<PAGE>   1


                                                                   EXHIBIT 10.34

                              SEVERANCE AGREEMENT

This Severance Agreement is entered into between C. Lee Cooke, Jr. ("Cooke")
and Sharps Compliance Corp. (formerly known as U.S. Medical Systems, Inc.)
("Sharps") and sets forth the Agreement as to the terms and conditions for
severance of Cooke's employment as Chief Executive Officer and President, the
termination of Cooke's Employment Agreement dated August 27, 1997 and all
benefits, rights and obligations arising from this Agreement.

In consideration of the mutual promises, covenants and agreements set forth
below, the adequacy and sufficiency of which are hereby acknowledged, the
parties agree as follows:

         1.      Cooke will cease employment with Sharps for all purposes
                 effective at the end of business July 22, 1998. Cooke will
                 submit the attached letter of resignation from his position as
                 Chief Executive Officer/President of Sharps. Cooke agrees to
                 be available to management for consulting on matters of Sharps
                 through September 5, 1998.

         2.      Cooke will receive the following compensation:

                 (a)      All cash in U.S. Medical Systems, Inc. ("Medical") at
                          July 31, 1998 ("Valuation Date"), that being
                          approximately $50,000, after giving effect to a
                          $40,000 payment to Sharps.

                 (b)      All accounts receivable in Medical at the Valuation
                          Date, that being approximately $14,000 and as more
                          specifically set forth on Schedule A attached hereto.

                 (c)      Personal property located at the offices of Medical
                          in Austin at the Valuation Date and as more
                          specifically described on Schedule B attached hereto,
                          said value being approximately $4,000.

                 (d)      All patents and trademarks of Medical as they exist
                          at the Valuation Date and as more specifically
                          described on Schedule C attached hereto, said patents
                          and trademarks to be conveyed to Cooke pursuant to
                          the terms of the Assignment of Patent and Trademarks
                          attached hereto as Exhibit 1 and incorporated herein
                          for all purposes.

                 (e)      Rights to the products of Medical as they exist at
                          the Valuation Date and as more specifically described
                          on Schedule D attached hereto.

                 (f)      Rights to the customer list as the customer list of
                          Medical exists at the Valuation Date and as more
                          specifically listed on Schedule E.

                 (g)      Rights to the corporate name U.S. Medical Systems,
                          Inc.

                 (h)      All of the capital stock of Medical Polymers, Inc.
<PAGE>   2
         The rights entitled to the cash, accounts receivable, personal
         property, products, customer list and corporate name and capital stock
         of Medical Polymers, Inc. will be conveyed to Cooke pursuant to the
         terms of the Bill of Sale attached hereto as Exhibit 2 and
         incorporated herein for all purposes.

         3.      Cooke hereby agrees to assume and pay all of the liabilities
                 and obligations of Medical, including existing accounts
                 payable and contingent liabilities of Medical as such
                 contingent liabilities pertain to unknown accounts payable or
                 contingent liabilities pertaining to products of Medical, as
                 such products exist at the Valuation Date, including those set
                 forth on Schedules F and G attached hereto.

         4.      After the Valuation Date, the parties agree that Sharps and
                 its 401(k) Retirement Plan, Executive Deferred Compensation
                 Plan or other existing plans have no further obligation or
                 liability to Cooke and his beneficiaries under any such plans,
                 any such liability or obligation being hereby expressly waived
                 by Cooke.

         5.      Notwithstanding anything to the contrary contained in
                 paragraph 3 herein, Cooke agrees to cooperate fully with
                 Sharps, its accountants and legal counsel, in investigating,
                 analyzing or defending any pending or future claims against or
                 litigation involving Sharps. Cooke agrees to maintain in
                 strict confidence any information or knowledge he has
                 regarding pending or future claims against or litigation
                 involving Sharps.

         6.      Subject to Cooke's obligations created in Paragraph 3 herein,
                 Sharps hereby releases and forever discharges Cooke from any
                 and all claims or causes of action it has against or may have
                 against Cooke for his actions or failure to act while employed
                 in his capacity as an employee, officer and director of Sharps
                 occurring prior to the Valuation Date of this Agreement.

         7.      Cooke hereby releases and forever discharges Sharps and all
                 predecessor, related and affiliated entities and all officers,
                 directors, employees, representatives and agents thereof (in
                 all capacities, including individually) from any claims,
                 demands, actions or causes of action which he may have had or
                 now has, whether known or unknown, contingent or otherwise,
                 whether at law or in equity, including, without limitation,
                 any and all claims relating to his employment with and
                 separation from Sharps; any compensation or benefits relating
                 to his employment; any claim of discrimination based upon his
                 race, color, creed, sex, age, national origin, disability or
                 handicap, if any; any claims relating to the discussions
                 between Sharps and its representatives regarding elimination
                 of his position or any other separation of the parties'
                 employment relationship; any claim that Sharps has violated
                 any federal, state or local statute, regulation or ordinance
                 with respect to his employment or separation thereof,
                 including without limitation, Title VII of the Civil Rights
                 Act of 1964, the Americans With Disabilities Act or the Texas
                 Commission on Human Rights Act.

         8.      Cooke hereby indemnifies and holds Sharps harmless from and
                 against, and shall promptly reimburse Sharps for any and all
                 loss, expense, damage, deficiency, liability or obligation,
                 including investigative and settlement costs and attorney's
                 fees, arising out of or in connection with the loss by Sharps
                 of any accounts payable or liabilities associated with the
                 products of Medical and conveyed to Cooke as such payables and
                 contingent liabilities pertaining to the products exist at the
                 Valuation Date.

                                     Page 2
<PAGE>   3
         9.      This Agreement shall be governed by the substantive laws of
                 the State of Texas without regard to conflict of laws
                 principles. If any provision is determined to be invalid or
                 unenforceable by a court of competent jurisdiction, the
                 remaining provisions shall continue in full force and effect.

         10.     Any dispute between the parties concerning the interpretation,
                 application or claimed breach of this Agreement shall be
                 submitted to confidential, binding arbitration in Travis
                 County, Texas, before an arbitrator appointed by the American
                 Arbitration Association in accordance with its published rules
                 and regulations. Prior to submitting the matter to
                 arbitration, the parties shall first attempt to resolve the
                 matter by the claimant notifying the other party in writing of
                 the claim, by giving the other party the opportunity to
                 respond in writing to the claim within ten (10) days of
                 receipt of the claim, and by giving the other party the
                 opportunity to meet and confer. If the matter is not resolved
                 in this manner, the dispute then may proceed to arbitration at
                 the request of either party. The parties shall bear equally
                 the arbitrator's fees and expenses, as well as the
                 administrative costs assessed by the American Arbitration
                 Association. The prevailing party shall be entitled to
                 reasonable actual damages, specific performance, costs and
                 attorney's fees. This agreement to arbitrate and the
                 arbitrator's award shall be enforceable in any court of
                 competent jurisdiction pursuant to the Texas General
                 Arbitration Act.

         11.     In entering into the Severance Agreement, both parties have
                 relied on the valuation appraisal opinion of CFO Services,
                 Inc., dated March 20, 1998, as such opinion pertained to the
                 valuation of the products of Medical, a copy of which is
                 attached hereto as Exhibit 3.

         12.     Cooke's right, title and interest in and under this Agreement
                 and all transaction documents may be subsequently assigned
                 and/or conveyed by Cooke.

         13.     The Closing of this transaction shall take place at the office
                 of the Company on or after September 2, 1998.

SHARPS COMPLIANCE CORP.
(Formerly known as U.S. Medical Systems, Inc.)

By: /s/ BURT KUNIK                                /s/ C. LEE COOKE, JR.
    ----------------------------------            ------------------------------
    Burt Kunik                                    C. Lee Cooke, Jr.
    Chairman of the Board                         Date: 9-14-98
    and Chief Executive Officer                         ------------------------
Date: 9-8-98
     ---------------------------------

                                     Page 3
<PAGE>   4
                                   Schedule A
                              -------------------
                              Accounts Receivable
                                    7/31/98



<TABLE>
<CAPTION>
<S>                                <C>
Albertsons                         $ 3,627.88
American Sales                       1,365.12
Bathurst Sales                       3,724.80
Fleming Companies, Inc.              2,398.56
Genovese Drugs                       1,128.96
H.E. Butt Grocery Co.                1,893.60
                                   ----------
               Total                14,138.92          
</TABLE>
<PAGE>   5
                                   Schedule B
                              -------------------- 
                              Real Property Assets



<TABLE>
<CAPTION>
                                                  Book Value
                                                  ----------
<S>                                               <C>
AT&T Phone System                                   1,962.86
Printing Dies - Miracle Grip(2)                       492.95
Rotary Dies - Mark Andy                               298.33
Art Work - Miracle Grip                             1,631.37
                                                  ----------
               Total                              $ 4,385.51
</TABLE>
<PAGE>   6
                                   Schedule C
                               ------------------
                               Patents/Trademarks

Patents

<TABLE>
<CAPTION>
                                             Patent         Date of
                Name                         Number         Patent
                ----                         ------         -------
<S>                                        <C>            <C>
1.   Disinfectant Mixture Containing       5,326,492      July 5, 1994
     Water Soluble Lubricating and
     Cleaning Agents and Methods

2.   Water-Based Human Tissue              5,342,617      Aug 30, 1994
     Lubricant

3.   Polymer-Based Cleaning and            5,348,678      Sept 20, 1994
     Lubricating Composition

4.   Stick Formulations for                5,597,849      January 28, 1997
     Topical Drug Delivery of
     Therapeutic Agents and Uses
     Thereof

5.   Stick Formulations for                5,622,993      Apr 22, 1997
     Topical Drug Delivery of
     Therapeutic Agents and Uses
     Thereof
</TABLE>

<TABLE>
<CAPTION>
                                           Registration         Date of
Trademark                                     Number         Registration
---------                                  ------------      -------------
<S>                                         <C>               <C>
1.   PDS                                    1,912,066         Aug 15, 1995

2.   Miracle Grip                           2,018,144         Nov 19, 1996
</TABLE>
<PAGE>   7
                                   Schedule D
                           ------------------------
                              Product Description
                             (commercial products)

1. PDS Clean, a dental handpiece cleaner.

2. Miracle Grip, a polymer-based denture adhesive.

3. QUITCH, a 1% hydrocortisone Anti-Itch product.

4. QUITCH-D, a 2% diphenhydramine itch and pain relief product.
<PAGE>   8
                                   Schedule E
                                 --------------
                                 Customer Lists

Midwest Dental Products, Inc

Albertsons, Inc

H.E. Butts Grocery Co

American Sales Stores

Bathurst Sales (Canada)

Fleming Companies, Inc.

Genovese Drug Stores

McKeeson Drug Company

Texas A&M University
<PAGE>   9
                                   Schedule F
                             ----------------------
                             CONTINGENT LIABILITIES
                                    7/31/98

<TABLE>
<S>                                          <C>
American Drug Stores                         $ 14,500.00
Eckerd Drug Stores                           $ 38,418.00
Walgreens Drug Stores                        $ 20,000.00
Shop-N-Save                                  $  3,400.00
Phar-Mor Drug Stores                         $    700.00
Wal-Mart                                     $  6,800.00
Bank One                                     $  1,600.00
Sharps Compliance                            $ 40,000.00
Pitney Bowes Credit Corp.                    $    398.00
Snyder Drug Stores                           $  2,200.00
Payco                                        $    700.00
TOTAL                                        $128,716.00
</TABLE>


<PAGE>   10
                                   Schedule G
                        -------------------------------
                        Operational Payables at 7/31/98

<TABLE>
<CAPTION>
        Vendor                                    Balance Due
        ------                                    -----------
<S>                                               <C>
Ameripac                                          $   822.80
Bank One                                            1,623.75
Burnet Storage                                        130.00
Martin Cook (Accounting)                            1,155.00
Dahill Industries, Inc                                 81.19
Faske, Lay & Co, LLP.                                 604.00
Fedex                                                 186.64
Gold Family Trust (Royalty)                         3,675.11
Robert Hodan (Royalty)                              3,675.11
Lewis Label                                         1,000.00
Kimberly Lyon (Office Mgr)                            784.00
Phoenix Home Life                                     398.20
TX Workers Compensation Fund                          590.00
USLD Communications                                   141.72
                                                  ----------
               Total                              $14,867.32
</TABLE>
<PAGE>   11


                                  BILL OF SALE

THE STATE OF TEXAS        )
                          )             KNOW ALL MEN BY THESE PRESENTS
COUNTY OF HARRIS          )

         THAT SHARPS COMPLIANCE CORP. (formerly U.S. Medical Systems, Inc.), a
Delaware corporation ("Seller"), for and in consideration of the purchase price
provided for in, and the other terms and conditions of, that certain Severance
Agreement dated September 2, 1998, by and between C. LEE COOKE, JR. ("Buyer")
and Seller (the "Agreement") (capitalized terms used and not otherwise defined
herein shall have the meanings ascribed to them in the Agreement) has bargained
and sold, and by these presents Seller does sell, assign, transfer and convey
unto Buyer all of Seller's right, title and interest in the following
(collectively, the "Assets"):

         (a)     All cash in U.S. Medical Systems, Inc. ("Medical") at July 31,
                 1998, (the "Valuation Date"), after giving effect to a $40,000
                 payment to Seller.

         (b)     All accounts receivable in Medical at the Valuation Date, as
                 more specifically set forth on Schedule A attached hereto.

         (c)     Personal property located at the offices of Medical in Austin
                 at the Valuation Date and as more specifically described on
                 Schedule B attached hereto.

         (d)     All patents and trademarks of Medical as they exist at the
                 Valuation Date and as more specifically described on Schedule
                 C attached hereto, said patents and trademarks to be conveyed
                 to Buyer pursuant to the terms of the Assignment of Patent and
                 Trademarks attached hereto as Exhibit 1 and incorporated
                 herein for all purposes.

         (e)     Rights to the products of Medical as they exist at the
                 Valuation Date and as more specifically described on Schedule
                 D attached hereto.

         (f)     Rights to the customer list as the customer list of Medical
                 exists at the Valuation Date and as more specifically listed
                 on Schedule E.

         (g)     Rights to the corporate name U.S. Medical Systems, Inc.

         (h)     All of the capital stock of Medical Polymers, Inc.

         Seller hereby acknowledges and agrees that this Bill of Sale is made
pursuant to and subject to all the terms and conditions of the Agreement,
including without limitation, Buyer's rights of indemnification under the
Agreement.
<PAGE>   12
                      ASSIGNMENT OF PATENTS AND TRADEMARKS

THE STATE OF TEXAS     )
                       )
COUNTY OF HARRIS       )

         WHEREAS, SHARPS COMPLIANCE CORP. (formerly U.S. Medical Systems,
Inc.), a Delaware corporation with offices at 9050 Kirby, Houston, Texas 77054
("Seller"), is the owner of the entire right, title and interest to United
States Patent Nos. 5,326,492 registered July 5, 1994; 5,342,617 registered
August 30, 1994; 5,348,678 registered September 20, 1994; 5,597,849 registered
January 28, 1997; and 5,622,993 registered April 22, 1997 (the "Patents"), the
inventions covered by the Patents (the "Inventions") and United States
Trademark Nos. 1,912,066 registered August 15, 1995 and 2,018,144 registered
November 19, 1996 (the "Trademarks") and Internet copyrights related to the
Trademarks; and

         WHEREAS, C. LEE COOKE, JR., a resident of Austin, Travis County, Texas
whose mailing address is Post Office Box 50442, Austin, Texas 78763
("Assignee"), is desirous of acquiring the entire right, title and interest in
and to the Patents, Inventions and Trademarks;

         NOW, THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, and intending to be legally bound
hereby, Assignor hereby assigns and transfers to Assignee the entire right,
title and interest in and to the Patents, Inventions and Trademarks, including
but not limited to all reissues, divisions, continuations and extensions of the
Patents and Trademarks, all rights of action arising from the Patents and
Trademarks, all claims for damages by reason of past infringement of the
Patents and Trademarks and the right to sue and collect damages for such
infringement, to be held and enjoyed by the Assignee for his own use and
benefit and for his successors and assigns as the same would have been held by
Assignor had this assignment not been made.

         DATED this 8th day of September, 1998.

ASSIGNOR:

SHARPS COMPLIANCE CORP.
a Delaware corporation

By: /s/ BURT KUNIK
    ---------------------------
    Burt Kunik
    Chairman of the Board
    and Chief Executive Officer

       SUBSCRIBED and SWORN TO before me this 8th day of September, 1998.

                                        /s/ PHYLLIS S. ROSS
                                        --------------------------------
                                        [NOTARY]