<PAGE>   1
                                                                    EXHIBIT 10.6

                        FIRST AMENDMENT TO SECOND AMENDED
                          AND RESTATED CREDIT AGREEMENT

     This FIRST AMENDMENT TO SECOND AMENDED AND RESTATED CREDIT AGREEMENT (this
"Amendment") is made and entered into as of May 5, 1998, by and among DYNAMEX
INC. (the "Borrower"), a Delaware corporation, DYNAMEX CANADA INC. ("Dynamex
Canada"), a federal Canadian corporation, DYNAMEX OPERATIONS EAST, INC.
("Dynamex East"), a Delaware corporation, DYNAMEX OPERATIONS WEST, INC.
("Dynamex West"), a Delaware corporation, ROAD RUNNER TRANSPORTATION, INC.
("Road Runner"), a Minnesota corporation, NEW YORK DOCUMENT EXCHANGE CORPORATION
("NYDEX"), a New York corporation, U.S.C. MANAGEMENT SYSTEMS, INC. ("USC"), a
New York corporation, DYNAMEX DEDICATED FLEET SERVICES, INC. ("Fleet Services"),
a Delaware corporation, CANNONBALL, INC. ("Cannonball"), an Illinois
corporation, NATIONSBANK OF TEXAS, N.A. ("NationsBank"), a national banking
association, BANKBOSTON, N.A. ("BankBoston"), a national banking association,
CREDITANSTALT CORPORATE FINANCE, INC. ("Creditanstalt"), a Delaware corporation,
THE BANK OF NOVA SCOTIA ("Scotia Bank"), a Canadian banking association, BANK
ONE, TEXAS, N.A. ("Bank One"), a national banking association, NATIONSBANK OF
TEXAS, N.A., as agent for itself and the other Lenders (in such capacity,
together with its successors in such capacity, the "Agent") and BANKBOSTON, N.A.
and CREDITANSTALT CORPORATE FINANCE, INC., as co-agents (the "Co-Agents").

                                    RECITALS:

     A. Pursuant to that certain Second Amended and Restated Credit Agreement
dated as of August 26, 1997, by and among the Borrower, Dynamex Canada, Dynamex
East, Dynamex West, Parcelway Courier Systems (B.C.) Ltd. (a British Columbia
corporation that has now been dissolved), Road Runner, NationsBank, BankBoston,
Creditanstalt-Bankverein, Scotia Bank, the Agent and BankBoston and
Creditanstalt-Bankverein as co-agents (as the same may be amended, renewed,
extended, restated or otherwise modified from time to time, the "Credit
Agreement"), the Lenders agreed to provide to the Borrower a senior secured
revolving credit and letter of credit facility (the "Credit Facility") in the
maximum aggregate principal amount of $75,000,000.

     B. Creditanstalt-Bankverein has recently assigned its Loans and Commitment
to Creditanstalt which has become a Lender under the Credit Agreement.

     C. The Borrower and its Subsidiaries have requested that the Lenders, the
Agent and the Co-Agents amend the Credit Agreement to increase the aggregate
amount of the Credit Facility to $115,000,000 and to amend the Credit Agreement
in certain other respects, and the Lenders, the Agent and the Co-Agents are
willing to agree to such amendments subject to the terms and conditions of this
Amendment.

     D. Pursuant to and subject to the terms and conditions of this Amendment,
Bank One has agreed to become a Lender under the Credit Agreement and to hold a
Commitment thereunder and certain of the other Lenders have agreed to increase
their Commitments under the Credit Agreement.

FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 1

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                                   AGREEMENTS:

     NOW, THEREFORE, in consideration of the premises and mutual covenants and
agreements contained herein and for other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties hereto
hereby agree as follows:

     1. Terms Defined. Unless otherwise defined or stated in this Amendment,
each capitalized term used in this Amendment has the meaning given to such term
in the Credit Agreement (as amended by this Amendment).

     2. New Co-Agent. The reference to "Creditanstalt-Bankverein, an Austrian
banking corporation" as a Co-Agent in the initial paragraph of the Credit
Agreement is hereby amended to refer to "Creditanstalt Corporate Finance, Inc.,
a Delaware corporation".

     3. Amendments to Article 1 - Definitions.

     (a) The following terms and definitions thereof set forth in Section 1.1 of
the Credit Agreement are hereby amended and restated to read in their entity as
follows:

         " 'Agent's Letter' means that certain Fee Letter dated as of May 7,
     1997, among NationsBank, NationsBanc Capital Markets, Inc. and the Borrower
     and that certain letter agreement dated as of April 16, 1998, among
     NationsBank, NationsBanc Montgomery Securities, LLC and the Borrower, and
     any and all amendments, modifications, supplements, renewals, extensions,
     restatements or replacements thereof."

         " 'Commitment' means, as to any Lender, the obligation of such Lender
     to make or continue Loans and incur or participate in Letter of Credit
     Liabilities hereunder in an aggregate principal amount at any one time
     outstanding up to but not exceeding the amount set forth opposite the name
     of such Lender on the signature pages hereto (or any amendment hereto)
     under the heading "Commitment" or, if such Lender is a party to an
     Assignment and Acceptance, the amount of the "Commitment" set forth in the
     most recent Assignment and Acceptance of such Lender, as the same may be
     reduced or terminated pursuant to Section 2.12 or 11.2, and "Commitments"
     means such obligations of all Lenders. As of the First Amendment Effective
     Date, the aggregate principal amount of the Commitments is $115,000,000."

         " 'Maturity Date' means May 1, 2001."


         " 'Required Lenders' means, at any date of determination, Lenders
     having in the aggregate at least sixty-six and two-thirds percent (66-2/3%)
     (in Dollar amount) of the aggregate amount of the outstanding Commitments
     (or, if such Commitments have terminated or expired, the aggregate
     outstanding principal amount of the Loans and the aggregate Letter of
     Credit Liabilities)."


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 2
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     (b) Section 1.1 of the Credit Agreement is hereby amended to add the
following new terms and definitions thereof, which terms shall appear in
alphabetical order in such Section 1.1:

         " 'First Amendment Effective Date' means the initial date (determined
     in good faith by the Agent) upon which that certain First Amendment to
     Second Amended and Restated Credit Agreement dated as of May 5, 1998, has
     been executed by all parties thereto (including the Borrower and its
     Subsidiaries and the Agent and the Lenders) and all conditions precedent to
     the effectiveness thereof have been satisfied."

         " 'Reference Lender' means NationsBank."

     (c) The phrase "in the form of Exhibit B or Exhibit C hereto" contained in
the definition of the term "Notes" in Section 1.1 of the Credit Agreement is
hereby amended and restated to read "in the form of Exhibit C or Exhibit D
hereto".

     (d) Clauses (b) and (c) of the definition of the term "Permitted
Acquisition" contained in Section 1.1 of the Credit Agreement are hereby amended
and restated to read in their entirety as follows:

         "(b) such Future Acquisition (which shall be deemed to include, in
     addition to the specific Future Acquisition, any one or more acquisitions
     related thereto which are consummated substantially concurrently with such
     Future Acquisition and which involve, as seller(s), the same Person(s) who
     are seller(s) with respect to such Future Acquisition or Affiliate(s) of
     such Person(s)) shall not involve an aggregate Cost of Acquisition paid or
     payable, in whatever form (but exclusive of any trade payables incurred in
     the ordinary course of business to the extent that the aggregate amount of
     such trade payables assumed does not exceed the aggregate amount of
     accounts receivable acquired in connection with such Future Acquisition),
     in excess of $10,000,000 unless such Future Acquisition has been approved
     in writing by the Agent and the Required Lenders;

         (c) such Future Acquisition and all other Future Acquisitions
     consummated or proposed to be consummated during any twelve-month period
     commencing on or after May 5, 1998 shall not involve an aggregate Cost of
     Acquisition paid or payable, in whatever form (but exclusive of any trade
     payables incurred in the ordinary course of business to the extent that the
     aggregate amount of such trade payables assumed does not exceed the
     aggregate amount of accounts receivable acquired in connection with such
     Future Acquisitions) in excess of $20,000,000 unless such Future
     Acquisition has been approved in writing by the Agent and the Required
     Lenders; provided, however, that no such approval referred to in this
     clause (c) shall be required with respect to any Future Acquisition (which
     shall be deemed to include, in addition to the specific Future Acquisition,
     any one or 


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 3
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     more acquisitions related thereto which are consummated substantially
     concurrently with such Future Acquisition and which involve, as seller(s),
     the same Person(s) who are seller(s) with respect to such Future
     Acquisition or Affiliate(s) of such Person(s)) which shall not involve an
     aggregate Cost of Acquisition paid or payable of $4,000,000 or more if (but
     only if) (i) the aggregate Cost of Acquisition paid or payable with respect
     to such Future Acquisition and all other Future Acquisitions consummated
     during the preceding twelve-month period commencing on or after May 5, 1998
     does not exceed $35,000,000, (ii) the Borrower complies with the terms and
     provisions of Article 5 hereof, and (iii) the Borrower notifies the Agent
     in writing of such Future Acquisition within 30 days after the consummation
     thereof;".

     4. The reference to "the Agent and NationsBank" contained in Section
2.10(c) of the Credit Agreement is hereby amended to refer to "the Agent,
NationsBank and NationsBanc Montgomery Securities, LLC".

     5. The reference to "Section 2.12(a)" contained in Section 2.1(a) of the
Credit Agreement is hereby amended to refer to "Section 2.12".

     6. The phrase "demonstrating (with calculations attached in reasonable
detail)" contained in clause (ii) of Section 8.17(a) of the Credit Agreement is
hereby amended and restated to read "representing".

     7. The reference to the amount "$200,000" contained in clause (f) of
Section 9.4 of the Credit Agreement is hereby amended to refer to $300,000".

     8. Section 10.1 of the Credit Agreement is hereby amended and restated to
read in its entirety as follows:

         "Section 10.1 Maximum Ratio of Total Debt to EBITDA. The Borrower and
     its consolidated Subsidiaries will not permit the ratio, calculated as of
     the end of each fiscal quarter of the Borrower commencing with the fiscal
     quarter ended April 30, 1997, and in accordance with Section 1.4, of (i)
     Total Debt to (ii) EBITDA for the four fiscal quarters of the Borrower then
     ended to be greater than the ratio of 3.00 to 1.00."

     9. Section 10.4 of the Credit Agreement is hereby amended and restated to
read in its entirety as follows:

         "Section 10.4 Capital Expenditures. The Borrower and its Subsidiaries
     will not permit the aggregate Capital Expenditures of the Borrower and its
     Subsidiaries during any fiscal year (exclusive of any purchase or
     acquisition of Capital Stock or assets permitted by clause (ii) of Section
     9.3) to exceed $5,000,000."


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 4
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     10. Bank One as a Lender; Commitments. Bank One is hereby added as a party
to the Credit Agreement as a Lender, and the Commitment of each of the Lenders
as of the First Amendment Date shall be as set forth opposite the name of such
Lender on the signature pages to this Amendment under the heading "Commitment".

     11. Conditions Precedent. The effectiveness of this Amendment is subject to
the satisfaction of each of the following conditions precedent, all of which
conditions precedent must be satisfied on or before May 31, 1998:

     (a) The Agent shall have received all of the following, each dated (unless
otherwise indicated) the date of this Amendment, in form and substance
satisfactory to the Agent:

         (i) Amendment Documents. This Amendment, Notes in the form of Exhibit B
     to the Credit Agreement in the appropriate principal amounts payable to the
     order of the Lenders whose Commitments are increased pursuant to this
     Amendment (one for each such Lender) dated as of the First Amendment
     Effective Date, a Reaffirmation of Guaranties and Security Documents
     pursuant to which the Guaranties and Security Documents are reaffirmed and
     the obligors thereunder agree that the Guaranties guarantee payment of, and
     the Security Documents secure, all Obligations (including the Obligations
     relating to the increased aggregate amount of the Commitments), the Fee
     Letter (as defined below) and any other agreement, document, instrument or
     certificate required by the Agent or the Lenders to be executed or
     delivered by the Borrower or any other Loan Party in connection with this
     Amendment, each duly executed by each of the parties thereto (the
     "Amendment Documents");

         (ii) Resolutions. Resolutions of the Board of Directors of the Borrower
     and the other Loan Parties certified by its Secretary or an Assistant
     Secretary which authorize the execution, delivery and performance by the
     Borrower and the other Loan Parties of this Amendment and the other
     Amendment Documents to which the Borrower or such Loan Party is or is to be
     a party;

         (iii) Legal Opinions. Legal opinions from Texas and Ontario counsel to
     the Borrower and its Subsidiaries;

         (iv) Financial Statements. Pro-forma consolidated financial statements
     of the Borrower and its Subsidiaries reflecting all acquisitions which have
     been consummated or which are to be consummated concurrently with this
     Amendment;

         (v) Fee Letter. A letter agreement between the Borrower and the Agent
     (the "Fee Letter") pursuant to which the Borrower agrees to pay (A) to the
     Agent certain fees as specified therein and (B) to the Agent, for
     distribution to each of the Lenders, a fee equal to 25 basis points on the
     increased amount (if any) of such Lender's Commitment;


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 5
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         (vi) Fees, Costs and Expenses. All fees, costs and expenses (including,
     without limitation, attorneys' fees and expenses) incurred by the Agent
     incident to this Amendment or required to be paid in accordance with (A)
     the Fee Letter or (B) Section 13.1 of the Credit Agreement to the extent
     incurred and submitted to the Borrower, shall have been paid in full by the
     Borrower; and

         (vii) Additional Information. The Agent shall have received such
     additional agreements, documents, instruments and information as the Agent
     or its legal counsel, Jenkens & Gilchrist, a Professional Corporation, may
     reasonably request to effect the transactions contemplated hereby;

     (b) The representations and warranties contained herein and in all other
Loan Documents, as amended hereby, shall be true and correct as of the date
hereof as if made again on and as of the date hereof (except if and to the
extent that such representations and warranties are or were expressly made only
as of another specific date);

     (c) As of the First Amendment Date, no material adverse change shall have
occurred with respect to the condition (financial or otherwise), results of
operations, businesses, operations, capitalization, assets, liabilities or
prospects of the Borrower, or of the Borrower and its Subsidiaries taken as a
whole, since July 31, 1997;

     (d) The Borrower shall have received, during May 1998, Net Proceeds from a
new Equity Issuance of its common stock which aggregate $25,000,000 or more in
amount, and the Agent shall have received a certification of such fact from the
Borrower in form and substance reasonably satisfactory to the Agent;

     (e) All corporate proceedings taken in connection with this Amendment, and
all legal matters incident thereto, shall be reasonably satisfactory to the
Agent and its legal counsel, Jenkens & Gilchrist, a Professional Corporation;
and

     (f) No Default or Event of Default shall have occurred and be continuing.

The Agent shall, promptly after all of the conditions precedent set forth in
this Paragraph 11 have been satisfied, so notify the Borrower and the Lenders in
writing. In the event that each of the aforesaid conditions precedent set forth
in this Paragraph 11 has not been satisfied on or before May 31, 1998, this
Amendment shall be of no force or effect.

     12. Representations and Warranties. Each of the Borrower and the other Loan
Parties hereby jointly and severally represent and warrant to, and agrees with,
the Agent and the Lenders that, as of the date of and after giving effect to
this Amendment, (a) the Subsidiaries of the Borrower identified on Schedule 1
hereto are the only Subsidiaries of the Borrower, and, with respect to each of
the Subsidiaries of the Borrower, the authorized Capital Stock, the par value
per share, the number of shares issued and outstanding and the owner(s) of such
issued and outstanding shares are as specified on such Schedule 1; (b) each
material action, suit, investigation or proceeding before or 


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 6
<PAGE>   7


by any Governmental Authority or arbitrator pending or, to the knowledge of any
Loan Party, threatened against or affecting any Loan Party or any Subsidiary of
the Borrower as of May 5, 1998, is disclosed on Schedule 2 hereto, and none of
such actions, suits, investigations or proceedings could, if adversely
determined, have a Material Adverse Effect or could adversely affect the ability
of the Borrower and the other Loan Parties to pay or perform their indebtedness,
liabilities or obligations under the Credit Agreement or the other Loan
Documents; (c) the execution, delivery and performance of this Amendment and any
and all other Amendment Documents executed and/or delivered in connection
herewith have been authorized by all requisite corporate action on the part of
the Borrower and the other Loan Parties and will not violate the Borrower's or
any Loan Party's corporate charter or bylaws; (d) the term Loan Documents as
defined in the Credit Agreement and as used in any of the Loan Documents
includes, without limitation, the Amendment Documents; (e) all representations
and warranties set forth in the Credit Agreement and in the Security Documents
are true and correct as if made again on and as of such date (except if and to
the extent that such representations and warranties were expressly made only as
of another specific date); (f) no Default or Event of Default has occurred and
is continuing, and (g) the Credit Agreement, the Notes, the Guaranties, the
Security Documents and the other Loan Documents (as amended by this Amendment)
are and remain legal, valid, binding and enforceable obligations of the Borrower
and the other Loan Parties (as applicable) which are parties thereto in
accordance with their terms.

     13. Governing Law. THIS AMENDMENT AND THE OTHER LOAN DOCUMENTS SHALL BE
GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS
(WITHOUT REGARD TO CONFLICTS OF LAWS PRINCIPLES) AND APPLICABLE LAWS OF THE U.S.

     14. Counterparts. This Amendment may be executed in any number of
counterparts, all of which when taken together shall constitute one agreement,
and any of the parties hereto may execute this Amendment by signing any such
counterpart.

     15. No Oral Agreements. THIS AMENDMENT, TOGETHER WITH THE CREDIT AGREEMENT
AND THE OTHER LOAN DOCUMENTS AS WRITTEN, REPRESENT THE FINAL AGREEMENTS BETWEEN
AND AMONG THE PARTIES HERETO AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR,
CONTEMPORANEOUS OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO
UNWRITTEN ORAL AGREEMENTS BETWEEN (A) THE BORROWER OR ANY OTHER LOAN PARTY AND
(B) THE AGENT OR ANY LENDER.

     16. Agreement Remains in Effect; No Waiver. Except as expressly provided
herein, all terms and provisions of the Credit Agreement and the other the Loan
Documents shall remain unchanged and in full force and effect and are hereby
ratified and confirmed. No waiver by the Agent or any Lender of any Default or
Event of Default shall be deemed to be a waiver of any other Default or Event of
Default. No delay or omission by the Agent or any Lender in exercising any
power, right or remedy shall impair such power, right or remedy or be construed
as a waiver thereof or an acquiescence therein, and no single or partial
exercise of any such power, right or remedy shall 


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 7
<PAGE>   8


preclude other or further exercise thereof or the exercise of any other power,
right or remedy under the Agreement, the Loan Documents or otherwise.

     17. Survival of Representations and Warranties. All representations and
warranties made in this Amendment or any other Loan Document shall survive the
execution and delivery of this Amendment and the other Loan Documents, and no
investigation by the Agent or any Lender or any closing shall affect the
representations and warranties or the right of the Agent and the Lenders to rely
upon such representations and warranties.

     18. Reference to Credit Agreement. This Amendment shall constitute a Loan
Document. Each of the Loan Documents, including the Credit Agreement, the
Amendment Documents and any and all other agreements, documents or instruments
now or hereafter executed and/or delivered pursuant to the terms hereof or
pursuant to the terms of the Credit Agreement as amended hereby, are (if and to
the extent necessary) hereby amended so that any reference in such Loan
Documents to the Credit Agreement shall mean a reference to the Credit Agreement
as amended hereby.

     19. Severability. Any provision of this Amendment held by a court of
competent jurisdiction to be invalid or unenforceable shall not impair or
invalidate the remainder of this Amendment and the effect thereof shall be
confined to the provision so held to be invalid or unenforceable.

     20. Successors and Assigns. This Amendment is binding upon and shall inure
to the benefit of the Agent, the Lenders, the Borrower and the other Loan
Parties and their respective successors and assigns; provided, however, that
neither the Borrower nor any of the other Loan Parties may assign or transfer
any of its rights or obligations hereunder without the prior written consent of
the Lenders.

     21. Headings. The headings, captions and arrangements used in this
Amendment are for convenience only and shall not affect the interpretation of
this Amendment.



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FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 8

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


                               THE BORROWER AND ITS SUBSIDIARIES:

                               DYNAMEX INC.
                               DYNAMEX CANADA INC.
                               DYNAMEX OPERATIONS EAST, INC.
                               DYNAMEX OPERATIONS WEST, INC.
                               ROAD RUNNER TRANSPORTATION, INC.
                               NEW YORK DOCUMENT
                                EXCHANGE CORPORATION
                               U.S.C. MANAGEMENT SYSTEMS, INC.
                               DYNAMEX DEDICATED FLEET
                                SERVICES, INC.
                               and
                               CANNONBALL, INC.


                               By:
                                  --------------------------------------
                               Name: Robert P. Capps
                               Title: Vice President-Chief Financial Officer



FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 9

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                               THE AGENT AND A LENDER:

Commitment: $45,000,000        NATIONSBANK OF TEXAS, N.A.,
                               individually and as the Agent

                               By:
                                  ----------------------------------------
                               Name:  Russell P. Hartsfield
                               Title: Senior Vice President


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 10

<PAGE>   11


                                       THE CO-AGENTS AND LENDERS:

Commitment: $25,000,000                BANKBOSTON, N.A.,
                                       individually and as a Co-Agent

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


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 11

<PAGE>   12


Commitment: $15,000,000                CREDITANSTALT CORPORATE FINANCE, INC.,
                                       individually and as a Co-Agent

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


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 12

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                                       ADDITIONAL LENDERS:

Commitment: $15,000,000                THE BANK OF NOVA SCOTIA

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


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 13


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Commitment: $15,000,000                BANK ONE, TEXAS, N.A.

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


FIRST AMENDMENT TO SECOND AMENDED
AND RESTATED CREDIT AGREEMENT - Page 14