Exhibit
10.23  THIS WARRANT, AND THE
SHARES OF COMMON STOCK ISSUABLE UPON EXERCISE HEREOF, HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES
LAWS AND MAY NOT BE REOFFERED OR SOLD, TRANSFERRED, PLEDGED, HYPOTHECATED OR
OTHERWISE DISPOSED OF, EXCEPT PURSUANT TO (1) REGISTRATION OR (2) AN OPINION OF
COUNSEL FOR THE COMPANY OR OTHER COUNSEL REASONABLY ACCEPTABLE TO THE COMPANY
TO THE EFFECT THAT SUCH REGISTRATION IS NOT REQUIRED.   WARRANTTo Purchase 223,777
Shares of Common Stock ofENDOCARDIAL
SOLUTIONS, INC.Effective May 1, 2003  Endocardial Solutions,
Inc., a Delaware corporation (the Company), for value received, hereby
certifies that Medtronic International, Ltd., a Delaware corporation, or its
registered assigns (the Holder), is entitled, subject to the terms set forth
below, upon exercise of this Warrant to purchase from the Company, at any time
or from time to time on or after the earlier of May 1, 2004 or a Change of
Control of Licensee (as defined in the License Agreement between Medtronic,
Inc. and the Company dated January 30, 1998), and on or before 11:59 p.m.
(Minneapolis, Minnesota time) on the five-year anniversary of the date hereof,
up to Two Hundred Twenty-three Thousand Seven Hundred Seventy-seven (223,777)
shares of Common Stock, $.01 par value, of the Company (Common Stock) at a
purchase price per share equal to $3.81 (subject to adjustment in accordance
with Section 4 hereof), which number of shares the Company hereby represents
and warrants to equal two and one-half percent (2.5%) of the total number of
shares of Common Stock issued and outstanding on January 30, 1998, and
which per share purchase price the Company hereby represents and warrants to
equal 1.25 times the average closing price of Common Stock for the twenty (20)
trading days ending on and including the trading day immediately preceding the
effective date hereof.  The shares
issuable upon exercise or conversion of this Warrant, and the purchase price
per share, each as adjusted from time to time pursuant to the provisions of
this Warrant, are hereinafter referred to as the Warrant Shares and the
Exercise Price, respectively.  This Warrant is further
subject to the following provisions, terms and conditions:  1.Exercise
of Warrant.  This Warrant may be
exercised by the Holder, in whole or in part (but not as to any fraction of a
share of Common Stock), by surrendering this Warrant, with the Exercise Form
attached hereto as Exhibit A filled-in and duly executed by such Holder or by
such Holders duly authorized attorney, to the Company at its principal office
accompanied  
   by payment of the
Exercise Price in the form of a check or wire transfer in the amount of the
Exercise Price multiplied by the number of shares as to which the Warrant is
being exercised.  2.Conversion
of Warrant.  (a)The
Holder shall also have the right (the Conversion Right) to convert all or any
portion of this Warrant into such number of shares (rounded to the nearest
whole share) of Company Common Stock equal to the quotient obtained by dividing
(i) the Aggregate Warrant Spread as of the date the Conversion Right is
exercised, by (ii) the Market Price of the Common Stock as of the date the
Conversion Right is exercised.  The
Conversion Right shall be exercisable at any time on or after the earlier of
May 1, 2004 or a Change of Control of Licensee (as defined in the License
Agreement between Medtronic, Inc. and the Company dated January 30, 1998),
or from time to time thereafter prior to expiration of this Warrant by
surrendering this Warrant with the Conversion Form attached hereto as Exhibit B
filled-in and duly executed by such Holder or by such Holders duly authorized
attorney to the Company at its principal office.  (b)For
purposes of this Section 2, the Aggregate Warrant Spread of all or a
portion of this Warrant as of a particular date shall equal (i) the Market
Price of the Common Stock multiplied by the number of shares of Common Stock
purchasable upon exercise of all or such portion of this Warrant on such date,
minus (ii) the Exercise Price multiplied by the number of shares of Common
Stock purchasable upon exercise of all or such portion of this Warrant on such
date.  For purposes of this
Section 2, the Market Price of the Common Stock as of a particular date
shall equal: (i) if the Common Stock is traded on an exchange or is quoted on
either the Nasdaq National Market or Small-Cap Market, then the average of the
closing or last sale prices, respectively, reported for the ten (10) trading
days immediately preceding such date, or (ii) if the Common Stock is not traded
on an exchange, the Nasdaq National Market, or the Nasdaq Small-Cap Market but
is traded in the local over-the-counter market, then the average of the mid-points
between the highest bid and lowest asked quotations for each of the ten (10)
trading days immediately preceding such date.  3.Effective
Date of Exercise or Conversion. 
Each exercise or conversion of this Warrant shall be deemed effective as
of the close of business on the day on which this Warrant is surrendered to the
Company as provided in Section 1 or Section 2(a) above.  At such time, the person or persons in whose
name or names any certificates for Warrant Shares shall be issuable upon such
exercise or conversion shall be deemed to have become the holder or holders of
record of the Warrant Shares represented by such certificates.  Within ten (10) days after the exercise or
conversion of this Warrant in full or in part, the Company will, at its expense,
cause to be issued in the name of and delivered to the Holder or such other
person as the Holder may (upon payment by such Holder of any applicable
transfer taxes) direct:  (i) a
certificate or certificates for the number of full Warrant Shares to which such
Holder is entitled upon such exercise or conversion, and (ii) unless this
Warrant has expired, a new Warrant or Warrants (dated the date hereof and in
form identical hereto) representing the right to purchase the remaining number
of shares of Common Stock, if any, with respect to which this Warrant has not
then been exercised or converted.  2 
   4.Adjustments
to Exercise Price.  The above
provisions are, however, subject to the following:  (a)(i)If
the Company shall at anytime after the date of this Warrant subdivide or
combine the outstanding shares of Common Stock or declare a dividend payable in
Common Stock, then the number of shares of Common Stock for which this Warrant
may be exercised as of immediately prior to the subdivision, combination or
record date for such dividend payable in Common Stock shall forthwith be
proportionately decreased, in the case of combination, or increased, in the
case of subdivision or dividend payable in Common Stock.  (ii)If
the Company shall at anytime after the date of this Warrant subdivide or
combine the outstanding shares of Common Stock or declare a dividend payable in
Common Stock, the Exercise Price in effect immediately prior to the
subdivision, combination or record date for such dividend payable in Common
Stock shall forthwith be proportionately increased, in the case of combination,
or decreased, in the case of subdivision or dividend payable in Common Stock.  (b)If
any capital reorganization or reclassification of the capital stock of the
Company, or share exchange, combination, consolidation or merger of the Company
with another corporation, or the sale of all or substantially all of its assets
to another corporation shall be effected in such a way that holders of Common
Stock shall be entitled to receive stock, securities or assets with respect to
or in exchange for Common Stock, then, as a condition of such reorganization,
reclassification, share exchange, combination, consolidation, merger or sale,
lawful and adequate provision shall be made whereby the Holder shall thereafter
have the right to receive upon exercise of this Warrant upon the basis and upon
the terms and conditions specified in this Warrant and in lieu of the shares of
the Common Stock of the Company into which this Warrant was immediately
theretofore exercisable or convertible, such shares of stock, securities or
assets as may be issued or payable with respect to or in exchange for a number
of outstanding shares of such Common Stock equal to the number of shares of
such stock into which this Warrant was immediately theretofore exercisable had
such reorganization, reclassification, share exchange, combination,
consolidation, merger or sale not taken place, and in any such case appropriate
provisions shall be made with respect to the rights and interests of Holder to
the end that the provisions hereof (including without limitation provisions for
adjustments of the Exercise Price and of the number of shares purchasable upon
exercise or conversion of this Warrant) shall thereafter be applicable, as
nearly as may be, in relation to any shares of stock, securities or assets
thereafter deliverable upon the exercise or conversion hereof.  The Company shall not effect any such share
exchange, combination, consolidation, merger or sale, unless prior to the
consummation thereof the successor corporation (if other than the Company)
resulting from such share exchange, combination, consolidation or merger or the
corporation purchasing such assets shall assume by written instrument executed
and mailed to the Holder at the last address of such Holder appearing on the
books of the Company, the obligation to deliver to such Holder such shares of
stock, securities or assets which, in accordance with the foregoing provisions,
such Holder may thereafter be entitled to receive upon exercise or conversion
of this Warrant.  (c)If
at anytime after the date of this Warrant the Company distributes to all
holders of Common Stock any assets (excluding ordinary cash dividends), debt
securities, or any rights  3 
   or warrants to purchase
debt securities, assets or other securities (including Common Stock), the
Exercise Price shall be adjusted in accordance with the formula:  E1 = E x (O
x M) - F O x M  where:  E1 =the
adjusted Exercise Price. E  =the current Exercise Price. M  =the average market price of
Common Stock for the 30 consecutive trading days commencing 45 trading days
before the record date mentioned below. O  =the number of shares of
Common Stock outstanding on the record date mentioned below. F  =the fair market value on
the record date of the aggregate of all assets, securities, rights or warrants
distributed.  The Companys Board of
Directors shall determine the fair market value in the exercise of its
reasonable judgment.  The adjustment shall be
made successively whenever any such distribution is made and shall become
effective immediately after the record date for the determination of
stockholders entitled to receive the distribution.  (d)Upon
any adjustment of the Exercise Price, then and in each such case, the Company
shall give written notice thereof, by first class mail, postage prepaid,
addressed to the Holder of this Warrant at the address of such Holder as shown
on the books of the Company, which notice shall state the Exercise Price
resulting from such adjustment and the increase or decrease, if any, in the
number of shares for which this Warrant may be exercised, setting forth in
reasonable detail the method of calculation and the facts upon which such
calculation is based.  5.Common
Stock.  As used herein, the term
Common Stock shall mean and include the Companys presently authorized shares
of common stock and shall also include any capital stock of any class of the
Company hereafter authorized which shall not be limited to a fixed sum or
percentage in respect of the rights of the holders thereof to participate in
dividends or in the distribution, dissolution or winding up of the Company.  6.No
Voting Rights.  This Warrant shall
not entitle the Holder to any voting rights or other rights as a shareholder of
the Company unless and until exercised or converted pursuant to the provisions
hereof.  7.Exercise
or Transfer of Warrant or Resale of Common Stock.  The Holder, by acceptance hereof, agrees to give written notice
to the Company before transferring this Warrant, in whole or in part, or
transferring any shares of Common Stock issued upon the exercise or conversion
hereof, of such Holders intention to do so, describing briefly the manner of
any proposed transfer.  Such notice
shall include an opinion of counsel reasonably satisfactory to the Company that
(i) the proposed exercise or transfer may be effected without registration or  4 
   qualification under the
Securities Act of 1933, as amended (the Act) and any applicable state
securities or blue sky laws, or (ii) the proposed exercise or transfer has been
registered under such laws.  Upon delivering
such notice, such Holder shall be entitled to transfer this Warrant or such
Warrant Shares, all in accordance with the terms of the notice delivered by
such Holder to the Company, provided that an appropriate legend may be endorsed
on the certificates for such shares respecting restrictions upon transfer
thereof necessary or advisable in the opinion of counsel to the Company to
prevent further transfer which would be in violation of Section 5 the Act
and applicable state securities or blue sky laws.  If in the opinion of
counsel to the Company or other counsel reasonably acceptable to the Company
the proposed transfer or disposition of this Warrant or the Warrant Shares
described in the written notice given pursuant to this Section 7 may not
be effected without registration of this Warrant or the Warrant Shares, the
Company shall promptly give written notice thereof to the Holder within 10 days
after the Company receives such notice, and such holder will limit its
activities in respect to such as, in the opinion of such counsel, is permitted
by law.  8.Covenants
of the Company.  The Company
covenants and agrees that all shares which may be issued upon conversion of
this Warrant will, upon issuance, be duly authorized and issued, fully paid,
nonassessable and free from all taxes, liens and charges with respect to the
issue thereof.  The Company further
covenants and agrees that the Company will at all times have authorized, and
reserved for the purpose of issue upon exercise hereof, a sufficient number of
shares of its Common Stock to provide for the exercise of this Warrant.  9.Certain
Notices.  The Holder shall be
entitled to receive from the Company immediately upon declaration thereof and
at least thirty (30) days prior to the record date for determination of
shareholders entitled thereto or to vote thereon (or if no record date is set,
prior to the event), written notice of any event which could require an
adjustment pursuant to Section 4 hereof or of the dissolution or
liquidation of the Company.  All notices
hereunder shall be in writing and shall be delivered personally or by telecopy
(receipt confirmed) to such party (or, in the case of an entity, to an
executive officer of such party) or shall be sent by a reputable express
delivery service or by certified mail, postage prepaid with return receipt
requested, addressed as follows:  if to Medtronic, to:  Medtronic, Inc.
World Headquarters
710 Medtronic Parkway, N.E.
Minneapolis, MN 55432-5604  with separate copies
thereof addressed to:  Attention:General
Counsel
FAX  (763) 572-5459  Attention:Vice
President and Chief Development Officer
FAX  (763) 505-2542  5 
   if to the Company to:  Endocardial
Solutions, Inc.
1350 Energy Lane, Suite 110
St. Paul, MN 55108-5254
Attention:Chief
Financial Officer  FAX  (651) 644-7897  Any party may change the
above-specified recipient and/or mailing address by notice to all other parties
given in the manner herein prescribed. 
All notices shall be deemed given on the day when actually delivered as
provided above (if delivered personally or by telecopy) or on the day shown on
the return receipt (if delivered by mail or delivery service).  10.Registration
Rights.  The Holders of this Warrant
and the Warrant Shares are entitled to the rights and benefits of all of the
terms, provisions and conditions of that certain Registration Rights Agreement
dated January 30, 1998 between Medtronic, Inc. and the Company, provided
an express sharing or assignment of such rights and benefits is made to each
such Holder by such Holders transferor.  11.Miscellaneous.  (a)No
amendment, modification or waiver of any provision of this Warrant shall be
effective unless the same shall be in writing and signed by the holder hereof.  (b)This
Warrant shall be governed by and construed in accordance with the laws of the
State of Minnesota.  (Signatures on the
following page)  6 
   IN WITNESS WHEREOF, the
Company has caused this Warrant to be signed by its authorized officer and
dated to be effective as of the date stated above.   ENDOCARDIAL SOLUTIONS,
  INC.By
  :  /s/ J.
  Robert Paulson, Jr.J. Robert Paulson, Jr.Chief Financial Officer  7 
   Exhibit A   NOTICE OF EXERCISE OF
  WARRANT 
  
  To Be Executed by the
  Registered Holder in Order to Exercise the Warrant   The undersigned hereby
irrevocably elects to exercise the attached Warrant to purchase, for cash
pursuant to Section 1 thereof,
                                    
shares of Common Stock issuable upon the exercise of such Warrant.  The undersigned requests that certificates
for such shares be issued in the name of
                                                        .  If this Warrant is not fully exercised, the
undersigned requests that a new Warrant to purchase the balance of shares
remaining purchasable hereunder be issued in the name of
                                            .   Date: 
                         ,[name of registered
  Holder][signature][street address][city, state, zip][tax identification
  number]  
   Exhibit B   NOTICE OF CONVERSION OF
  WARRANT  
  
  To Be Executed by the
  Registered Holder in Order to Convert the Warrant on a Cashless Basis   The undersigned hereby
irrevocably elects to convert, on a cashless basis, a total of
                          
shares of Common Stock otherwise purchasable upon exercise of the attached
Warrant into such lesser number of shares of Common Stock as determined by
Section 2 of the Warrant.  The
undersigned requests that certificates for such shares be issued in the name of
                                                    .  If this Warrant is not fully converted, the
undersigned requests that a new Warrant to purchase the balance of shares
remaining purchasable hereunder be issued in the name of
                                                    .   Date: 
                        ,[name of registered
  Holder][signature][street address][city, state, zip][tax identification
  number]