned authority, duly commissioned, qualified and sworn within and for the
State and Parish aforesaid, personally came and appeared:

                    1.  Thomas J. Howlin

                    2.  Michael P. Prudhomme

to me known to be the identical persons who executed the above and foregoing
instrument, who declared and acknowledged to me, Notary, in the presence of the
undersigned competent witnesses, that they are respectively (1) the Senior Vice
President and (2) the Secretary of Cleco Power LLC (the "Company"); that the
                                                         -------
seal impressed beside their respective signatures on the foregoing Second
Supplemental Indenture is the official seal of the Company; that the aforesaid
instrument was signed and sealed by them, on this date, on behalf of the Company
by authority of a resolution duly adopted by the Board of Directors (Managers)
of the Company on December 15, 2000; and that the above named persons
acknowledge said instrument to be the free act and deed of the Company.

                              1.  /s/ THOMAS J. HOWLIN
                                  ------------------------------
                                  Name:  Thomas J. Howlin
                                  Title: Sr. Vice President


                              2.  /s/ MICHAEL P. PRUDHOMME
                                  ------------------------------
                                  Name:  Michael P. Prudhomme
                                  Title: Secretary


WITNESSES:


/s/ SHANNON HARVEY
---------------------------

/s/ K. MICHAEL SAWRIE
---------------------------


                            /s/ BEATRICE P. NEWCOMB
                            -----------------------------
                                    Notary Public
<PAGE>

STATE OF NEW YORK

COUNTY OF NEW YORK


     BE IT KNOWN, that on this 8 day of January, 2001, before me, the
undersigned authority, duly commissioned, qualified and sworn within and for the
State and County aforesaid, personally came and appeared:

                         1.   Robert A. Massimillo

                         2.   MaryBeth Lewicki

to me known to be the identical persons who executed the above and foregoing
instrument, who declared and acknowledged to me, Notary, in the presence of the
undersigned competent witnesses, that they are respectively (1) the Assistant
Vice President and (2) the Vice President of The Bank of New York (the
"Trustee"); that the seal impressed beside their respective signatures on the
 -------
foregoing Second Supplemental Indenture is the official seal of the Trustee;
that the aforesaid instrument was signed and sealed by them, on this date, on
behalf of the Trustee by authority of its By-laws; and that the above named
persons acknowledge said instrument to be the free act and deed of the Trustee.

                                  1.  /s/ ROBERT A. MASSIMILLO
                                      ------------------------------------
                                      Name:  Robert A. Massimillo
                                      Title: Assistant Vice President


                                  2.  /s/ MARYBETH LEWICKI
                                      ------------------------------------
                                      Name:  MaryBeth Lewicki
                                      Title: Vice President


WITNESSES:


/s/ ADA L. LI
-----------------------------

/s/ [Illegible]
-----------------------------


                             /s/ WILLIAM J. CASSELS
                             ----------------------------
                                     Notary Public