<PAGE>

                                                                     EXHIBIT 4.4

                              FIRST AMENDMENT TO
                               CREDIT AGREEMENT

                                 BY AND AMONG

                      ENTERPRISE PRODUCTS OPERATING L.P.,

                               BANKBOSTON, N.A.,
                      SOCIETE GENERALE, SOUTHWEST AGENCY

                                      AND

                          FIRST UNION NATIONAL BANK,
                               AS CO-ARRANGERS,

                           THE CHASE MANHATTAN BANK,
                  AS CO-ARRANGER AND AS ADMINISTRATIVE AGENT,

                                 BANK ONE, NA,
                  AS CO-ARRANGER AND AS DOCUMENTATION AGENT,

                           THE BANK OF NOVA SCOTIA,
                   AS CO-ARRANGER AND AS SYNDICATION AGENT,

                                      AND

                               THE SEVERAL BANKS
                       FROM TIME TO TIME PARTIES HERETO

                                     WITH

                         FIRST UNION CAPITAL MARKETS,
                           ACTING AS MANAGING AGENT

                                      AND

                            CHASE SECURITIES INC.,
                   ACTING AS LEAD ARRANGER AND BOOK MANAGER

                       EFFECTIVE AS OF JANUARY 24, 2000

AGGREGATE $350,000,000
REVOLVING CREDIT FACILITY
<PAGE>

                              FIRST AMENDMENT TO
                               CREDIT AGREEMENT

     This FIRST AMENDMENT TO CREDIT AGREEMENT (this "First Amendment") executed
effective as of the 24th day of January, 2000 (the "Effective Date"), is by and
among ENTERPRISE PRODUCTS OPERATING L.P., a limited partnership formed under the
laws of the State of Delaware (the "Company"); each of the banks that is a
signatory hereto or which becomes a signatory hereto and to the hereinafter
described Credit Agreement (individually, together with its successors and
assigns, a "Bank" and, collectively, the "Banks"); THE CHASE MANHATTAN BANK,
BANKBOSTON, N.A., THE BANK OF NOVA SCOTIA, BANK ONE, NA (formerly known as The
First National Bank of Chicago), SOCIETE GENERALE, SOUTHWEST AGENCY, and FIRST
UNION NATIONAL BANK, as Co-Arrangers; BANK ONE, NA (formerly known as The First
National Bank of Chicago), as Documentation Agent, THE BANK OF NOVA SCOTIA, as
Syndication Agent; and THE CHASE MANHATTAN BANK ("Chase"), as Administrative
Agent for the Banks hereunder (in such capacity, together with its successors in
such capacity, the "Agent"), with FIRST UNION CAPITAL MARKETS acting as Managing
Agent and CHASE SECURITIES INC. acting as Lead Arranger and Book Manager.

                               R E C I T A L S:

     WHEREAS, the Company, the Agent, the Documentation Agent, the Syndication
Agent and the Banks are parties to that certain Credit Agreement dated as of
July 28, 1999 (the "Credit Agreement"), pursuant to which the Banks agreed to
make loans to and extensions of credit on behalf of the Company; and

     WHEREAS, the Company and the Banks desire to amend the Credit Agreement in
the particulars hereinafter provided;

     NOW, THEREFORE, in consideration of the premises and the mutual covenants
herein contained, the parties hereto agree as follows:


                            SECTION 1.  DEFINITIONS

      1.1 Terms Defined Above.  As used in this First Amendment, each of the
terms "Bank", "Banks", "Company", "Credit Agreement", "Effective Date" and
"First Amendment" shall have the meaning assigned to such term hereinabove.

      1.2 Terms Defined in Credit Agreement.  Each term defined in the Credit
Agreement and used herein without definition shall have the meaning assigned to
such term in the Credit Agreement, unless expressly provided to the contrary.
<PAGE>

      1.3 Other Definitional Provisions.

          (a) The words "hereby", "herein", "hereinafter", "hereof", "hereto"
     and "hereunder" when used in this First Amendment shall refer to this First
     Amendment as a whole and not to any particular Article, Section, subsection
     or provision of this First Amendment.

          (b) Section, subsection and Exhibit references herein are to such
     Sections, subsections and Exhibits to this First Amendment unless otherwise
     specified.


     SECTION 2.  AMENDMENTS TO CREDIT AGREEMENT

     The Company, the Agent and the Banks agree that the Credit Agreement is
hereby amended, effective as of the Effective Date, in the following
particulars.

      2.1 Amendments and Supplements to Definitions.

          (a) The term "Agreement", which is defined in subsection 1.1 of the
     Credit Agreement, is hereby amended to mean the Credit Agreement, as
     amended by this First Amendment, and as the same may from time to time be
     further amended, supplemented or modified.

          (b) Subsection 1.1 of the Credit Agreement is hereby further amended
     and supplemented by adding the following new definition where
     alphabetically appropriate, which reads in its entirety as follows:

               "First Amendment": the First Amendment to Credit Agreement dated
          as of January ___, 2000, by and among the Company, the Agent, the
          Documentation Agent, the Syndication Agent and the Banks.

      2.2 Amendments to Section 7.

          (a) Subsection 7.1 of the Credit Agreement is hereby amended as
     follows:

               (i)  Clause (j) of subsection 7.1 is hereby amended in its
          entirety to read as follows:

                    "(j) Debt arising out of or pursuant to the issuance by
               the Company of senior unsecured notes if, at the time of issuance
               thereof, the Company has a rating no lower than BBB- from
               Standard & Poor's or Baa3 from Moody's, and no Default or Event
               of Default has occurred and is continuing or would result
               therefrom; and"

                                    Page 2
<PAGE>

               (ii) Subsection 7.1 is hereby further amended by adding thereto a
          new clause, to be clause (k), which reads in its entirety as follows:

                    "(k)  Guarantee Obligations of a series of Taxable
               Industrial Development Revenue Bonds issued by the Mississippi
               Business Finance Corporation in connection with the Pascagoula
               gas processing plant."

          (b) Subsection 7.6 of the Credit Agreement is hereby amended by adding
     thereto two (2) new clauses, to be clauses (n) and (o), which read in their
     entirety as follows:

                    "(n)  Capital contributions or other Investments to
               consummate the acquisition of a 33-1/3% interest in Destin
               Pipeline Company, L.L.C. from Southern Natural Gas Company.

                    (o) Capital contributions or other Investments in connection
               with the construction of a proposed 270-mile (approximate)
               liquids pipeline from Breaux Bridge, Louisiana to Mt. Belvieu,
               Texas."

                             SECTION 3. CONDITIONS

     The enforceability of this First Amendment against the Agent and the Banks
is subject to the satisfaction of the following conditions precedent:

      3.1 Loan Documents.  The Agent shall have received multiple original
counterparts, as requested by the Agent, of this First Amendment executed and
delivered by a duly authorized officer of the Company, the Agent, the
Documentation Agent, and each Bank and otherwise in form and substance
satisfactory to the Agent.

      3.2 Representations and Warranties.  Except as affected by the
transactions contemplated in the Credit Agreement and this First Amendment, each
of the representations and warranties made by the Company in or pursuant to the
Loan Documents, including the Credit Agreement, shall be true and correct in all
material respects as of the Effective Date, as if made on and as of such date.

      3.3 No Default.  No Default or Event of Default shall have occurred and be
continuing as of the Effective Date.

      3.4 No Change.  No event shall have occurred since September 30, 1999,
which, in the reasonable opinion of the Banks, could have a material adverse
effect on the condition (financial or otherwise), business, operations or
prospects of the Company.

      3.5 Other Instruments or Documents.  The Agent or any Bank or counsel to
the Agent shall receive such other instruments or documents as they may
reasonably request.

                                    Page 3
<PAGE>

      3.7 Events. The following events shall have occurred or shall occur
contemporaneously with the execution of this First Amendment:

          (a) execution of the Second Amendment to the Existing Credit
     Agreement;

          (b) execution of the Third Amendment to the EPCO Credit Agreement; and

          (c) receipt by the applicable Banks of the amendment fee pertaining to
     this First Amendment.

     SECTION 4. MISCELLANEOUS

      4.1 Adoption, Ratification and Confirmation of Credit Agreement.  Each of
the Company, the Agent and the Banks does hereby adopt, ratify and confirm the
Credit Agreement, as amended hereby, and acknowledges and agrees that the Credit
Agreement, as amended hereby, is and remains in full force and effect.

      4.2 Successors and Assigns.  This First Amendment shall be binding upon
and inure to the benefit of the parties hereto and their respective successors
and assigns permitted pursuant to the Credit Agreement.

      4.3 Counterparts.  This First Amendment may be executed by one or more of
the parties hereto in any number of separate counterparts, and all of such
counterparts taken together shall be deemed to constitute one and the same
instrument and shall be enforceable as of the Effective Date upon the execution
of one or more counterparts hereof by the Company, the Agent, the Documentation
Agent, the Syndication Agent and the Banks. In this regard, each of the parties
hereto acknowledges that a counterpart of this First Amendment containing a set
of counterpart execution pages reflecting the execution of each party hereto
shall be sufficient to reflect the execution of this First Amendment by each
necessary party hereto and shall constitute one instrument.

      4.4 Number and Gender.  Whenever the context requires, reference herein
made to the single number shall be understood to include the plural; and
likewise, the plural shall be understood to include the singular.  Words
denoting sex shall be construed to include the masculine, feminine and neuter,
when such construction is appropriate; and specific enumeration shall not
exclude the general but shall be construed as cumulative.  Definitions of terms
defined in the singular or plural shall be equally applicable to the plural or
singular, as the case may be, unless otherwise indicated.

      4.5 Entire Agreement.  This First Amendment constitutes the entire
agreement among the parties hereto with respect to the subject hereof.  All
prior understandings, statements and agreements, whether written or oral,
relating to the subject hereof are superseded by this First Amendment.


                                    Page 4
<PAGE>

      4.6 Invalidity.  In the event that any one or more of the provisions
contained in this First Amendment shall for any reason be held invalid, illegal
or unenforceable in any respect, such invalidity, illegality or unenforceability
shall not affect any other provision of this First Amendment.

      4.7 Titles of Articles, Sections and Subsections.  All titles or headings
to Articles, Sections, subsections or other divisions of this First Amendment or
the exhibits hereto, if any, are only for the convenience of the parties and
shall not be construed to have any effect or meaning with respect to the other
content of such Articles, Sections, subsections, other divisions or exhibits,
such other content being controlling as the agreement among the parties hereto.

      4.8 GOVERNING LAW.  THIS FIRST AMENDMENT SHALL BE DEEMED TO BE A CONTRACT
MADE UNDER AND SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE
INTERNAL LAWS OF THE STATE OF NEW YORK.

     THIS FIRST AMENDMENT, THE CREDIT AGREEMENT, AS AMENDED HEREBY, THE NOTES,
     AND THE OTHER LOAN DOCUMENTS REPRESENT THE FINAL AGREEMENT BETWEEN THE
     PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS,
     OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES.

     THERE ARE NO UNWRITTEN OR ORAL AGREEMENTS BETWEEN THE PARTIES.



                        [Signatures begin on next page]

                                    Page 5
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have caused this First Amendment to
 be duly executed and delivered by their proper and duly authorized officers as
 of the Effective Date.

                              COMPANY:

                              ENTERPRISE PRODUCTS OPERATING L.P.


                              By: Enterprise Products GP, LLC, General Partner

                              By: /s/ GARY L. MILLER
                                  --------------------------------------------
                                      Gary L. Miller
                                      Executive Vice President and Chief
                                      Financial Officer


                              BANKS AND AGENTS:


                              THE CHASE MANHATTAN BANK, as
                              Administrative Agent and as a Bank

                              By: /s/ PETER LING
                                  --------------------------------------------
                                      Vice President


                              BANK ONE, NA (formerly known as The First
                              National Bank of Chicago), as Documentation Agent
                              and as a Bank

                              By: /s/ KENNETH J. FATUR
                                  --------------------------------------------
                                      Vice President


                              THE BANK OF NOVA SCOTIA, as Syndication
                              Agent and as a Bank

                              By: /s/ F. C. H. ASHBY
                                  --------------------------------------------
                                      Senior Manager Loan Operations


                      [First Amendment Signature Page 1]
<PAGE>

                              FIRST UNION NATIONAL BANK

                              By: /s/ ROBERT R. WETTEROFF
                                  --------------------------------------------
                                      Senior Vice President


                              SOCIETE GENERALE, SOUTHWEST AGENCY

                              By: /s/ PAUL E. CORNELL
                                  --------------------------------------------
                                      Managing Director


                              BANKBOSTON, N.A.

                              By: /s/ CHRISTOPHER HOLMGREN
                                  --------------------------------------------
                                      Director


                              THE FUJI BANK, LIMITED, NEW YORK BRANCH

                              By: /s/ JACQUES AZAGURY
                                  --------------------------------------------
                                      Senior Vice President and Manager


                              BANK OF TOKYO-MITSUBISHI, LTD.,
                              HOUSTON AGENCY

                              By: /s/ MICHAEL G. MEISS
                                  --------------------------------------------
                                      Vice President


                              TORONTO DOMINION (TEXAS), INC.

                              By: /s/ CAROLYN R. FAETH
                                  --------------------------------------------
                                      Vice President


                      [First Amendment Signature Page 2]
<PAGE>

                            CREDIT AGRICOLE INDOSUEZ

                            By: /s/ DOUGLAS A. WHIDDEN
                                --------------------------------------------
                                    Vice President - Senior Relationship Manager

                            By: /s/ PATRICK COCQUEREL
                                --------------------------------------------
                                    First Vice President, Managing Director
                                    Head of Houston Representative Office


                            DG BANK DEUTSCHE GENOSSEN
                            SCHAFTBANK AG, CAYMAN ISLAND BRANCH

                            By: /s/ MARK K. CONNELLY
                                --------------------------------------------
                                    Vice President


                            By: /s/ LYNNE McCARTHY
                                --------------------------------------------
                                    Vice President


                            GUARANTY FEDERAL BANK, F.S.B.

                            By: /s/ JIM R. HAMILTON
                                --------------------------------------------
                                    Vice President


                            CREDIT LYONNAIS NEW YORK BRANCH

                            By: /s/ PHILIPPE SOUSTRA
                                --------------------------------------------
                                    Senior Vice President


                            MEESPIERSON CAPITAL CORP.

                            By:
                                --------------------------------------------
                            Name:
                                 -------------------------------------------
                            Title:
                                  ------------------------------------------


                      [First Amendment Signature Page 3]
<PAGE>

                            HIBERNIA NATIONAL BANK

                            By: /s/ NANCY G. MORAGAS
                                --------------------------------------------
                                    Assistant Vice President



                              THE DAI-ICHI KANGYO BANK, LTD.

                              By:
                                 -------------------------------------------
                              Name:
                                   -----------------------------------------
                              Title:
                                    ----------------------------------------






                      [First Amendment Signature Page 4]