
<PAGE>
 
                                                                    EXHIBIT 99.3

                         AMENDMENT TO RIGHTS AGREEMENT
                                        

          Amendment Number One, dated as of May 26, 1998, to the Rights
Agreement, dated as of March 1, 1996 (the "Rights Agreement"), between MAY &
SPEH, INC., a Delaware corporation (the "Company"), and HARRIS TRUST AND SAVINGS
BANK, an Illinois banking corporation, as Rights Agent (the "Rights Agent").

          WHEREAS, the Company and the Rights Agent entered into the Rights
Agreement specifying the terms of the Rights (as defined therein);

          WHEREAS, the Company desires to amend the Rights Agreement in
accordance with Section 27 of the Rights Agreement;

          WHEREAS, the Company proposes to enter into an Agreement and Plan of
Merger, dated as of May 26, 1998 (the "Merger Agreement"), among the Company,
Acxiom Corporation ("Parent") and ACX Acquisition Co., Inc. ("Sub").

          WHEREAS, as a condition to the Merger Agreement and in order to induce
Parent to enter into the Merger Agreement, the Company proposes to enter into a
Stock Option Agreement, dated as of May 26, 1998, between the Company and Parent
(the "Stock Option Agreement"), pursuant to which the Company will grant Parent
an irrevocable option (the "Option") to purchase up to 19.9% of the number of
shares (the "Option Shares") of common stock, par value $.01 per share ("Common
Stock"), of the Company issued and outstanding immediately prior to the grant of
the Option;

          WHEREAS, as a condition to the Merger Agreement and in order to induce
Parent to enter into the Merger Agreement, certain holders of shares of  Common
Stock (each, a "Stockholder" and collectively, the "Stockholders"), each propose
to enter into an irrevocable proxy, dated as of May 26, 1998, between such
Stockholder and Parent, pursuant to which such Stockholder will grant Parent an
irrevocable proxy  (each, a "Proxy" and collectively, the "Proxies") to vote
such Stockholder's shares of Common Stock; and

          WHEREAS, the Board of Directors of the Company has determined it
advisable and in the best interest of the stockholders of the Company to amend
the Rights Agreement to enable the Company to enter into the Merger Agreement
and the Stock Option Agreement and consummate the transactions contemplated
thereby without causing Parent to become an "Acquiring Person" (as defined in
the Rights Agreement).

          NOW, THEREFORE, in consideration of the premises and mutual agreements
set forth herein and in the Rights Agreement, the parties hereby agree as
follows:
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1.   Definitions.  Capitalized terms used and not otherwise defined herein shall
     have the meaning assigned to such terms in the Rights Agreement.

2.   Amendments to the Rights Agreement.  The Rights Agreement is hereby amended
     as set forth in this Section 2.

     a.   Section 1 of the Rights Agreement, "Certain Definitions", is hereby
          amended and restated by deleting the definition of "Acquiring Person"
          thereof and inserting in lieu thereof the following:

          "Acquiring Person" shall mean any Person (as such term is hereinafter
defined) who or which, together with all Affiliates and Associates (as such
terms are hereinafter defined) of such Person, shall be the Beneficial Owner (as
such term is hereinafter defined) of 15% or more of the Common Shares of the
Company then outstanding, but shall not include the Company, any Subsidiary (as
such term is hereinafter defined) of the Company, any employee benefit plan of
the Company or any Subsidiary of the Company, any Person holding Common Shares
for or pursuant to the terms of any such plan, or any Grandfathered Person.
Notwithstanding the foregoing, no Person (including, without limitation, any
Grandfathered Person) shall become an "Acquiring Person" as the result of (a) an
acquisition of Common Shares by the Company which, by reducing the number of
shares outstanding, increases the proportionate number of shares beneficially
owned by such Person to 15% or more of the Common Shares of the Company then
outstanding; (b) the acquisition by such Person of newly issued Common shares
directly from the Company (it being understood that a purchase from an
underwriter or other intermediary is not directly from the Company); or (c) that
the Parent, and its Affiliates and Associates shall not be deemed to be an
Acquiring Person as a result of either (i) the grant of the Option (as such term
is defined in the Stock Option Agreement) pursuant to the Stock Option
Agreement, or at any time following the exercise thereof and the issuance of
shares of Common Shares in accordance with the terms of the Stock Option
Agreement or (ii) the grant of the Proxies by and between the Stockholders and
Parent, or at any time following the delivery and execution thereof; provided,
however, that if a Person shall become the Beneficial Owner of 15% or more of
the Common Shares of the Company then outstanding by reason of share purchases
by the Company or the receipt of newly issued Common Shares directly from the
Company and shall, after such share purchases or direct issuance by the Company,
become the Beneficial Owner of any additional Common Shares of the Company, then
such Person shall be deemed to be an "Acquiring Person;" provided further,
however, that any transferee from such Person who becomes the Beneficial Owner
of 15% or more of the Common Shares of the Company then outstanding shall
nevertheless be deemed to be an "Acquiring Person."  Notwithstanding the
foregoing, if the Board of Directors of the Company determines in good faith
that a Person who would otherwise be an "Acquiring Person," as defined pursuant
to the foregoing provisions of this paragraph, has become such inadvertently,
and such Person divests as promptly as practicable (and in any event within ten
business days after notification by the Company) a sufficient number of Common
Shares so that such Person would no longer be an Acquiring Person, as defined
pursuant to the foregoing provisions of this paragraph, then such Person shall
not be deemed to be an "Acquiring Person" for any purposes of this Agreement.

                                       2
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     b.   Section 7(a) of the Rights Agreement is hereby amended by deleting
          subsections 7(a)(i), 7(a)(ii), and 7(a)(iii) and inserting in lieu
          thereof the following:

               (i) the close of business on the tenth anniversary of the
     effective date of this Agreement (the "Final Expiration Date"), (ii) the
     time at which the Rights are redeemed as provided in Section 23 hereof (the
     "Redemption Date"), (iii) the time immediately prior to the Effective Time
     (as such term is defined in that certain Agreement and Plan of Merger dated
     as of May 26, 1998, among the Company, Acxiom Corporation and ACX
     Acquisition Co., Inc. (the earliest to occur of (i), (ii) and (iii) being
     herein referred to as the "Expiration Date"), and (iv) the time at which
     such Rights are exchanged as provided in Section 24 hereof.

3.   Miscellaneous.

     a.   The term "Agreement" as used in the Rights Agreement shall be deemed 
          to refer to the Rights Agreement as amended hereby.

     b.   The foregoing amendment shall be effective as of the date first above
          written, and, except as set forth herein, the Rights Agreement shall
          remain in full force and effect and shall be otherwise unaffected
          hereby.

     c.   This Amendment may be executed in two or more counterparts, each of
          which shall be deemed to be an original, but all for which together
          shall constitute one and the same instrument.

     d.   This Amendment shall be deemed to be a contract made under the laws of
          the State of Delaware and for all purposes shall be governed by and
          construed in accordance with the laws of such State applicable to
          contracts to be made and performed entirely within such State.

                                       3
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          IN WITNESS WHEREOF, the parties hereto have caused this Amendment
Number One to be duly executed and attested, all as of the day and year first
above written.


Attest:                                  MAY & SPEH, INC.


By:  /s/ Andy Jonusaitis               By:   /s/ Peter I. Mason
    ---------------------------            ---------------------
     Name: Andy Jonusaitis                  Name: Peter I. Maxon
     Title: General Counsel                 Title: Chairman, President and CEO



Attest:                                  HARRIS TRUST AND SAVINGS BANK


By:  /s/ Sue M. Shadel                 By:   /s/ Palmer Haffner
    ---------------------------            ---------------------
     Name: Sue M. Shadel                    Name: Palmer Haffner
     Title: Assistant Vice President        Title: Vice President
