
<PAGE>
 
                                                                       EXHIBIT 8

                               IRREVOCABLE PROXY


               IRREVOCABLE PROXY, dated as of June 1, 1998, by and between
Acxiom Corporation, a Delaware corporation (the "Parent"), and each of the
entities named on Exhibits A to the signature pages hereto (each a "Stockholder"
and collectively, the "Stockholders").

               WHEREAS, the Parent, ACX Acquisition Co., Inc., a Delaware
corporation and a wholly owned subsidiary of Parent ("Sub"), and May & Speh,
Inc., a Delaware corporation (the "Company"), have entered into an Agreement and
Plan of Merger, dated as of May 26, 1998 (the "Merger Agreement"), providing,
among other things, for the merger (the "Merger") of Sub with and into the
Company, as a result of which each of the outstanding shares of Common Stock,
par value $.01 per share, of the Company (the "Company Common Stock") will be
converted into the right to receive .80 of a share of the Common Stock, par
value $.10 per share, of Parent (the "Parent Common Stock"), and the Company
will become a wholly owned subsidiary of Parent; and

               WHEREAS, the Stockholders are the owners of record of an
aggregate of 2,014,094 shares (the "Shares") of the Company Common Stock and
each Stockholder individually is the owner of record of the number of Shares set
forth next to such Stockholder's name on Exhibits A to the signature pages
hereto; and

               WHEREAS, as a condition to its willingness to enter into the
Merger Agreement, Parent has requested that each Stockholder agree, and each
Stockholder has agreed,
<PAGE>
 
to grant Parent an irrevocable proxy (the "Proxy") with respect to the Shares
owned of record by such Stockholder, upon the terms and subject to the
conditions hereof;

               NOW, THEREFORE, to induce Parent to enter into the Merger
Agreement and in consideration of the aforesaid and the mutual representations,
warranties, covenants and agreements set forth herein and in the Merger
Agreement, the parties hereto agree as follows:

               1.   Each Stockholder hereby constitutes and appoints Parent,
during the term of this Agreement, as such Stockholder's true and lawful proxy
and attorney-in-fact, with full power of substitution, to vote all of the Shares
(and any and all securities issued or issuable in respect thereof) which such
Stockholder is entitled to vote, for and in the name, place and stead of such
Stockholder, at any annual, special or other meeting of the stockholders of the
Company, and at any adjournment or adjournments thereof, or pursuant to any
consent in lieu of a meeting or otherwise, in favor of any proposal to approve
and adopt the Merger Agreement and any transactions contemplated thereby. All
power and authority hereby conferred is coupled with an interest and is
irrevocable. In the event that Parent is unable to exercise such power and
authority for any reason, each Stockholder agrees that it will vote all the
Shares owned of record by such Stockholder in favor of approval and adoption of
the Merger Agreement and the transactions contemplated thereby, at any such
meeting or adjournment thereof, or provide its written consent thereto.

               2.   Each Stockholder hereby covenants and agrees that such
Stockholder will not, and will not agree to, directly or indirectly, sell,
transfer, assign, pledge, hypothecate, cause to be redeemed or otherwise dispose
of any of the Shares owned of record by

                                       2
<PAGE>
 
such Stockholder or grant any proxy or interest in or with respect to such
Shares or deposit such Shares into a voting trust or enter into a voting
agreement or arrangement with respect to such Shares.  Each Stockholder further
covenants and agrees that such Stockholder will not initiate or solicit,
directly or indirectly, any inquiries or the making of any proposal with respect
to engage in negotiations concerning, provide any confidential information or
data to, or have any discussions with, any person relating to, any acquisition,
business combination or purchase of all or any significant portion of the assets
of, or any equity interest in (other than the Shares owned of record by such
Stockholder), the Company or any subsidiary thereof.

               3.   Each Stockholder represents and warrants to Parent, that the
number of Shares set forth next to such Stockholder's name on the signature
pages hereto are all of the shares of Company Common Stock owned beneficially
and of record by such Stockholder on the date hereof; such Stockholder owns such
Shares free and clear of all liens, charges, claims, encumbrances and security
interests of any nature whatsoever; and except as provided herein, such
Stockholder has not granted any proxy with respect to such Shares, deposited
such Shares into a voting trust or entered into any voting agreement or other
arrangement with respect to such Shares.

               4.   Any shares of Company Common Stock issued to any Stockholder
upon the exercise of any stock options that are currently exercisable or become
exercisable during the term of this Agreement shall be deemed Shares for
purposes of this Agreement.

                                       3
<PAGE>
 
               5.   This Proxy shall be governed by and construed in accordance
with the laws of the State of Delaware without giving effect to the provisions
thereof relating to conflicts of law.

               6.   This Proxy shall be binding upon, inure to the benefit of,
and be enforceable by the successors and permitted assigns of the parties
hereto. This Proxy and the rights hereunder may not be assigned or transferred
by Parent, except that Parent may assign its rights hereunder to any direct or
indirect subsidiary.

               7.   This Proxy shall terminate at the earlier of (I) the
effectiveness of the Merger, (ii) the termination of the Merger Agreement in
accordance with its terms, or (iii) upon notice of termination given by Parent
to each Stockholder.

               8.   This Proxy is granted in consideration of the execution and
delivery of the Merger Agreement by Parent.  Each Stockholder agrees that such
Proxy is coupled with an interest sufficient in law to support an irrevocable
power and shall not be terminated by any act of such Stockholder, by lack of
appropriate power or authority or by the occurrence of any other event or
events.

               9.   The parties acknowledge and agree that performance of their
respective obligations hereunder will confer a unique benefit on the other and
that a failure of performance will not be compensable by money damages.  The
parties therefore agree that this Proxy shall be specifically enforceable and
that specific enforcement and injunctive relief shall be available to Parent and
each Stockholder for any breach of any agreement, covenant or representation
hereunder.  This Proxy shall revoke all prior proxies given by any Stockholder
at any time with respect to the Shares.

                                       4
<PAGE>
 
               10.  Each Stockholder will, upon request, execute and deliver any
additional documents and take such actions as may reasonably be deemed by Parent
to be necessary or desirable to complete the Proxy granted herein or to carry
out the provisions hereof.

               11.  If any term, provision, covenant, or restriction of this
Proxy is held by a court of competent jurisdiction to be invalid, void or
unenforceable, the remainder of the terms, provisions, covenants and
restrictions of this Proxy shall remain in full force and effect and shall not
in any way be affected, impaired or invalidated.

               12.  This Proxy may be executed in counterparts, each of which
shall be deemed to be an original but which together shall constitute one and
the same document.

                                       5
<PAGE>
 
               IN WITNESS WHEREOF, Parent and the Stockholder have caused this
Proxy to be duly executed on the date first above written.



                                   LAWRENCE J. SPEH, AS TRUSTEE OF THE 
                                   TRUSTS LISTED ON EXHIBIT A HERETO

 
                                   /s/ Lawrence J. Speh 
                                   -----------------------------------------
                                   Lawrence J. Speh, as Trustee


                                   ACXIOM CORPORATION


                                   By /s/ Charles D. Morgan
                                     ---------------------------------------
                                   Name:  Charles D. Morgan
                                   Title: President and CEO
<PAGE>
 
                                   EXHIBIT A

<TABLE>
<CAPTION>
------------------------------------------------------------------------------------------------------------
                                                                                                 NUMBER OF
                                              NAME                                                SHARES
------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------
<S>                                                                                              <C>
Lawrence J. Speh GST Exempt Trust dated November 19, 1989                                            431,467
------------------------------------------------------------------------------------------------------------
Cathleen Malinger GST Exempt Trust dated November 19, 1989                                           256,948
------------------------------------------------------------------------------------------------------------
Albert J. Speh III GST Exempt Trust dated November 19, 1989                                          364,023
------------------------------------------------------------------------------------------------------------
Albert J. Speh III Primary Trust dated December 23, 1985                                              23,328
------------------------------------------------------------------------------------------------------------
Jonathan A. Speh GST Non-Exempt Trust dated November 19, 1989                                         43,485
------------------------------------------------------------------------------------------------------------
Jonathan A. Speh GST Non-Exempt Trust dated November 19, 1989                                         25,383
------------------------------------------------------------------------------------------------------------
Lawrence J. Speh, Jr. Primary Trust dated December 23, 1985                                           43,485
------------------------------------------------------------------------------------------------------------
Lawrence J. Speh, Jr. GST Non-Exempt Trust dated November 19, 1989                                    27,161
------------------------------------------------------------------------------------------------------------
Kevin Malinger Primary Trust dated December 23, 1985                                                   5,328
------------------------------------------------------------------------------------------------------------
Lorene Malinger Primary Trust dated December 23, 1985                                                  4,328
------------------------------------------------------------------------------------------------------------
Lynette Malinger Primary Trust dated December 23, 1985                                                 4,328
------------------------------------------------------------------------------------------------------------
Albert J. Speh IV GST Non-Exempt Trust dated November 19, 1989                                        12,149
------------------------------------------------------------------------------------------------------------
Megan Jorgensen GST Non-Exempt Trust dated November 19, 1989                                             160
------------------------------------------------------------------------------------------------------------
Shannon Golden Primary Trust dated December 23, 1985                                                   7,776
------------------------------------------------------------------------------------------------------------
Shannon Neal GST Non-Exempt Trust dated November 19, 1989                                             10,856
------------------------------------------------------------------------------------------------------------
Michelle Speh Primary Trust Dated December 23, 1985                                                    7,776
------------------------------------------------------------------------------------------------------------
Michelle Sharko GST Non-Exempt Trust dated November 19, 1989                                          10,856
------------------------------------------------------------------------------------------------------------
Kevin T. Malinger 1995 Trust dated September 28, 1995                                                 50,600
------------------------------------------------------------------------------------------------------------
Kevin Malinger GST Non-Exempt Trust dated November 19, 1989                                           32,875
------------------------------------------------------------------------------------------------------------
Lorene T. Malinger 1995 Trust dated September 28, 1995                                                51,600
------------------------------------------------------------------------------------------------------------
Lorene Maliner GST Non-Exempt Trust dated November 19, 1989                                           32,875
------------------------------------------------------------------------------------------------------------
Lynette D. Malinger 1995 Trust dated September 28, 1995                                               51,600
------------------------------------------------------------------------------------------------------------
Lynette Malinger GST Non-Exempt Trust dated November 19, 1989                                         32,875
------------------------------------------------------------------------------------------------------------
Shannon Neal 1995 Trust dated September 28, 1995                                                      51,600
------------------------------------------------------------------------------------------------------------
Albert J. Speh IV 1995 Trust dated September 28, 1995                                                 51,600
------------------------------------------------------------------------------------------------------------
Michelle E. Sharko 1995 Trust dated September 28, 1995                                                51,600
------------------------------------------------------------------------------------------------------------
Albert J. Speh, Jr. Great Grandchildren's Trust dated December 29, 1995 f/b/o Alanna R.               10,838
 Golden
------------------------------------------------------------------------------------------------------------
Albert J. Speh, Jr. Great Grandchildren's Trust dated December 29, 1995 f/b/o Justin D. Bennett       10,838
------------------------------------------------------------------------------------------------------------
Albert J. Speh, Jr. Great Grandchildren's Trust dated December 29, 1995 f/b/o Sarah R. Neal           10,838
------------------------------------------------------------------------------------------------------------
Albert J. Speh, Jr. Great Grandchildren's Trust dated December 29, 1995 f/b/o Matthew A.              10,838
 Sharko
------------------------------------------------------------------------------------------------------------
Albert J. Speh, Jr. Great Grandchildren's Trust dated December 29, 1995 f/b/o Brittney R.             10,838
 Sharko
------------------------------------------------------------------------------------------------------------
Albert J. Speh, Jr. Great Grandchildren's Trust dated December 29, 1995 f/b/o Nathan J. Sharko        10,838
------------------------------------------------------------------------------------------------------------
Total...........................................................................................   1,751,090
------------------------------------------------------------------------------------------------------------
</TABLE>
<PAGE>
 
          IN WITNESS WHEREOF, Parent and the Stockholder have caused this Proxy
to be duly executed on the date first above written.

                                   ALBERT J. SPEH, JR., AS TRUSTEE OF THE 
                                   TRUSTS LISTED ON EXHIBIT A HERETO

                                   /s/ Albert J. Speh
                                   ------------------------------------------
                                   Albert J. Speh, Jr., as Trustee


                                   ACXIOM CORPORATION


                                   By /s/ Charles D. Morgan
                                     ----------------------------------------
                                   Name:  Charles D. Morgan
                                   Title: President and CEO
<PAGE>
 
                                   EXHIBIT A

<TABLE>
<CAPTION>
----------------------------------------------------------------
                                                      NUMBER OF
                        NAME                            SHARES
----------------------------------------------------------------
----------------------------------------------------------------
<S>                                                   <C>
The Albert J. Speh, Jr. Foundation                       163,329
----------------------------------------------------------------
Erik Jorgensen 1995 Trust dated September 28, 1995        29,099
----------------------------------------------------------------
Michael Speh 1995 Trust dated September 28, 1995          40,976
----------------------------------------------------------------
Megan Jorgensen 1995 Trust dated September 28, 1995       29,600
----------------------------------------------------------------
Total..................................................  263,004
----------------------------------------------------------------
</TABLE>
