Document:

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                                                                 EXHIBIT 10.10.1

                 PROMISSORY NOTE AND WARRANT PURCHASE AGREEMENT

         THIS PROMISSORY NOTE AND WARRANT PURCHASE AGREEMENT ("Agreement") is
made as of the 22nd day of May, 1998, by and among Odyssey HealthCare, Inc., a
Delaware corporation (the "Company"), those persons whose names are set forth on
Exhibit A hereto (collectively referred to herein as "Founders"), and the
Purchasers identified on Exhibit B attached hereto (collectively referred to
herein as "Purchasers" and individually as a "Purchaser").

                                    RECITALS:

         WHEREAS, the Purchasers desire to purchase, and the Company desires to
issue, convertible promissory notes (the "Notes") with an aggregate principal
amount of One Million Five Hundred Thousand Dollars ($1,500,000);

         WHEREAS, in consideration of the purchase by the Purchasers of the
Notes, the Company desires to sell and issue warrants (the "Warrants") to
purchase that number of shares of the Company's Series B Convertible Preferred
Stock ("Series B Stock") as determined in this Agreement and in the Warrants;

         WHEREAS, the Company, the Founders and certain of the Purchasers are
parties to an Amended and Restated Registration Rights Agreement, dated as of
February 12, 1997 (the "Rights Agreement"), which grants certain registration
and other rights to the parties thereof, and to an Amended and Restated
Stockholders' Agreement, dated as of February 12, 1997 (the "Stockholders'
Agreement"), which grants certain information and other rights to the parties
thereof,

         WHEREAS, the Company, the Founders and the Purchasers holding (i) at
least a majority of the outstanding shares of Restricted Stock (as such term is
defined in the Rights Agreement) wish to amend the Rights Agreement to include
as Preferred Shares (as such term is defined in the Rights Agreement) the Series
B Stock issuable upon exercise of the Warrants (the "Warrant Shares"), and (ii)
at least a majority of Shares (as such term is defined in the Stockholders'
Agreement) wish to amend the Stockholders' Agreement to include as Preferred
Shares (as such term is defined in the Stockholders' Agreement) the Warrant
Shares; and

         WHEREAS, the parties also wish to set forth certain representations,
warranties, covenants, and agreements relating to the purchase of the Notes and
Warrants provided for herein.

         NOW, THEREFORE, THE PARTIES HEREBY AGREE AS FOLLOWS:

         1. Authorization and Issuance of Notes and Warrants.

                  1.1 Authorization. The Company has authorized the sale and
issuance of the Notes and Warrants to the Purchasers.

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                  1.2 Sale and Issuance of Notes. Subject to the terms and
conditions hereof, the Company agrees to sell and issue to each of the
Purchasers, and the Purchasers severally agree to purchase from the Company, a
Note in the form attached as Exhibit C hereto, in the amount set forth opposite
such Purchaser's name on Exhibit B hereto.

                  1.3 Sale and Issuance of Warrants. Subject to the terms and
conditions hereof, the Company agrees to sell and issue to each of the
Purchasers, and the Purchasers severally agree to purchase from the Company,
Warrants originally exercisable, at an exercise price of $1.25 per share, for
that number of shares of Series B Stock set forth opposite such Purchaser's name
on Exhibit B hereto, in the form attached hereto as Exhibit D at a purchase
price of $.025 for each share of Series B Stock for which such Warrants are
originally exercisable, which Warrants and Warrant Shares shall be subject to
adjustment, as described in the Warrants.

         2. Closing.

                  2.1 Closing; Closing Date. The closing of the issuance of the
Notes and Warrants under this Agreement (the "Closing") shall take place on the
date of this Agreement (the "Closing Date"), in accordance with arrangements
mutually satisfactory to the Purchasers and counsel for the Company.

                  2.2 Closing Delivery. At the Closing, upon delivery to the
Company by wire transfer or check made payable to the order of the Company of
the aggregate purchase price for the Note and the Warrant set forth opposite
such Purchaser's name on Exhibit B hereto, the Company will deliver to each
Purchaser (a) a Note payable to the Purchaser in the principal amount set forth
opposite such Purchaser's name on Exhibit B hereto and (b) a Warrant to purchase
that number of shares of Series B Stock set forth opposite such Purchaser's name
on Exhibit B hereto.

         3. Amendments to the Rights Agreement. Each Purchaser agrees to be
bound by the terms and conditions of the Rights Agreement. In light of the
foregoing and in order to grant the Purchasers the registration rights and other
rights set forth in the Rights Agreement in respect of the Warrant Shares, the
Rights Agreement shall be amended as follows:

                           (a) The term "Preferred Shares" as set forth in
Section 1 of the Rights Agreement shall include the Warrant Shares hereunder.

         4. Amendments to the Stockholders' Agreement. Each Purchaser agrees to
be bound by the terms and conditions of the Stockholders' Agreement. In light of
the foregoing and in order to grant the Purchasers the information rights and
other rights set forth in the Stockholders' Agreement in respect of the Warrant
Shares, the Stockholders' Agreement shall be amended as follows:

                           (a) The term "Preferred Shares" as set forth in the
recitals of the Stockholders' Agreement shall include the Warrant Shares
hereunder.

                           (b) The issuance of the Notes, Warrants and Warrant
Shares shall be excluded from the right of first refusal in Section 2 of the
Stockholders' Agreement.

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         5. Amendment to Certificate of Incorporation. In order to authorize a
sufficient number of shares of Series B Stock for issuance upon exercise of the
Warrants, the Company shall adopt and file with the Secretary of State of the
State of Delaware on or before the Closing an amendment to its Second Amended
and Restated Certificate of Incorporation (the "Certificate of Incorporation")
substantially in the form attached hereto as Exhibit E to authorize an
additional _____________ shares of Series B Stock.

         6. Representations And Warranties of the Company.

                  6.1 Authorization. All corporate action on the part of the
Company, its officers, directors, and shareholders necessary for the
authorization, execution, and delivery of this Agreement, the performance of all
the Company's obligations hereunder and for the authorization, issuance, sale,
and delivery of the Notes, the Warrants, and the Warrant Shares has been taken
or will be taken prior to the Closing. This Agreement, the Notes and the
Warrants when executed and delivered, shall constitute the valid and legally
binding obligations of the Company enforceable in accordance with their
respective terms, subject to the laws of general application relating to
bankruptcy, insolvency, and the relief of debtors.

                  6.2 Validity of Notes, Warrants and Warrant Shares. The Notes
and Warrants, when issued in accordance with the terms of this Agreement, shall
be duty and validly issued. The issuance of the Warrants and any subsequent
issuance of the Warrant Shares are not and will not be subject to any rights of
first refusal or preemptive rights and, when issued, sold, and delivered in
compliance with the provisions of this Agreement and the terms of the Warrants
and in accordance with the Company's Certificate of Incorporation, as amended,
the Warrants and the Warrant Shares will be validly issued, fully paid, and
nonassessable, and will be free of any liens or encumbrances; provided, however,
that the Warrants and the Warrant Shares may be subject to restrictions on
transfer under state and/or federal securities laws as set forth herein or as
otherwise required by such laws at the time a transfer is proposed.

                  6.3 Governmental Consents. All consents, approvals, orders, or
authorizations of, or registrations, qualifications, designations, declarations,
or filings with, any governmental authority, required on the part of the Company
in connection with the valid execution and delivery of this Agreement, the
offer, sale, or issuance of the Notes, the Warrants, and the Warrant Shares, or
the consummation of any other transaction contemplated hereby shall have been
obtained and will be effective at the Closing, except for notices required or
permitted to be filed with certain state and federal securities commissions,
which notices will be filed on a timely basis.

         7. Representations and Warranties of the Purchasers. Each Purchaser,
severally and not jointly, hereby represents and warrants to the Company as
follows:

                  7.1 Legal Authority. It has the requisite legal power to enter
into this Agreement, to purchase the Note and Warrants hereunder and to carry
out and perform its obligations under the terms of this Agreement.

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                  7.2 Due Execution. This Agreement has been duly authorized,
executed, and delivered by it, and, upon execution and delivery by the Company,
this Agreement will be a valid and binding agreement of it.

                  7.3 Investment Representations.

                           (a) It is acquiring the Note and Warrants for its own
account, not as nominee or agent, for investment and not with a view to, or for
resale in connection with, any distribution or public offering of the Note,
Warrants, or Warrant Shares within the meaning of the Securities Act of 1933, as
amended (the "1933 Act").

                           (b) It understands that (i) the Note, Warrants, and
Warrant Shares have not been registered under the 1933 Act by reason of a
specific exemption therefrom, that they must be held by it indefinitely, and
that Purchaser must, therefore, bear the economic risk of such investment
indefinitely, unless a subsequent disposition thereof is registered under the
1933 Act or is exempt from such registration; and (ii) the Note, Warrants, and
each certificate representing the Warrant Shares will be endorsed with the
following legend:

         "THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
         1933, AS AMENDED. THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED,
         HYPOTHECATED OR OTHERWISE TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE
         REGISTRATION STATEMENT UNDER SUCH ACT OR PURSUANT TO AN OPINION OF
         COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT
         REQUIRED, OR UNLESS SOLD PURSUANT TO RULE 144 UNDER SUCH ACT."

                           (c) It has been furnished with such materials and has
been given access to such information relating to the Company as it or its
qualified representative has requested and it has been afforded the opportunity
to ask questions regarding the Company, the Notes, and the Warrants, all as it
has found necessary to make an informed investment decision.

                           (d) By reason of its business or financial
experience, or the business or financial experience of its professional advisor,
it has the capacity to protect its own interests in connection with this
transaction.

                           (e) If it is a corporation, partnership, trust, or
other entity, it was not formed for the specific purpose of acquiring the Notes
or Warrants offered hereunder.

                           (f) It is an "accredited investor" as provided under
the 1933 Act and regulations adopted thereunder; and all information supplied by
such Purchaser to the Company with respect to his or its purchase of the Notes
and Warrants has been and shall be true, complete, and accurate.

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         8. Miscellaneous.

                  8.1 Governing Law. This Agreement shall be governed by and
construed under the laws of the State of Texas as applied to agreements among
Texas residents, made and to be performed entirely within the State of Texas.

                  8.2 Successors and Assigns. Except as otherwise expressly
provided herein, the terms and conditions of this Agreement shall inure to the
benefit of, and be binding upon, the successors, assigns, heirs, executors, and
administrators of the parties hereto.

                  8.3 Entire Agreement. This Agreement, the Exhibits hereto, and
the other documents delivered pursuant hereto constitute the full and entire
understanding and agreement among the parties with regard to the subjects hereof
and no party shall be liable or bound to any other party in any manner by any
representations, warranties, covenants, or agreements except as specifically set
forth herein or therein.

                  8.4 Separability. Any invalidity, illegality, or limitation of
the enforceability with respect to any Purchaser of any one or more of the
provisions of this Agreement, or any part thereof, whether arising by reason of
the law of any such Purchaser's domicile or otherwise, shall in no way affect or
impair the validity, legality, or enforceability of this Agreement with respect
to other Purchasers. In case any provision of this Agreement shall be invalid,
illegal, or unenforceable, the validity, legality, and enforceability of the
remaining provisions shall not in any way be affected or impaired thereby.

                  8.5 Amendment and Waiver. Any term of this Agreement may be
amended and the observance of any term of this Agreement may be waived with the
written consent of the Company and the Purchasers of more than 50% of the
outstanding principal amount of the Notes.

                  8.6 Communications. All notices or other communications
hereunder shall be in writing and shall be given by personal delivery,
facsimile, overnight courier service, or by registered or certified mail
(postage prepaid and return receipt requested) addressed as set forth below (or
at such other address as a party may designate by notice to the other parties):

                  If to the Company:

                  ODYSSEY HEALTHCARE, INC.
                  717 North Harwood Drive
                  Suite 2580
                  Dallas, Texas 75201

                  If to the Purchasers:

                  At the respective addresses indicated for such Purchasers on
                  the signature pages hereof

Notice sent pursuant to or required by this Agreement shall be deemed given (i)
in the case of personal delivery, on the date of such delivery, (ii) in the case
of telex or facsimile transmission, on the date on which the sender receives
confirmation by telex or facsimile transmission that

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such notice was received by the addressee, provided that a copy of such
transmission is additionally sent by overnight air courier or mail as set forth
in (iii) or (iv), respectively, below; (iii) in the case of overnight air
courier, on the next business day following the day sent, with receipt confirmed
by the courier; and (iv) in the case of mailing by first class certified or
registered mail, postage prepaid, return receipt requested, on the fifth
business day following such mailing.

                  8.7 Expenses. The Company shall bear all expenses and legal
fees incurred by it and by the Purchasers with respect to this Agreement and the
transactions contemplated hereby; provided, however, that the Purchasers' legal
fees shall be fixed at Seven Thousand Dollars ($7,000).

                  8.8 Titles and Subtitles. The titles of the paragraphs and
subparagraphs of this Agreement are for convenience of reference only and are
not to be considered in construing this Agreement.

                  8.9 Counterparts. This Agreement may be executed in any number
of counterparts, each of which shall be deemed an original, but all of which
together shall constitute one instrument.

                  8.10 Miscellaneous. Each Purchaser hereby agrees that, if so
requested by the Company and the underwriter, such Purchaser shall not publicly
sell any securities issued upon exercise of the Warrants or conversion of the
Notes (other than securities being registered in such offering) without the
consent of such underwriters, until one hundred eighty (180) days following the
effective date of the registration statement relating to the Company's initial
underwritten public offering, provided that said one hundred eighty (180) day
period may be extended for up to an additional sixty (60) days upon the majority
vote of both the Company's Board of Directors and the Company's shareholders;
provided, however, all persons entitled to registration rights with respect to
shares of Common Stock who are not parties to the Rights' Agreement, all other
persons selling shares of Common Stock in such offering and all executive
officers and directors of the Company shall also have agreed not to sell
publicly their Common Stock under circumstances pursuant to the terms set forth
in this Section 8.10.

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         IN WITNESS WHEREOF, the Company has caused this Promissory Note and
Warrant Purchase Agreement to be signed by its duly authorized officer.

                                          ODYSSEY HEALTHCARE, INC.

                                          By:   /s/ Bradley J. Velie
                                             -----------------------------------

                                          Name:     Bradley J. Velie
                                               ---------------------------------

                                          Title:    VP
                                                --------------------------------

                                          PURCHASER:

                                          --------------------------------------
                                          (Please insert Purchaser name above)

                                          By:
                                             -----------------------------------
                                                        (sign here)

                                          Title:
                                                --------------------------------

<PAGE>   8

                                          FOUNDERS:

                                          --------------------------------------
                                                  Richard C. Burnham

                                          --------------------------------------
                                                  David C. Gasmire

                                          --------------------------------------
                                                  David W. Cross

                                          --------------------------------------
                                                  David L. Steffy

                                          --------------------------------------
                                                  Robert H. Calland

<PAGE>   9

                                          THREE ARCH PARTNERS, L.P.

                                          By: Three Arch Management, L.P.
                                          Its: General Partner

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

                                          THREE ARCH ASSOCIATES, L.P.

                                          By: Three Arch Management, L.P.
                                          Its: General Partner

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

<PAGE>   10

                                    EXHIBIT A

                              SCHEDULE OF FOUNDERS

Richard C. Burnham

David C. Gasmire

David W. Cross

David L. Steffy

Robert H. Calland

                                      E-1
<PAGE>   11

                                    EXHIBIT B

                             SCHEDULE OF PURCHASERS

<TABLE>
<CAPTION>

                                                NUMBER OF SHARES
                                                   OF SERIES B         PURCHASE
                                                   CONVERTIBLE         PRICE OF
                                                 PREFERRED STOCK      WARRANT AT
                                    AMOUNT      EXERCISABLE UNDER     $0.025 PER         TOTAL
             NAME                   OF NOTE          WARRANTS            SHARE         INVESTMENT
-----------------------------    -------------  -----------------    -------------    -------------

<S>                              <C>                     <C>       <C>              <C>
Three Arch Partners, L.P.        $  318,910.21           25,512    $      637.80    $  319,548.01
Three Arch Associates, L.P.          71,746.06            5,739           143.48        71,889.54
Weiss, Peck & Greer Venture
     Associates III, L.P.           175,144.05           14,011           350.28       175,494.33
WPG Enterprise Fund II, L.P.        210,635.79           16,850           421.25       211,057.04
Oak Investment Partners VI          371,593.11           29,727           743.18       372,336.29
Oak VI Affiliates                     8,669.97              693            17.33         8,687.30
Highland Capital Partners III
     Limited Partnership            166,448.83           13,315           332.88       166,781.71
Highland Entrepreneurs' Fund
     III Limited Partnership          6,935.37              554            13.85         6,949.22
Collinson Howe Venture
     Partners, Inc.                  10,836.51              866            21.65        10,858.16
David L. Steffy                     159,080.10           12,726           318.15       159,398.26
                                 -------------    -------------    -------------    -------------
                                 $1,500,000.00          119,993    $    2,999.85     1,502,999.85
                                 =============    =============    =============    =============
</TABLE><PAGE>   1
                                                                EXHIBIT 10.10.2

         THIS WARRANT AND THE SECURITIES ISSUABLE UPON THE EXERCISE HEREOF HAVE
         NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. THEY
         MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED, OR OTHERWISE
         TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT
         UNDER SUCH ACT, OR AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY
         THAT REGISTRATION IS NOT REQUIRED UNDER SUCH ACT, OR UNLESS SOLD
         PURSUANT TO RULE 144 UNDER SUCH ACT.

                              WARRANT TO PURCHASE
                      SERIES B CONVERTIBLE PREFERRED STOCK
                                       OF
                            ODYSSEY HEALTHCARE, INC.

                            VOID AFTER MAY 21, 2008

                  This Warrant is issued to ___________________, or its
registered assigns ("Holder") by Odyssey HealthCare, Inc., a Delaware
corporation (the "Company"), on May 22, 1998 (the "Warrant Issue Date") at a
purchase price of $.025 for each share of Preferred Stock (as defined below)
that this Warrant is originally exercisable. This Warrant is issued pursuant to
the terms of that certain Promissory Note and Warrant Purchase Agreement dated
as of the date hereof (the "Purchase Agreement").

                  1. Purchase of Shares. Subject to the terms and conditions
hereinafter set forth and set forth in the Purchase Agreement, the Holder is
entitled, upon surrender of this Warrant at the principal office of the Company
(or at such other place as the Company shall notify the holder hereof in
writing), to purchase from the Company up to ________________ (_________) fully
paid and nonassessable shares of Series B Convertible Preferred Stock of the
Company (the "Preferred Stock"). The number of shares of Preferred Stock
issuable pursuant to this Section 1 (the "Shares") shall be subject to
adjustment pursuant to Section 8 hereof.

                  2. Exercise Price. The purchase price for the Shares shall be
$1.25, as adjusted from time to time pursuant to Section 8 hereof (the
"Exercise Price").

                  3. Exercise Period. This Warrant shall be exercisable, in
whole or in part, during the term commencing on the Warrant Issue Date and
ending at 5:00 p.m. on May 21, 2008; provided, however, that in the event of
(a) the closing of the Company's sale or transfer of all or substantially all
of its assets or (b) the closing of the acquisition of the Company by another
entity by means of merger, consolidation or other transaction or series of
related transactions, resulting in the exchange of the outstanding shares of
the Company's capital stock such that the stockholders of the Company prior to
such transaction own, directly or indirectly, less than 50%

<PAGE>   2

of the voting power of the surviving entity, this Warrant shall, on the date of
such event, no longer be exercisable and become null and void. In the event of
a proposed transaction of the kind described above, the Company shall notify
the holder of the Warrant at least fifteen (15) days prior to the consummation
of such event or transaction.

                  4. Method of Exercise. While this Warrant remains outstanding
and exercisable in accordance with Section 3 above, the Holder may exercise, in
whole or in part, the purchase rights evidenced hereby. Such exercise shall be
effected by:

                           (a) the surrender of the Warrant, together with a
duly executed copy of the form of Notice of Election attached hereto, to the
Secretary of the Company at its principal offices; and

                           (b) the payment to the Company of an amount equal to
the aggregate Exercise Price for the number of Shares being purchased.

                  5. Net Exercise. In lieu of exercising this Warrant pursuant
to Section 4, the Holder may elect to receive, without the payment by the
Holder of any additional consideration, shares of Preferred Stock equal to the
value of this Warrant (or the portion thereof being canceled) by surrender of
this Warrant at the principal office of the Company together with notice of
such election, in which event the Company shall issue to the holder hereof a
number of shares of Preferred Stock computed using the following formula:

                                            Y(A-B)
                                            ------
                                    X=         A

            Where X = The number of shares of Preferred Stock to be issued to
                      the Holder pursuant to this net exercise;

                  Y = The number of Shares in respect of which the net issue
                      election is made:

                  A = The fair market value of one share of the Preferred Stock
                      at the time the net issue election is made;

                  B = The Exercise Price (as adjusted to the date of the net
                      issuance).

For purposes of this Section 5, the fair market value of one share of Preferred
Stock (or, Common Stock to the extent all such Preferred Stock has been
converted into the Company's Common Stock) as of a particular date shall be
determined in good faith by the Board of Directors of the Company; provided,
that, (i) if the Warrant is being exercised upon the closing of the Company's
first underwritten public offering pursuant to an effective registration
statement under the Securities Act of 1933, as amended, the value will be the
initial "Price to Public" of one share of such Preferred Stock (or Common Stock
issuable upon conversion of such Preferred Stock) specified in the final
prospectus with respect to such offering and (ii) if there is a public trading
market for the Company's Preferred Stock (or Common Stock) the value will be
the closing price of such shares on the day before the date of exercise.

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                  6. Certificates for Shares. Upon the exercise of the purchase
rights evidenced by this Warrant, one or more certificates for the number of
Shares so purchased shall be issued as soon as practicable thereafter (with
appropriate restrictive legends, if applicable), and in any event within thirty
(30) days of the delivery of the subscription notice.

                  7. Issuance of Shares. The Company covenants that the Shares,
when issued pursuant to the exercise of this Warrant, will be duly and validly
issued, fully paid and nonassessable and free from all taxes, liens, and
charges with respect to the issuance thereof.

                  8. Adjustment of Exercise Price and Number of Shares. The
number of and kind of securities purchasable upon exercise of this Warrant and
the Exercise Price shall be subject to adjustment from time to time as follows:

                     (a) Subdivisions, Combinations and Other Issuances. If the
Company shall at any time prior to the expiration of this Warrant subdivide its
Preferred Stock, by split-up or otherwise, or combine its Preferred Stock, or
issue additional shares of its Preferred Stock as a dividend with respect to
any shares of its Preferred Stock, the number of Shares issuable on-the
exercise of this Warrant shall forthwith be proportionately increased in the
case of a subdivision or stock dividend, or proportionately decreased in the
case of a combination. Appropriate adjustments shall also be made to the
purchase price payable per share, but the aggregate purchase price payable for
the total number of Shares purchasable under this Warrant (as adjusted) shall
remain the same. Any adjustment under this Section 8(a) shall become effective
at the close of business on the date the subdivision or combination becomes
effective, or as of the record date of such dividend, or in the event that no
record date is fixed, upon the making of such dividend.

                     (b) Reclassification, Reorganization and Consolidation. In
case of any reclassification, capital reorganization, or change in the
Preferred Stock of the Company (other than as a result of a subdivision,
combination, or stock dividend provided for in Section 8(a) above), then, as a
condition of such reclassification, reorganization, or change, lawful provision
shall be made, and duly executed documents evidencing the same from the Company
or its successor shall be delivered to the Holder, so that the Holder shall
have the right at any time prior to the expiration of this Warrant to purchase,
at a total price equal to that payable upon the exercise of this Warrant, the
kind and amount of shares of stock and other securities and property receivable
in connection with such reclassification, reorganization, or change by a holder
of the same number of shares of Preferred Stock as were purchasable by the
Holder immediately prior to such reclassification, reorganization, or change.
In any such case appropriate provisions shall be made with respect to the
rights and interest of the Holder so that the provisions hereof shall
thereafter be, applicable with respect to any shares of stock or other
securities and property deliverable upon exercise hereof, and appropriate
adjustments shall be made to the purchase price per share payable hereunder,
provided the aggregate purchase price shall remain the same.

                     (c) Notice of Adjustment. When any adjustment is required
to be made in the number or kind of shares purchasable upon exercise of the
Warrant, or in the Warrant Price, the Company shall promptly notify the holder
of such event and of the number of

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shares of Preferred Stock or other securities or property thereafter
purchasable upon exercise of this Warrant.

                  9. No Fractional Shares or Scrip. No fractional shares or
scrip representing fractional shares shall be issued upon the exercise of this
Warrant, but in lieu of such fractional shares the Company shall make a cash
payment therefor on the basis of the Exercise Price then in effect.

                  10. No Stockholder Rights. Prior to exercise of this Warrant,
the Holder shall not be entitled to any rights of a stockholder with respect to
the Shares, including (without limitation) the right to vote such Shares,
receive dividends or other distributions thereon, exercise preemptive rights or
be notified of stockholder meetings, and such holder shall not be entitled to
any notice or other communication concerning the business or affairs of the
Company. However, nothing in this Section 10 shall limit the right of the
Holder to be provided the Notices required under this Warrant or the Purchase
Agreement.

                  11. Transfers of Warrant. Subject to compliance with
applicable federal and state securities laws, this Warrant and all rights
hereunder are transferable in whole by the Holder to any person or entity upon
written notice to the Company. The transfer shall be recorded on the books of
the Company upon the surrender of this Warrant, properly endorsed, to the
Company at its principal offices, and the payment to the Company of all
transfer taxes and other governmental charges imposed on such transfer.

                  12. Successors and Assigns. The terms and provisions of this
Warrant and the Purchase Agreement shall inure to the benefit of, and be
binding upon, the Company and the Holders hereof and their respective
successors and assigns.

                  13. Amendments and Waivers. Any term of this Warrant may be
amended and the observance of any term of this Warrant may be waived (either
generally or in a particular instance and either retroactively or
prospectively), with the written consent of the Company and the holders of more
than 50% of shares of Preferred Stock issued or issuable upon exercise of
Warrants issued pursuant to the Purchase Agreement that are then outstanding.
Any waiver or amendment effected in accordance with this Section shall be
binding upon each holder of any Shares purchased under this Warrant at the time
outstanding (including securities into which such Shares have been converted),
each future holder of all such Shares, and the Company.

                  14. Effect of Amendment or Waiver. The Holder acknowledges
that by the operation of Section 13 hereof, the holders of more than 50% of
shares of Preferred Stock issued or issuable upon exercise of Warrants issued
pursuant to the Purchase Agreement will have the right and power to diminish or
eliminate all rights of such holder under this Warrant or under the Purchase
Agreement.

                  15. Notices. All notices required under this Warrant and
shall be deemed to have been given or made for all purposes (i) upon personal
delivery, (ii) upon confirmation receipt that the communication was
successfully sent to the applicable number if sent by facsimile; (iii) one day
after being sent, when sent by professional overnight courier service, or

                                       4
<PAGE>   5

(iv) five days after posting when sent by registered or certified mail. Notices
to the Company shall be sent to the principal office of the Company (or at such
other place as the Company shall notify the Holder hereof in writing). Notices
to the Holder shall be sent to the address of the Holder on the books of the
Company (or at such other place as the Holder shall notify the Company hereof
in writing).

                  16. Attorneys' Fees. If any action of law or equity is
necessary to enforce or interpret the terms of this Warrant, the prevailing
party shall be entitled to its reasonable attorneys' fees, costs and
disbursements in addition to any other relief to which it may be entitled.

                  17. Captions. The section and subsection headings of this
Warrant are inserted for convenience only and shall not constitute a part of
this Warrant in construing or interpreting any provision hereof.

                  18. Governing Law. This Warrant shall be governed by the laws
of the State of Texas as applied to agreements among Texas residents made and
to be performed entirely within the State of Texas.

                                       5
<PAGE>   6

                  IN WITNESS WHEREOF, the Company caused this Warrant to be
executed by an officer thereunto duly authorized.

                                     ODYSSEY HEALTHCARE, INC.

                                     By:
                                          -------------------------------------

                                     Name:
                                           ------------------------------------

                                     Title:
                                            -----------------------------------

<PAGE>   7
                               NOTICE OF EXERCISE

To: ODYSSEY HEALTHCARE, INC.

                  The undersigned hereby elects to [check applicable
subsection]:

-----------       (a)  Purchase _______________ shares of Series B Convertible
                       Preferred Stock of Odyssey HealthCare, Inc., pursuant to
                       the terms of the attached Warrant and payment of the
                       Exercise Price per share required under such Warrant
                       accompanies this notice;

                  OR

-----------       (b)  Exercise the attached Warrant for [all of the shares]
                       [_______ of the shares] [cross out inapplicable phrase]
                       purchasable under the Warrant pursuant to the net
                       exercise provisions of Section 5 of such Warrant.

                  The undersigned hereby represents and warrants that the
undersigned is acquiring such shares for its own account for investment
purposes only, and not for resale or with a view to distribution of such shares
or any part thereof.

                                 WARRANTHOLDER:

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

                                 By:
                                     ------------------------------------------
                                             [NAME]

                                 Address:
                                          -------------------------------------

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

Date:
       ------------------

Name in which shares should be registered:

-----------------------------------------
<PAGE>   8

                            LIST OF WARRANT HOLDERS

<TABLE>
<CAPTION>
                                                                             NUMBER OF
                HOLDER NAME                                     DATE           SHARES
                -----------                                     ----         ---------
<S>                                                            <C>           <C>
 1  Three Arch Partners, L.P.                                  5/22/98        25,512
 2  Three Arch Associates, L.P.                                5/22/98         5,739
 3  Weiss, Peck & Greer Venture Associates III, L.P.           5/22/98        14,011
 4  WPG Enterprise Fund II, L.P.                               5/22/98        16,850
 5  Oak Investment Partners VI                                 5/22/98        29,727
 6  Oak VI Affiliates                                          5/22/98           693
 7  Highland Capital Partners III Limited Partnership          5/22/98        13,315
 8  Highland Entrepreneurs Fund III Limited Partnership        5/22/98           554
 9  Collinson Home Venture Partners, Inc.                      5/22/98           866
10  David L. Steffy                                            5/22/98        12,726
                                                                             -------
    Total outstanding                                                        119,993
</TABLE>

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