<PAGE>
                                                                   EXHIBIT 10.34


                                 AMENDMENT NO. 1


         This AMENDMENT NO. 1, dated as of September 28, 2001 (this
"AMENDMENT"), is made to that certain Amended and Restated Credit Agreement,
dated as of April 6, 2001 (the "CREDIT AGREEMENT"), among TEPPCO Partners, L.P.
(the "BORROWER"), SunTrust Bank, as administrative agent (the "ADMINISTRATIVE
AGENT"), and certain lenders party thereto (the "LENDERS").

                             PRELIMINARY STATEMENT:

         The Borrower, the Lenders and the Administrative Agent previously
entered into the Credit Agreement providing for a $500,000,000 revolving credit
facility for the Borrower scheduled to expire on April 6, 2004. The Borrower has
requested that the Lenders agree to the amendment of the Credit Agreement as set
forth herein, and the Lenders have agreed to such request, subject to the terms
and conditions of this Amendment. Therefore, for good and valuable
consideration, the receipt and adequacy of which are hereby acknowledged, the
parties agree as follows:

         SECTION 1. DEFINITIONS. Capitalized terms used but not defined herein
have the meanings assigned to such terms in the Credit Agreement.

         SECTION 2. AMENDMENT. Section 10.2 of the Credit Agreement is, subject
to the satisfaction of the conditions precedent set forth in Section 3, hereby
amended and restated in its entirety as follows:

                         SECTION 10.2. MAXIMUM FUNDED DEBT TO PRO FORMA EBITDA.

                         As of the last day of each fiscal quarter of the
                Borrower, the ratio of Consolidated Funded Debt to Pro Forma
                EBITDA for the period consisting of four consecutive fiscal
                quarters taken as a single accounting period and ending on such
                day will be less than the amount specified below for such fiscal
                quarter:


<Table>
<Caption>

                       QUARTER(S) ENDING                         RATIO
                       -----------------                         -----


<S>                    <C>                                     <C>
                       03/31/01 through 12/31/01               5.00 to 1.00

                       3/31/02 and thereafter                  4.50 to 1.00
</Table>


         SECTION 3. CONDITIONS OF EFFECTIVENESS. Section 2 of this Amendment
shall become effective as of the date first set forth above when each of the
following conditions shall have been fulfilled:

                  (i) the Required Lenders and the Borrower shall have executed
         and delivered to the Administrative Agent a counterpart of this
         Amendment; and


<PAGE>

                                                                               2


                  (ii) the representations and warranties set forth in Section 4
         hereof shall be true and correct on and as of the date of effectiveness
         of this Amendment as though made on and as of such date.

         SECTION 4. REPRESENTATIONS AND WARRANTIES. The Borrower represents and
warrants that (a) the representations and warranties contained in Article VII of
the Credit Agreement, as amended hereby (with each reference therein to (i)
"this Agreement", "hereunder" and words of like import referring to the Credit
Agreement being deemed to be a reference to this Amendment and the Credit
Agreement as amended hereby and (ii) "Credit Documents", "thereunder" and words
of like import being deemed to include this Amendment and the Credit Agreement,
as amended hereby) are true and correct on and as of the date hereof as though
made on and as of such date, and (b) no event has occurred and is continuing, or
would result from the execution and delivery of this Amendment, that constitutes
an Event of Default.

         SECTION 5. EFFECT ON THE CREDIT AGREEMENT. Except as specifically
provided above, the Credit Agreement shall continue to be in full force and
effect and is hereby in all respects ratified and confirmed. The execution,
delivery and effectiveness of this Amendment shall not, except as expressly
provided herein, operate as a waiver of any right, power or remedy of the
Lenders under the Credit Agreement, nor constitute a waiver of any provision of
the Credit Agreement.

         SECTION 6. COSTS AND EXPENSES. The Borrower agrees to pay on demand all
costs and expenses of the Administrative Agent in connection with the
preparation, execution and delivery of this Amendment, including, without
limitation, the reasonable fees and out-of-pocket expenses of counsel for the
Administrative Agent with respect thereto, and all costs and expenses
(including, without limitation, counsel fees and expenses), if any, in
connection with the enforcement (whether through negotiations, legal proceedings
or otherwise) of this Amendment.

         SECTION 7. EXECUTION IN COUNTERPARTS. This Amendment may be executed in
any number of counterparts and by different parties hereto in separate
counterparts, each of which when so executed and delivered shall be deemed to be
an original and all of which taken together shall constitute but one and the
same instrument.

         SECTION 8. GOVERNING LAW. This Amendment shall be governed by, and
construed in accordance with, the internal laws of the State of the New York.










<PAGE>


                                                                             S-1

         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed and delivered by their respective duly authorized officers as of
the date first above written.

                                TEPPCO PARTNERS, L.P., as Borrower

                                By TEXAS EASTERN PRODUCTS
                                   PIPELINE COMPANY, LLC, as General
                                   Partner

                                   By:    /s/ CHARLES H. LEONARD
                                      ------------------------------------------
                                      Name:   Charles H. Leonard
                                      Title:  Sr. VP, CFO & Treasurer


                                SUNTRUST BANK, as Administrative Agent
                                and Lender

                                By:   /s/ STEVEN J. NEWBY
                                   ---------------------------------------------
                                   Name:  Steven J. Newby
                                   Title: Vice President

<PAGE>
                                                                               2


                                   UBS AG, STAMFORD BRANCH



                                   By:   /s/ GREGORY H. RAUE
                                      -----------------------------------
                                      Name:  Gregory H. Raue
                                      Title: Executive Director
                                             Leverage Finance



                                   By:   /s/ WILFRED V. SAINT
                                      -----------------------------------
                                      Name:  Wilfred V. Saint
                                      Title: Associate Director
                                             Banking Products
                                             Services, US
<PAGE>
                                                                               3

                                   BANK ONE, NA

                                   By:   /s/ JOSEPH C. GIAMPETRONI
                                      -----------------------------------
                                      Name:  Joseph C. Giampetroni
                                      Title: Director
<PAGE>
                                                                               4


                                   FIRST UNION NATIONAL BANK



                                   By:   /s/ RUSSELL CLINGMAN
                                      -----------------------------------
                                      Name:  Russell Clingman
                                      Title: Vice President
<PAGE>
                                                                               5

                                   THE BANK OF NEW YORK


                                   By:   /s/ PETER W. KELLER
                                      -----------------------------------
                                      Name:  Peter W. Keller
                                      Title: Vice President


<PAGE>
                                                                               6


                                   ROYAL BANK OF CANADA


                                   By:   /s/ DAVID A. MCCLUSKEY
                                      -----------------------------------
                                      Name:  David A. McCluskey
                                      Title: Manager

<PAGE>
                                                                               7

                                   CREDIT LYONNAIS NEW YORK BRANCH



                                   By:   /s/ BERNARD WEYMULLER
                                      -----------------------------------
                                      Name:  Bernard Weymuller
                                      Title: Senior Vice President
<PAGE>
                                                                               8

                                   WESTDEUTSCHE LANDESBANK
                                   GIROZENTRALE, NEW YORK BRANCH


                                   By:   /s/ WALTER T. DUFFY III
                                      -----------------------------------
                                      Name:  Walter T. Duffy III
                                      Title: Associate Director


                                   By:   /s/ ANTHONY ALESSANDRO
                                      -----------------------------------
                                      Name:  Anthony Alessandro
                                      Title: Manager
<PAGE>
                                                                               9


                                   BAYERISCHE HYPO-UND VEREINSBANK
                                   AG, NEW YORK BRANCH


                                   By:   /s/ STEVEN ATWELL
                                      -----------------------------------
                                      Name:  Steven Atwell
                                      Title: Director


                                   By:   /s/ HETAL N. RAITHATHA
                                      -----------------------------------
                                      Name:  Hetal N. Raithatha
                                      Title: Associate

<PAGE>
                                                                              10

                               THE FUJI BANK, LIMITED



                               By:   /s/ JACQUES AZAGURY
                                  --------------------------------------
                                  Name:  Jacques Azagury
                                  Title: Senior Vice President & Manager
<PAGE>
                                                                              11


                                          KBC BANK N.V.


                                          By:   /s/ ROBERT SNAUFFER
                                             -----------------------------
                                             Name:  Robert Snauffer
                                             Title: First Vice President


                                          By:   /s/ ERIC RASKIN
                                             -----------------------------
                                             Name:  Eric Raskin
                                             Title: Vice President

<PAGE>
                                                                              12

                                        BANK OF AMERICA, NATIONAL
                                        ASSOCIATION

                                        By:   /s/ RONALD E. MCKAIG
                                           -------------------------------
                                           Name:  Ronald E. McKaig
                                           Title: Managing Director

<PAGE>
                                                                            S-13


                                        THE INDUSTRIAL BANK OF JAPAN,
                                        LIMITED


                                        By:
                                           -------------------------------
                                           Name:
                                           Title:
<PAGE>
                                                                            S-14



                                        THE DAI-ICHI KANGYO BANK, LTD.

                                        By:
                                           -------------------------------
                                           Name:
                                           Title:
<PAGE>
                                                                            S-15

                                        THE SANWA BANK LIMITED

                                        By:
                                           -------------------------------
                                           Name:
                                           Title:
<PAGE>
                                                                            S-16



                                        SUMITOMO MITSUI BANKING
                                        CORPORATION

                                        By:
                                           -------------------------------
                                           Name:
                                           Title:
<PAGE>
                                                NATEXIS BANQUES POPUAIRES



                                                By:   /s/ LOUIS P. LAVILLE, III
                                                   ----------------------------
                                                   Name:  Louis P. Laville, III
                                                   Title: Vice President/Manager




                                                By:   /s/ DANIEL PAYER
                                                   ----------------------------
                                                   Name:  Daniel Payer
                                                   Title: Vice President