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                                                                  Exhibit 10.17

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.

                                   WARRANT

                    To Purchase Shares of Common Stock of

                         ENDOCARDIAL SOLUTIONS, INC.

                               February 2, 1999


     Endocardial Solutions, Inc., a Delaware corporation (the "Company"), for 
value received, hereby certifies that Medtronic Asset Management, Inc., a 
Minnesota 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 that number of shares of Common Stock, $.01 par 
value, of the Company ("Common Stock") determined by dividing (i) the 
outstanding balance of principal and accrued interest owed at the time of 
exercise of this Warrant by the Company pursuant to that certain Promissory 
Note of the Company issued on date hereof to Medtronic Asset Management, Inc. 
(the "Promissory Note") by (ii) the exercise price per share applicable at 
the time of exercise (the "Exercise Price").  Until adjusted as provided by 
the terms of this Warrant, the Exercise Price shall be $10.08, which the 
Company hereby represents and warrants to equal the average closing price per 
share of Common Stock for the twenty (20) trading days ending on and 
including the trading day immediately preceding the date hereof.  The shares 
issuable upon exercise or conversion of this Warrant as adjusted from time to 
time pursuant to the provisions of this Warrant, are hereinafter referred to 
as the "Warrant Shares." 

     This Warrant is further subject to the following provisions, terms and 
conditions:

     1.   CONDITIONS TO EXERCISE. This Warrant may be exercised only during 
the period beginning immediately before a Change of Control of the Company, 
as defined below, or if earlier, upon the occurrence of an Event of Default, 
as defined below, and ending on the date on which all outstanding principal 
and accrued interest under the Promissory Note is paid in full. For purposes 
of this Warrant, an Event of Default means an Event of Default under the Note 
Purchase Agreement dated of even date herewith by and between the Company and 
Medtronic Asset Management, Inc.  For purposes of this Warrant, a "Change of 
Control of the Company" means any of the following events: (i) any "person" 
(as such term is used in Sections 13(d) and 14(d) of the Securities Exchange 
Act of 1934), other than Medtronic, acquires "beneficial ownership" (as 
defined in Rule 13d-3 under the Securities Exchange Act of 1934), directly or 
indirectly, of securities of the Company or of an entity that 

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directly or indirectly owns the Company, or is an affiliate that directly or 
indirectly controls the Company, (referred to as "the Company Parent") 
representing 20% or more of the combined voting power (with respect to the 
election of directors) of the Company's or the Company Parent's, as the case 
may be, then outstanding securities; (ii) the consummation of a merger, share 
exchange, combination or consolidation of the Company or the Company Parent, 
as the case may be, with or into any other corporation, which would result in 
the voting securities of the Company or the Company Parent, as the case may 
be, outstanding immediately prior thereto continuing to represent (either by 
remaining outstanding or by being converted into voting securities of the 
surviving entity) less than 80% of the combined voting power (with respect to 
the election of directors) of the securities of the Company or the Company 
Parent, as the case may be, or of such surviving entity outstanding 
immediately after such merger, share exchange, combination or consolidation; 
or (iii) the consummation of a plan of complete liquidation of the Company or 
the Company Parent, as the case may be, or (iv) the consummation of an 
agreement for the sale or disposition by the Company or the Company Parent, 
as the case may be, of all or substantially all of the Company's or the 
Company Parent's, as the case may be, business or assets.

     2.   MANNER OF EXERCISE.  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 amount of the Exercise Price multiplied 
by the number of shares as to which the Warrant is being exercised.  The 
Exercise Price may be paid by cancellation of all or a portion of the Note 
Balance or in the form of a check or wire transfer of funds.

     3.   CONVERSION OF WARRANT.

          (a)  The Holder shall also have the right (the "Conversion Right") at
     any time when this Warrant may be exercised 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 that this Warrant is exercisable pursuant to
     Section 1 above, 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 3, 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 Warrant, 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 

                                       2
<PAGE>

     the mid-points between the highest bid and lowest asked quotations for 
     each of the ten (10) trading days immediately preceding such date.

     4.   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 2 or Section 3(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.

     5.   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.

               (iii) Upon the occurrence of an Event of Default, if the Market
     Price of the Common Stock (as defined in Section 3(b)) on the date of the
     Event of Default is lower than the Exercise Price in effect immediately
     prior to such Event of Default, then the Exercise Price shall be changed to
     the Market Price of the Common Stock on the date of the Event of Default.

          (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 

                                       3
<PAGE>

     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 could be 
     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 maximum number 
     of shares of such stock into which this Warrant would have been 
     exercisable had such reorganization, reclassification, share exchange, 
     combination, consolidation, merger or sale represented a Change of 
     Control of the Company as defined in Section 1 of this Warrant, 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 or warrants to purchase
     debt securities, assets or other securities (including Common Stock), the
     Exercise Price shall be adjusted in accordance with the formula:

               E(1) = E x (O x M) - F
                      ---------------
                          O x M

     where:

               E(1) =  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.

                                       4
<PAGE>

          (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.

     6.   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.

     7.   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.

     8.   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 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.

     9.   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.

                                       5
<PAGE>

     10.  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.
     Corporate Center
     7000 Central Avenue N.E.
     Minneapolis, MN 55432

with separate copies thereof addressed to:

     Attention:      General Counsel
     FAX (612) 572-5459

     Attention:      Vice President, Corporate Development and Associate 
                     General Counsel
     FAX (612) 572-5404

if to the Company to:

     Endocardial Solutions, Inc.
     1350 Energy Lane, Suite 110
     St. Paul, MN 55108-5254
     Attention:      President and Chief Executive 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).

     11.  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 Note Purchase Agreement dated of 
even date herewith between the Company and Medtronic Asset Management, Inc., 
provided an express sharing or assignment of such rights and benefits is made 
to each such Holder by such Holder's transferor.

                                       6
<PAGE>

     12.  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.

     IN WITNESS WHEREOF, the Company has caused this Warrant to be signed by 
its authorized officer and dated as of the date stated above.

                                       ENDOCARDIAL SOLUTIONS, INC.


                                       By:  [COPY]
                                           ----------------------------------
                                            James W. Bullock, President and
                                            Chief Executive Officer




                                       7
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                                                                      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 2 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]


<PAGE>

                                                                      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 3 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]