<PAGE>
                                                                     EXHIBIT 4.3


                       FIRST AMENDMENT TO RIGHTS AGREEMENT

         This First Amendment to Rights Agreement (this "Amendment"), dated as
of February 19, 2004, between TROVER SOLUTIONS, INC., a Delaware corporation
formerly known as Healthcare Recoveries, Inc. (the "Company"), and NATIONAL CITY
BANK, a national banking association (the "Rights Agent").

                              W I T N E S S E T H:

         WHEREAS, the Company and the Rights Agent are parties to a Rights
Agreement (the "Rights Agreement"), dated as of February 12, 1999 (capitalized
terms that are used in this Agreement but not otherwise defined shall have the
meanings ascribed to them in the Rights Agreement);

         WHEREAS, pursuant to the Rights Agreement, the Board of Directors of
the Company declared a dividend of one Right for each share of Common Stock of
the Company outstanding on March 1, 1999, and authorized the issuance of one
Right for each share of Common Stock that became outstanding after that date and
prior to the Distribution Date;

         WHEREAS, Section 27 of the Rights Agreement provides that, prior to the
Stock Acquisition Date, the Company may in its sole and absolute discretion, and
the Rights Agent shall, if the Company so directs, supplement or amend any
provision of the Rights Agreement without the approval of any holders of the
Rights or the Common Stock;

         WHEREAS, the Board of Directors has determined that it is in the best
interests of the Company and its shareholders to enter into an Agreement and
Plan of Merger, to be dated the same date as this Amendment (the "Merger
Agreement"), providing for the merger of an indirect wholly owned subsidiary of
Thomas Weisel Capital Partners, L.P. with and into the Company (the "Merger");


<PAGE>

         WHEREAS, the Company has determined that it is appropriate to amend the
Rights Agreement in order to ensure that neither the execution and delivery of
the Merger Agreement, nor the consummation of any of the transactions provided
for in the Merger Agreement, will cause the Rights to become exercisable or
trigger any other adverse consequence under the Rights Agreement and to provide
for the expiration of the Rights and the Rights Agreement upon the consummation
of the Merger; and

         WHEREAS, the Board of Directors of the Company has approved this
Amendment and authorized its appropriate officers to execute and deliver the
same to the Rights Agent.

         NOW, THEREFORE, in accordance with the procedures for amendment set
forth in Section 27 of the Rights Agreement, and in consideration of the
foregoing and the mutual agreements set forth in this Amendment, the parties
hereby agree as follows:

         1.       Amendments. The Rights Agreement is amended as follows:

                  (a)      The definition of "Acquiring Person" set forth in
Section 1(a) of the Rights Agreement is amended by adding the following sentence
to the end of that definition:

                  Notwithstanding the foregoing, no Person shall be or become an
                  Acquiring Person by reason of (i) the execution and delivery
                  of the Agreement and Plan of Merger, dated as of February 19,
                  2004, among TSI Holding Co., Inc., a Delaware corporation
                  ("Parent"), TSI Acquisition Co., Inc., a Delaware corporation
                  and a wholly owned subsidiary of Parent ("Subsidiary"), and
                  the Company (as it may be amended from time to time, the
                  "Merger Agreement") or the execution and delivery of any
                  amendment thereto, (ii) the merger of Subsidiary with and into
                  the Company pursuant to and in accordance with the provisions
                  of the Merger Agreement or (iii) the consummation of any other
                  transaction contemplated by the Merger Agreement.


                  (b)      The definition of "Stock Acquisition Date" set forth
in Section 1(dd) of the Rights Agreement is amended by adding the following
sentence to the end of that definition:

                  Notwithstanding anything else contained in this Agreement, a
                  Stock Acquisition Date shall not be deemed to have occurred by
                  reason of the public announcement of (i) the execution and
                  delivery of the Merger Agreement or of any amendment to the
                  Merger Agreement, (ii) the merger of Subsidiary with and into
                  the



                                       2

<PAGE>

                  Company pursuant to and in accordance with the provisions of
                  the Merger Agreement or (iii) the consummation of any other
                  transaction contemplated by the Merger Agreement.

                  (c)      Section 7(a) of the Rights Agreement is amended to
provide in its entirety as follows:

                  Subject to Section 7(e), the registered holder of any Right
                  Certificate may exercise the Rights evidenced thereby (except
                  as otherwise provided herein, including without limitation,
                  the restrictions on exercisability set forth in Section 9(b),
                  Section 11(a)(iii) and Section 23(a)), in whole or in part at
                  any time after the Distribution Date upon surrender of the
                  Right Certificate, with the form of election to purchase on
                  the reverse side thereof duly executed (with such signature
                  duly guaranteed), to the Rights Agent at the principal office
                  of the Rights Agent designated for such purpose, together with
                  payment of the aggregate Purchase Price with respect to each
                  Right exercised, subject to adjustment as hereinafter
                  provided, at or prior to the earliest of (i) the Close of
                  Business on March 1, 2009 ("Final Expiration Date"), (ii) the
                  effective time of the merger of Subsidiary with and into the
                  Company provided for in the Merger Agreement (the "Effective
                  Time"), (iii) the time at which the Rights are redeemed as
                  provided in Section 23 (such date being herein referred to as
                  the "Expiration Date"), or (iv) the time at which such Rights
                  are exchanged as provided in Section 24.

                  (d)      Section 23 of the Rights Agreement is amended by
adding the following new paragraph (c) to the end of that Section:

                  Notwithstanding anything else contained in this Agreement,
                  upon the Effective Time, this Agreement, the Rights and all
                  rights of the holders of the Rights under or in respect of the
                  Rights or this Agreement shall be deemed to have been
                  terminated with effect from immediately prior to the Effective
                  Time, and thereafter shall be of no further force or effect.

         2.       Company Officer's Certificate. The Rights Agent acknowledges
receipt of a certificate from an officer of the Company which states that this
Amendment is in compliance with the terms of Section 27 of the Rights Agreement.

         3.       Rights Agreement Remains in Full Force and Effect. The Rights
Agreement, as amended by this Amendment, shall and does remain in full force and
effect in accordance with its terms.


                                       3

<PAGE>

         4.       Successors. All the covenants and provisions of this Amendment
by or for the benefit of the Company or the Rights Agent shall be binding on and
inure to the benefit of their respective successors and assigns.

         5.       Benefits of this Agreement. Nothing in this Amendment shall be
construed to give to any person or corporation other than the Company, the
Rights Agent and the registered holders of the Right Certificates (and, prior to
the Distribution Date, the Common Stock) any legal or equitable right, remedy or
claim under this Amendment. This Amendment shall be for the sole and exclusive
benefit of the Company, the Rights Agent and the registered holders of the Right
Certificates (and, prior to the Distribution Date, the Common Stock).

         6.       Governing Law. 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.

         7.       Counterpart. This Amendment 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.

         8.       Descriptive Headings. Descriptive headings of the several
sections of this Amendment are inserted for convenience only and shall not
control or affect the meaning or construction of any of the provisions of this
Agreement.

         9.       Severability. If any term, provision, covenant or restriction
of this Amendment is held by a court of competent jurisdiction or other
authority to be invalid, void or unenforceable, the remainder of the terms,
provisions, covenants and restrictions of this Amendment shall remain in full
force and effect and shall in no way be affected, impaired or invalidated.

                  [remainder of page intentionally left blank]


                                       4
<PAGE>


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


                                           TROVER SOLUTIONS, INC.


Attest: /s/ Mary Ann Blake                 By:     /s/ Douglas R. Sharps
       ------------------------------           -------------------------------
       Name:  Mary Ann Blake                    Name:  Douglas R. Sharps
       Title: Vice President                    Title: Executive Vice President


                                           NATIONAL CITY BANK

Attest: /s/ Victor W. Latessa              By:    /s/ Matthew Hostelley
       ------------------------------           -------------------------------
       Name:  Victor W. Latessa                 Name:   Matthew Hostelley
       Title: Vice President                    Title:  Vice President


                                       5