Document:

AMENDMENT NO. 4 TO THE
                                RIGHTS AGREEMENT
                             DATED DECEMBER 30, 1988

     THIS AGREEMENT is made and entered into as of this 15th day of December,
2000, by and between A.G. Edwards, Inc., a Delaware corporation (the "Company"),
and Bank of New York, a New York corporation (the "Rights Agent").

                                   WITNESSETH:

     WHEREAS, the Company and Boatmen's Trust Company executed a Rights
Agreement dated December 30, 1988 which was thereafter amended by Amendments No.
1, 2 and 3 to the Rights Agreement entered into as of May 24, 1991, June 22,
1995 and July 11, 1997, respectively (collectively, the "Rights Agreement");

     WHEREAS, pursuant to Section 26 of the Rights Agreement, the Company and
Rights Agent are authorized to amend the Rights Agreement without the approval
of any holders of Rights Certificates if, prior to the Distribution Date (as
defined in the Rights Agreement), the Company deems the change to be necessary
or desirable; and

     WHEREAS, the Company so deems it desirable and in the best interests of the
Company and its stockholders to amend and change certain provisions of the
Rights Agreement as set forth herein.

     NOW, THEREFORE, in consideration of the premises and the mutual agreements
herein set forth, the parties hereby agree as follows:

     SECTION 1.  Amendment of Rights Agreement.  (a)  Section 1(a) of the Rights
Agreement is hereby amended by striking therefrom the phrase ", without the
prior approval of a majority of the Continuing Directors (as such term is
hereinafter defined)".

     (b)  Each of the definitions of "Continuing Director," "Offer," "Triggering
Event," "Whole Board," and "Voting Stock" in Sections 1(h), 1(m), 1(s), 1(t) and
1(u), respectively, of the Rights Agreement are hereby deleted and replaced with
"(RESERVED)".

     (c)  Sections 1(j) and 11(a) of the Rights Agreement are hereby amended by
replacing the references therein to "a majority of the Continuing Directors"
with "the Board of Directors of the Company"; and Section 11(c) of the Rights
Agreement is hereby amended by replacing the reference therein to "a majority of
the Continuing Directors in office at the time" with "its Board of Directors".

     (d)  Section 7(b) of the Rights Agreement, as amended, is hereby amended by
replacing the reference therein to "$90.00 as of June 22, 1995" with "$150.00 as
of December 15, 2000".

     (e)  Section 11(c) of the Rights Agreement is hereby amended by adding at
the end of such Section the following:
     "Notwithstanding the foregoing, the Board of Directors of the Company shall
     not be authorized to effect such exchange at any time after any Person
     (other than the Company, any Subsidiary of the Company, any employee
     benefit plan of the Company or any such Subsidiary, or any entity holding
     shares of Common Stock for or pursuant to the terms of any such plan),
     together with all Affiliates and Associates of such Person, becomes the
     Beneficial Owner of 50% or more of the shares of Common Stock then
     outstanding."

     (f)  Section 13 of the Rights Agreement is hereby amended by adding, at the
end of the first sentence of each of paragraphs (a), (b) and (c) of such
Section, the following:

     "; provided, however, that in no event shall the consideration to be paid
     upon the exercise of one Right be less than the aggregate par value of the
     shares of capital stock of the Company issuable upon exercise of one Right"

     (g)  Section 23 of the Rights Agreement is hereby amended in its entirety
to read as follows:

     "(a)The Board of Directors of the Company may, at its option, at any time
     prior to such time as any Person becomes an Acquiring Person, redeem all
     but not less than all of the then outstanding Rights at a redemption price
     of $.01 per Right, appropriately adjusted to reflect any stock split, stock
     dividend or similar transaction occurring after the date hereof (such
     redemption price being hereinafter referred to as the "Redemption Price").
     The redemption of the Rights by the Board of Directors of the Company may
     be made effective at such time, on such basis and with such conditions as
     the Board of Directors of the Company, in its sole discretion, may
     establish.

     (b)  Immediately upon the action of the Board of Directors of the Company
     ordering the redemption of the Rights pursuant to Section 23(a), evidence
     of which shall have been filed with the Rights Agent, and without any
     further action and without any notice, the right to exercise the Rights
     will terminate and the only right thereafter of the holders of Rights shall
     be to receive the Redemption Price.  The Company shall promptly give public
     notice of any such redemption; provided, however, that the failure to give,
     or any defect in, any such notice shall not affect the validity of such
     redemption.  Within ten days after the action of the Board of Directors
     ordering any such redemption of the Rights, the Company shall give notice
     of such redemption to the Rights Agent and the holders of the then
     outstanding Rights by mailing such notice to the Rights Agent and to all
     such holders at their last addresses as they appear upon the registry books
     of the Rights Agent or, prior to the Distribution Date, on the registry
     books of the transfer agent for the Common Stock.  Any notice which is
     given in the manner herein provided shall be deemed given, whether or not
     the holder receives the notice.  Each such notice of redemption will state
     the method by which the payment of the Redemption Price will be made.
     Neither the Company nor any of its Affiliates or Associates may redeem,
     acquire or purchase for value any Rights at any time in any manner other
     than that specifically set forth in this Section 23 or in Section 24
     hereof, and other than in connection with the purchase of Common Shares
     prior to the Distribution Date."

     (h)  Section 26 of the Rights Agreement is hereby amended by adding at the
end of such Section the following:

     "Without limiting the foregoing, the Company may at any time prior to such
     time as any Person becomes an Acquiring Person amend this Agreement to
     lower the thresholds set forth in Section 1(a) hereof to not less than 10%
     (the "Reduced Threshold"); provided, however, that no Person who
     beneficially owns a number of shares of Common Stock equal to or greater
     than the Reduced Threshold shall become an Acquiring Person unless such
     Person shall, after the public announcement of the Reduced Threshold,
     increase its beneficial ownership of the then outstanding shares of Common
     Stock (other than as a result of an acquisition of such shares by the
     Company) to an amount equal to or greater than the greater of (x) the
     Reduced Threshold or (y) the sum of (i) the lowest beneficial ownership of
     such Person as a percentage of the outstanding shares of Common Stock as of
     any date on or after the date of the public announcement of such Reduced
     Threshold plus (ii) .001%."

     (i)  Section 30 of the Rights Agreement is hereby amended by replacing the
reference therein to "Missouri" with "Delaware".

     (j)  Exhibit B (Summary of Rights to Purchase Common Stock) to the Rights
Agreement is hereby amended in its entirety to the effect set forth in the
Attachment to this Amendment No. 4.

     SECTION 2.  Savings Clause.  All of the provisions of the Rights Agreement
not amended by this Agreement shall remain in full force and effect.

     SECTION 3.  Miscellaneous.  (a) This Agreement, as it amends the Rights
Agreement, constitutes the entire agreement and understanding of the parties
with respect to the subject matter hereof, and it supersedes all prior
negotiations, commitments, representations and undertakings of the parties with
respect to the subject matter hereof.  Any terms used herein, which are not
defined herein, shall have the meaning attached to them in the Rights Agreement.

     (b)  This Agreement shall be binding upon and inure to the benefit of the
Company, the Rights Agent and their respective successors and permitted assigns.

     (c)  This Agreement 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 made and to be
performed entirely within such State.

     (d)  This Agreement may be executed in any number of counterparts and each
of such counterparts shall for all purposes be deemed to be an original, and all
such counterparts shall together constitute but one and the same instrument.

                           (SIGNATURE PAGE TO FOLLOW)

     IN WITNESS WHEREOF, the parties have caused this Agreement to be duly
executed and their respective corporate seals to be hereto affixed and attested,
all on the day and year first above written.

     ATTEST:                            A.G. EDWARDS, INC.

     By:  /s/ Mary H. Vahlkamp               By: /s/ Douglas L. Kelly
           Name:  Mary H. Vahlkamp              Name:  Douglas L. Kelly
           Title:  Assistant Secretary          Title: Vice President

     ATTEST:                            BANK OF NEW YORK
                                             RIGHTS AGENT

     By:   /s/ Christine Briggs              By: /s/ Robert J. Rinaudo
       Name:  Christine Briggs                  Name:  Robert J. Rinaudo
       Title: Assistant Vice President          Title: Assistant Vice President

                                 ATTACHMENT
                      (Exhibit B to Rights Agreement)

                                                   EXHIBIT B

                   SUMMARY OF RIGHTS TO PURCHASE COMMON STOCK

     On December 30, 1988, the Board of Directors of A.G. Edwards, Inc. (the
"Company") declared a dividend distribution of one Right for each outstanding
share of common stock, $1.00 par value (the "Common Stock"), of the Company to
stockholders of record at the close of business on January 18, 1989 (the "Record
Date").  Except as set forth below, each Right, when exercisable, entitles the
registered holder to purchase from the Company one share of Common Stock, at a
price of $150.00 per share (the "Purchase Price"), subject to adjustment.  The
Purchase Price may be paid in cash or certified check, or by surrender of shares
of Common Stock of the Company.  The description and terms of the Rights are set
forth in a Rights Agreement (as amended, the "Rights Agreement") between the
Company and the Bank of New York, a New York corporation, as Rights Agent.

     Initially, the Rights will be attached to all Common Stock certificates
representing shares then outstanding, and no separate Rights certificates will
be distributed.  Until the earlier to occur of (i) a public announcement that,
without the prior consent of the Company, a person or group of affiliated or
associated persons (an "Acquiring Person") has acquired, or obtained the right
to acquire beneficial ownership of 20% or more of the outstanding Common Stock
of the Company or (ii) ten days (unless such date is extended by the Board of
Directors) following the commencement of (or a public announcement of an
intention to make) a tender offer or exchange offer which would result in any
person or group and related persons becoming an Acquiring Person (the earlier of
such dates being called the "Distribution Date"), the Rights will be evidenced,
with respect to any of the Common Stock certificates outstanding as of the
Record Date, by such Common Stock certificate together with this Summary of
Rights.  The Company may reduce the threshold at which a person or group becomes
an Acquiring Person from 20% to not less than 10% of the outstanding common
stock.

     A person shall not be deemed to be an Acquiring Person, and therefore the
Rights Certificates will not be distributed, if the person represents to the
Company that:  (i) the person did not intend to beneficially own 20% or more of
the Company's Common Stock; (ii) the person intends to sell, within five (5)
business days, enough shares so he will beneficially own less than 20% of the
Company's Common Stock; and, (iii) such person in fact sells such shares to an
unaffiliated party or parties and someone other than the Company.  The Rights
Agreement provides that, until the Distribution Date, the Rights will be
transferred with and only with Common Stock certificates.  From as soon as
practicable after the Record Date and until the Distribution Date (or earlier
redemption or expiration of the Rights), new Common Stock certificates issued
after the Record Date upon transfer or new issuance of the Common Stock will
contain a notation incorporating the Rights Agreement by reference.  Until the
Distribution Date (or earlier redemption or expiration of the Rights), the
surrender for transfer of any certificates for Common Stock outstanding as of
the Record Date (with or without this Summary of Rights attached) will also
constitute the transfer of the Rights associated with the Common Stock
represented by such certificate.  As soon as practicable following the
Distribution Date, separate certificates evidencing the Rights ("Rights
Certificates") will be mailed to holders of record of the Common Stock as of the
close of business on the Distribution Date and the separate Rights Certificates
alone will evidence the Rights.

     The Rights are not exercisable until the Distribution Date.  The Rights
will expire on the earlier of June 25, 2005, or the time at which the Rights are
redeemed by the Company as described below.

     The Purchase Price payable, and the number of shares of Common Stock or
other securities or property issuable, upon exercise of the Rights are subject
to adjustment from time to time to prevent dilution (i) in the event of a stock
dividend on, or a subdivision, combination or reclassification of the Common
Stock, (ii) upon the grant to holders of the Common Stock of certain rights or
warrants to subscribe for Common Stock, certain convertible securities or
securities having the same or more favorable rights, privileges and preferences
as the Common Stock at less than the current market price of the Common Stock or
(iii) upon the distribution to holders of the Common Stock of evidences of
indebtedness or assets (excluding regular quarterly cash dividends out of
earnings or retained earnings) or of subscription rights or warrants (other than
those referred to above).

     In the event that, after the first date of public announcement by the
Company or an Acquiring Person that an Acquiring Person has become such, the
Company is involved in a merger or other business combination transaction in
which the Common Stock is exchanged or changed, or more than 50% of the
Company's assets or earning power are sold (in one transaction or a series of
transactions), proper provision shall be made so that each holder of a Right
shall thereafter have the right to receive, upon the exercise thereof at the
then current Purchase Price of the Right, that number of shares of common stock
of the acquiring company (or, in the event there is more than one acquiring
company, the acquiring company receiving the greatest portion of the assets or
earning power transferred) which at the time of such transaction would have a
market value of two times the Purchase Price of the Right (such right being
called the "Merger Right").

     In the event that a person becomes the beneficial owner of 20% or more of
the then outstanding shares of Common Stock of the Company, proper provision
shall be made so that each holder of a Right will for a 60-day period thereafter
have the right to receive upon exercise that number of shares of Common Stock
having a market value of two times the Purchase Price of the Right, subject to
the availability of a sufficient number of authorized but unissued shares (such
right being called the "Subscription Right").  The 60 day subscription period
may be increased or decreased by the Board of Directors.  Except as described
below, the holder of a Right will continue to have the Merger Right whether or
not such holder exercises the Subscription Right.  By action of the Board of
Directors, the Company may permit the Rights to be exercised for 50% of the
shares of Common Stock that would otherwise be purchasable in consideration of
the surrender to the Company of the Rights so exercised and without other
payment of the Purchase Price.  However, the Board of Directors shall not be
authorized to effect such exchange at any time after any person or group of
affiliated or associated persons becomes the beneficial owner of 50% or more of
the Common Stock then outstanding.  Rights so exercised are deemed exercised in
full and will be cancelled.

     Upon the occurrence of any of the events giving rise to the exercisability
of the Subscription Right or the Merger Right, any Rights that are or were at
any time owned by an Acquiring Person engaging in any of such transactions or
receiving the benefits thereof on or after the time the Acquiring Person becomes
such shall become void insofar as they relate to the Subscription Right or the
Merger Right.

     With certain exceptions, no adjustments in the Purchase Price will be
required until cumulative adjustments require an adjustment of at least 1% in
such Purchase Price.  No fractions of shares will be issued and, in lieu
thereof, an adjustment in cash will be made based on the market price of the
Common Stock on the last trading date prior to the date of exercise.

     At any time prior to such time as any Person becomes an Acquiring Person
(the "Stock Acquisition Date") the Company may redeem the Rights in whole, but
not in part, at a price of $.01 per Right (the "Redemption Price") which
redemption shall be effective upon the action of the Board of Directors.  Upon
the effective date of the redemption of the Rights, the right to exercise the
Rights will terminate and the only right of the holders of Rights will be to
receive the Redemption Price.

     Until a Right is exercised, the holder thereof, as such, will have no
rights as a stockholder of the Company, including, without limitation, the right
to vote or to receive dividends.

     A copy of the Rights Agreement has been filed with the Securities and
Exchange Commission as an Exhibit to a Registration Statement on Form 8-A.  A
copy of the Rights Agreement is available free of charge from the Company.  This
summary description of the Rights does not purport to be complete and is
qualified in its entirety by reference to the Rights Agreement, which is
incorporated herein by reference.<PAGE>   1

                                                                     EXHIBIT 4.1

COMMON STOCK                    [LOGO]                              COMMON STOCK
   NUMBER                                                              SHARES

                                THIRD WAVE
                               TECHNOLOGIES
INCORPORATED UNDER                                       SEE REVERSE FOR CERTAIN
    THE LAWS                                                 DEFINITIONS AND
  OF DELAWARE                                                  RESTRICTIONS

  COMMON PAR             THIRD WAVE TECHNOLOGIES, INC.         CUSIP 88428W 10 8

THIS CERTIFIES THAT

IS THE OWNER OF
   FULLY PAID AND NON-ASSESSABLE SHARES OF COMMON STOCK, $0.001 PAR VALUE, OF

                         THIRD WAVE TECHNOLOGIES, INC.

   transferable on the books of the Corporation by the holder hereof in person
or by duly authorized attorney upon surrender of this Certificate properly
endorsed.

   WITNESS the facsimile seal of the Corporation and the facsimile signatures of
its duly authorized officers.

Dated
                                [CORPORATE SEAL]
                                  AUG. 16, 2000
                                     DELAWARE

/s/ [SIGNATURE ILLEGIBLE]                              /s/ [SIGNATURE ILLEGIBLE]
-----------------------------                          -------------------------
       VICE PRESIDENT,                                      CHIEF EXECUTIVE
GENERAL COUNSEL AND SECRETARY                            OFFICER AND PRESIDENT

Countersigned and Registered:
    EquiServe Trust Company, N.A.

              Transfer Agent
               and Registrar

By  /s/ [SIGNATURE ILLEGIBLE]
    -------------------------
       Authorized Signature
<PAGE>   2
                         THIRD WAVE TECHNOLOGIES, INC.

     The Corporation will furnish without charge to each Stockholder who so
requests, the powers, designations, preferences and relative, participating,
optional or other special rights of each class of stock or series thereof of
the Corporation, and the qualifications, limitations or restrictions of such
preferences and/or rights. Such request may be made to the Corporation or the
Transfer Agent.

--------------------------------------------------------------------------------

     The following abbreviations, when used in the inscription on the face of
this certificate, shall be construed as though they were written out in full
according to applicable laws or regulations:

          TEN COM - as tenants in common
          TEN ENT - as tenants by the entireties
           JT TEN - as joint tenants with right of survivorship and not as
                    tenants in common
UNIF GIFT MIN ACT -                Custodian
                    ---------------         ---------------
                         (Cust)                 (Minor)
                    under Uniform Gifts to Minors

                    Act
                       -------------------
                             (State)

    Additional abbreviations may also be used though not in the above list.

     For Value received, _______________ hereby sell, assign and transfer unto

  PLEASE INSERT SOCIAL SECURITY OR
OTHER IDENTIFYING NUMBER OF ASSIGNEE

        ---------------------

--------------------------------------------------------------------------------
             PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS OF ASSIGNEE

--------------------------------------------------------------------------------

--------------------------------------------------------------------------------

------------------------------------------------------------------------- Shares
of the capital stock represented by the within Certificate, and do hereby
irrevocably constitute and appoint
                                   ---------------------------------------------

-------------------------------------------------------------------- Attorney to
transfer the said stock on the books of the within-named Corporation with full
power of substitution in the premises.

Dated,                                   X
      -------------------------------     --------------------------------------
                                         X
                                          --------------------------------------
                                          NOTICE: THE SIGNATURE(S) TO THIS
                                          ASSIGNMENT MUST CORRESPOND WITH THE
                                          NAME(S) AS WRITTEN UPON THE FACE OF
                                          THE CERTIFICATE, IN EVERY PARTICULAR,
                                          WITHOUT ALTERATION OR ENLARGEMENT, OR
                                          ANY CHANGE WHATEVER.

SIGNATURE GUARANTEED:
                     --------------------------------------
                     THE SIGNATURE(S) MUST BE GUARANTEED BY
                     AN ELIGIBLE GUARANTOR INSTITUTION
                     (BANKS, STOCKBROKERS, SAVINGS AND LOAN
                     ASSOCIATIONS AND CREDIT UNIONS WITH
                     MEMBERSHIP IN AN APPROVED SIGNATURE
                     GUARANTEE MEDALLION PROGRAM), PURSUANT
                     TO S.E.C. RULE 17AO-15.

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