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                                                                     EXHIBIT 4.3

                            ODYSSEY HEALTHCARE, INC.
            SECOND AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT

         THIS SECOND AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT (this
"AGREEMENT") dated as of July 1, 1998, is made and entered into by and among (i)
ODYSSEY HEALTHCARE, INC., a Delaware corporation (the "COMPANY"), (ii) RICHARD
R. BURNHAM, DAVID C. GASMIRE, DAVID W. CROSS, DAVID L. STEFFY, ROBERT H.
CALLAND, THREE ARCH PARTNERS, L.P. and THREE ARCH ASSOCIATES, L.P. (said five
individuals and said entities referred to individually as "FOUNDER" and
collectively as "FOUNDERS"), (iii) CAPITAL RESOURCE LENDERS III, LP., a Delaware
limited partnership ("CRL III") and CRP INVESTMENT PARTNERS III, L.L.C., a
Delaware limited liability company ("CRP INVESTMENT" and, together with CRL III,
the "NOTE PURCHASERS"), and (iv) the persons set forth on Schedule B hereto
(such persons referred to individually as "INVESTOR" and collectively as
"INVESTORS"). This Agreement amends, restates and supersedes the Amended and
Restated Registration Rights Agreement dates as of February 12, 1997 by and
among the Company, the founders and certain of the Investors.

                                    RECITALS

         WHEREAS, the Founders are the holders of an aggregate of 3,643,000
shares of Common Stock, $0.001 par value per share, of the Company;

         WHEREAS, the Company has previously issued and sold to certain of the
Investors (i) 7,091,091 shares of Series A Convertible Preferred Stock, $0.001
par value per share, of the Company the "SERIES A CONVERTIBLE PREFERRED STOCK")
pursuant to that certain Series A Convertible Preferred Stock Purchase Agreement
dated as of January 26, 1996 (the "SERIES A PURCHASE AGREEMENT") by and among
the Company and certain of the Investors and (ii) 6,400,000 shares of Series B
Convertible Preferred Stock, $0.001 par value per share, of the Company (the
"SERIES B CONVERTIBLE PREFERRED STOCK") pursuant to that certain Series B
Convertible Preferred Stock Purchase Agreement dated as of February 12, 1997 (
the "SERIES B PURCHASE AGREEMENT") by and among the Company and certain of the
Investors;

         WHEREAS, the Company has previously issued and sold to certain of the
Investors (i) its convertible promissory notes in the aggregate principal amount
of $1,500,000 and (ii) warrants (the "PREFERRED WARRANTS") for the purchase
(subject to adjustment as provided therein) of an aggregate of 119,993 shares of
Series B Preferred Stock, in each case pursuant to that certain Promissory Note
and Warrant Purchase Agreement dated as of May 22, 1998 (the "BRIDGE NOTE
PURCHASE AGREEMENT") by and among the Company, the Founders and certain of the
Investors;

         WHEREAS, certain of the Investors propose to purchase an aggregate of
2,857,137 shares of Series C Convertible Preferred Stock, $0.001 par value per
share, of the Company (the "SERIES C CONVERTIBLE PREFERRED Stock") pursuant to a
certain Series C Convertible Preferred Stock Purchase Agreement dated as of the
date hereof (the "SERIES C PURCHASE AGREEMENT") by and among the Company and
certain of the Investors;


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         WHEREAS, the Note Purchasers propose to purchase (i) 12.0% Senior
Subordinated Notes due 2005 in the aggregate principal amount of $12,000,000
from the Company and certain of its subsidiaries and (ii) Common Stock Purchase
Warrants (the "NOTE WARRANTS") for the purchase (subject to adjustment as
provided therein) of an aggregate of 1,943,520 shares of Common Stock, $0.001
par value per share of the Company, in each case pursuant to that certain Senior
Subordinated Note and Warrant Purchase Agreement dated as of the date hereof
(the "NOTE PURCHASE AGREEMENT") among the Company and the Note Purchasers; and

         WHEREAS, as a condition precedent to the parties closing under the
Series C Agreement and the Note Purchase Agreement, the parties have required
that this Agreement be executed and delivery by the Company the Founders and the
Investors.

         NOW, THEREFORE, the parties agree as follows:

         1. CERTAIN DEFINITIONS. As used in this Agreement, the following terms
shall have the following respective meanings:

                  "Commission shall mean the Securities and Exchange Commission,
         or any other federal agency at the time administering the Securities
         Act.

                  "Common Stock" shall mean the Common Stock, $0.001 par value,
         of the Company, as constituted as of the date of this Agreement.

                  "Conversion Shares shall mean (i) shares of Common Stock
         issued or issuable upon conversion of the Preferred Shares, (ii) the
         Note Warrant Shares and (iii) any shares of Common Stock issued as (or
         issuable upon the conversion or exercise of any warrant, right, or the
         security which is issued as) a dividend or other distribution with
         respect to, in exchange for, or in replacement of the shares referenced
         in clauses (i) and (ii) above.

                  "Exchange Act" shall mean the Securities Exchange Act of 1934,
         as amended, or any similar federal statute, and the rules and
         regulations of the Commission thereunder, all as the same shall be in
         effect at the time.

                  "Founders' Stock" shall mean all shares of Common Stock held
         by the Founders, except such shares which have been (a) registered
         under the Securities Act pursuant to an effective registration
         statement filed thereunder and disposed of in accordance with the
         registration statement covering them, (b) publicly sold pursuant to
         Rule 144 under the Securities Act, or (c) acquired by any person or
         entity which, by virtue of Section 13(a), is not entitled to the
         benefits of and rights conferred by this Agreement.

                  "Note Warrant Shares" shall mean the shares of Common Stock
         issued or issuable upon exercise of the Note Warrants issued pursuant
         to the Note Purchase Agreement.

                  "Preferred Shares" shall mean (i) the shares of Series A
         Convertible Preferred Stock issued pursuant to the Series A Purchase
         Agreement, (ii) the shares of Series B Convertible Preferred Stock
         issued pursuant to the Series B Purchase Agreement, (iii) the


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         shares of Series C Convertible Preferred Stock issued pursuant to the
         Series C Purchase Agreement, and (iv) the Preferred Warrant Shares.

                  "Preferred Warrant Shares" shall mean the shares of Series B
         Convertible Preferred Stock issued or issuable upon exercise of the
         Preferred Warrants issued pursuant to the Bridge Note Purchase
         Agreement.

                  "Registrable Stock" shall mean all shares of Restricted Stock
         and all shares of Founders Stock (and all shares of Common stock issued
         by the Company in respect of such shares).

                  "Registration Expenses" shall have the meaning set forth in
         Section 8 hereof.

                  "Restricted Stock" shall mean the Conversion Shares, excluding
         Conversion Shares which have been (a) registered under the Securities
         Act pursuant to an effective registration statement filed thereunder
         and disposed of in accordance with the registration statement covering
         them, (b) publicly sold pursuant to Rule 144 under the Securities Act,
         or (c) acquired by any person or entity which, by virtue of Section
         13(a), is not entitled to the benefits of and rights conferred by this
         Agreement.

                  "Securities Act" shall mean the Securities Act of 1933, as
         amended, or any similar federal statute, and the rules and regulations
         of the Commission thereunder, all as the same shall be in effect at the
         time.

                  "Selling Expenses" shall have the meaning set forth in Section
         8 hereof.

         2. RESTRICTIVE LEGEND. Each certificate representing Preferred Shares,
Conversion Shares or Founders' Stock, shall, except as otherwise provided in
this Section 2 or in Section 3, be stamped or otherwise imprinted with a legend
substantially in the following form:

                  "THE ISSUANCE OF THIS SECURITY HAS NOT BEEN REGISTERED UNDER
                  THE SECURITIES ACT OF 1933, AS AMENDED (the "ACT"), OR THE
                  SECURITIES LAWS OF ANY STATE AND THIS SECURITY MAY NOT BE
                  TRANSFERRED OR OTHERWISE DISPOSED OF UNLESS SUCH TRANSACTION
                  HAS BEEN REGISTERED UNDER THE ACT AND ALL APPLICABLE STATE
                  SECURITIES LAWS OR AN EXEMPTION FROM REGISTRATION IS
                  AVAILABLE."

A certificate shall not bear such legend if in the opinion of counsel
satisfactory to the Company (it being agreed that Vinson & Elkins L.L.P. shall
be satisfactory) the securities being sold thereby may be publicly sold without
registration under the Securities Act.

         3. NOTICE OF PROPOSED TRANSFER. Prior to any proposed transfer of any
Registrable Stock (other than under the circumstances described in Sections 4, 5
or 6 hereof) the holder thereof shall give written notice to the Company of its
intention to effect such transfer. Each such notice shall describe the manner of
the proposed transfer and, if requested by the Company, shall be accomplished by
an opinion of counsel reasonably satisfactory to the Company (it being agreed
that Vinson & Elkins L.L.P. shall be satisfactory) to the effect that the
proposed transfer


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may be effected without registration under the Securities Act, whereupon the
holder of such stock shall be entitled to transfer such stock in accordance with
the terms of its notice; provided, however, that no such opinion of counsel
shall be required for a transfer to one or more partners of the transferor (in
the case of a transferor that is a corporation or partnership). Each certificate
for Registrable Stock transferred as above provided shall bear the legend set
forth in Section 2 hereof, except that such certificate shall not bear such
legend if (i) such transfer is in accordance with the provisions of Rule 144 (or
any other rule permitting public sale without registration under the Securities
Act) or (ii) the opinion of counsel referred to above is to the further effect
that the transferee and any subsequent transferee (other than an affiliate of
the Company) would be entitled to transfer such securities in a public sale
without registration under the Securities Act. The restrictions provided for in
this Section 3 shall not apply to securities which are not required to bear the
legend prescribed by Section 2 in accordance with the provisions of that
Section.

         4. REQUIRED REGISTRATION. (a) At any time after the earlier of (i) six
(6) months after any registration statement covering a public offering of
securities of the Company under the Securities Act shall have become effective,
and (ii) the fourth anniversary of the date of this Agreement, the holders of
Restricted Stock constituting at least sixty-six and two-thirds percent (66
2/3%) of the total shares of Restricted Stock then outstanding may request the
Company to register under the Securities Act all or any portion of the shares of
Restricted Stock held by such requesting holder or holders for sale in the
manner specified in such notice, provided that the minimum offering price of
such Restricted Stock shall be at least $1,000,000. For purposes of this Section
4 and Sections 5, 6, 13(a) and 13(d), the term "Restricted Stock" shall be
deemed to include (i) the number of shares of Restricted Stock which would be
issuable to a holder of Preferred Shares upon conversion of all Preferred Shares
held by such holder at such time, (ii) the number of shares of Restricted Stock
which would be issuable, at such time, to a holder of Preferred Warrants upon
the exercise of such Preferred Warrant and subsequent conversion of the
Preferred Warrant Shares, and (iii) the number of shares of Restricted Stock
which would be issuable, at such time, to a holder of Note Warrants upon the
exercise of such Note Warrants, provided, however, that the only securities
which the Company shall be required to register in any underwritten public
offering contemplated by this Section 4 or Sections 5 and 6, a holder of
Preferred Shares, Preferred Warrants, Preferred Warrant Shares or Note Warrants
shall be entitled to sell such Preferred Shares, Preferred Warrants, Preferred
Warrant Shares or Note Warrants to the Underwriters for conversion or exercise,
as the case may be, and sale of the shares of Common Stock issued upon
conversion or exercise thereof. Notwithstanding anything to the contrary
contained herein, no request may be made under this Section 4 within one hundred
eighty (180) days after the effective date of a registration statement filed by
the Company covering a firm commitment underwritten public offering in which the
holders of Restricted Stock shall have been entitled to join pursuant to
Sections 5 or 6 in which there shall have been effectively registered all shares
of Restricted Stock as to which registration shall have been requested;
provided, further, that such one hundred eighty (180) day period may be extended
for up to an additional sixty (60) days by a majority vote of both the Company's
Board of Directors and the Company's shareholders.

                  (b) Following receipt of any notice under Section 4(a), the
Company shall immediately notify all holders of Restricted Stock from whom
notice has not been received and shall use its best efforts to register under
the Securities Act, for public sale in accordance with


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the method of disposition specified in such notice from requesting holders, the
number of shares of Restricted Stock specified in such notice (and in all
notices received by the Company from other holders within thirty (30) days after
the giving of such notice by the Company). If such method of disposition shall
be an underwritten public offering, the holders of sixty-six and two-thirds
percent (66 2/3%) of the shares of Restricted Stock to be sold in such offering
may designate the managing underwriter of such offering, subject to the approval
of the Company, which approval shall not be unreasonably withheld or delayed.
The Company shall be obligated to register Restricted Stock pursuant to this
Section 4 on two occasions only, provided, however, that such obligation shall
be deemed satisfied only when a registration statement covering all shares of
Restricted Stock specified in notices received as aforesaid, for sale in
accordance with the method of disposition specified by the requesting holders,
shall have become effective and, if such method of disposition is a firm
commitment underwritten public offering, all such shares shall have been sold
pursuant thereto.

                  (c) The Founders shall be entitled to include in any
registration statement referred to in this Section 4, for sale in accordance
with the method of disposition specified by the requesting holders, Founders'
Stock to be sold by the Founders for their own account, except as and to the
extent that, in the opinion of the managing underwriter (if such method of
disposition shall be an underwritten public offering), such inclusion would
adversely affect the marketing of the Restricted Stock to be sold. In such
event, the number of shares of Founders' Stock to be registered on behalf of the
Founders, if any, shall be computed as set forth in Section 4(e) below. At the
time the Company shall give notice to the holders of Restricted Stock required
by Section 4(b), it shall also give the same notice to the Founders, whereupon
the Founders shall give written notice to the Company within thirty (30) days
after receipt of such notice if they propose to dispose of any shares of
Founders' Stock held by them pursuant to such registration, stating the number
of shares of Founders' Stock to be disposed of by such Founder or Founders.

                  (d) The Company shall also be entitled in any registration
statement referred to in this Section 4, for sale in accordance with the method
of disposition specified by the requesting holders, shares of Common Stock to be
sold by the Company for its own account, except as and to the extent that, in
the opinion of the managing underwriter (if such method of disposition shall be
an underwritten public offering), such inclusion would adversely affect the
marketing of the Restricted Stock to be sold. In such event, no shares of Common
Stock shall be registered on behalf of the Company, as set forth in Section 4(e)
below. Except for registration statements on Form S-4, S-8 or any successor
thereto, the Company will not file with the Commission any other registration
statement with respect to its Common Stock, whether for its own account or that
of other stockholders, from the date of receipt of a notice from requesting
holders pursuant to Section 4(a) until the completion of the period of
distribution of the registration contemplated thereby.

                  (e) Whenever a registration requested pursuant to this Section
4 is for an underwritten public offering, only shares of Common Stock which are
to be included in the underwriting may be included in the registration.
Notwithstanding the provisions of Section 4(c) and 4(d), if the underwriter (or
managing underwriter if there is more than one underwriter) determines that the
marketing factors require a limitation of the total number of shares of


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Common Stock to be underwritten, then the number of shares to be included in the
registration in the underwriting shall be allocated as follows:

                  Eighty-five percent (85%) among all holders who indicated to
         the Company their decision to distribute any of their Restricted Stock
         in accordance with the provisions of Sections 4(a) and 4(b) hereof
         through such underwriting, in proportion, as nearly as practicable, to
         the respective number of shares of Restricted Stock owned by such
         holders at the time of filing the registration statement. The remaining
         fifteen percent (15%) of shares of Common Stock to be included shall be
         allocated among the holders of Founders' Stock who have indicated to
         the Company their decision to distribute any of the Founders' Stock in
         accordance with Section 4(b) hereof through such underwriting, in
         proportion, as nearly as practicable, to the respective number of
         shares of Restricted Stock and Founders' Stock owned by such holders at
         the time of filing the registration statement.

         No stock excluded from the underwriting by virtue of the underwriter's
marketing limitation shall be included in such registration. If any Founder
disapproves of any such underwriting, such person may elect to withdraw
therefrom by written notice to the holders of Restricted Stock and the
underwriter (or managing underwriter if there is more than one underwriter). The
securities so withdrawn from such underwriting shall also be withdrawn from such
registration.

         Notwithstanding the foregoing, in any case other than a firm commitment
underwritten initial public offering, the number of shares of Restricted Stock
shall not be reduced if any shares are to be included in such underwriting for
the account of any person other than the Company or requesting holders of
Restricted Stock and in no event may less than one-fourth (1/4th) of the total
number of shares of Common Stock to be included in such underwriting be made
available for shares of Restricted Stock. Notwithstanding the foregoing
provisions, the Company may withdraw any registration statement referred to in
this Section 4 without thereby incurring any liability to holders of Registrable
Stock.

         5. INCIDENTAL REGISTRATION. (a) If the Company at any time (other than
pursuant to Section 4 or Section 6) proposes to registered any of its securities
under the Securities Act for sale to the public, whether for its own account or
for the account of other security holders or both (except with respect to
registration statements on Forms S-4, S-8 or their respective successors or
another form not available for registering the Registrable Stock for sale to the
public), each such time it will give written notice to all holders of
outstanding Registrable Stock of its intention so to do. Upon the written
request of any such holder, received by the Company within thirty (30) days
after the giving of any such notice by the Company, to register any of its
Registrable Stock (which request shall state the intended method of disposition
thereof), the Company will use its best efforts to cause the Registrable Stock
as to which registration shall have been so requested to be included in the
securities to be covered by the registration statement proposed to be filed by
the Company, all to the extent requisite to permit the sale or other disposition
by the holder (in accordance with its written request) of such Registrable Stock
so registered. In the event that any registration pursuant to this Section 5
shall be, in whole or in part, an underwritten public offering of Common Stock,
the number of shares of Registrable Stock to be included in such an underwriting
may be reduced if and to the extent that the managing underwriter shall be of
the


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opinion that such inclusion would adversely affect the marketing of the
securities to be sold by the Company therein, as provided for in Section 5(b).

                  (b) Whenever a proposed registration is for an underwritten
public offering pursuant to this Section 5, only shares which are to be included
in the underwriting may be included in the registration. Notwithstanding the
provisions of Section 5(a), if the underwriter (or managing underwriter if there
is more than one underwriter) determines that marketing factors require a
limitation of the total number of shares of Common Stock to be underwritten or a
limitation of the total number of shares of Registrable Stock to be
underwritten, then the number of shares of Registrable Stock to be included in
the registration in the underwriting shall be allocated as follows:

                  The Company shall be permitted to issue the maximum number of
         shares recommended by the underwriter (or managing underwriter if there
         is more than one underwriter). To the extent that the underwriter's
         marketing limitation on shares to be included in the offering permits
         additional shares to be offered, Founders' Stock and Restricted Stock
         shall be allocated among the holders of Founders' Stock and Restricted
         Stock who have indicated to the Company their decision to distribute
         any of the Founders' Stock or Restricted Stock through such
         underwriting, in proportion, as nearly as practicable, to the
         respective number of shares of Founders' Stock and Restricted Stock
         owned by such holders at the time of filing the registration statement.

         No stock excluded from the underwriting by virtue of the underwriter's
marketing limitation shall be included in such registration. If any holder of
Restricted Stock of Founders' Stock disapproves of any such underwriting, such
person may elect to withdraw therefrom by written notice to the Company and the
underwriter (or managing underwriter if there is more than one underwriter). The
securities so withdrawn from such underwriting shall also be withdrawn from such
registration.

         6. REGISTRATION ON FORM S-3. If any time (i) a holder or holders of at
least forty percent (40%) of the Preferred Shares, the Note Warrants, the Note
Warrant Shares or Restricted Stock request that the Company file a registration
statement on Form S-3 or any successor thereto for a public offering of all or
any portion of the shares of Restricted Stock held by such requesting holder or
holders, the reasonably anticipated aggregate price to the public of which would
exceed $1,000,000 and (ii) the Company is a registrant entitled to use Form S-3
or any successor thereto to register such shares, then the Company shall use its
best efforts to register under the Securities Act on From S-3 or any successor
thereto, for public sale in accordance with the method of disposition specified
in such notice, the number of shares of Restricted Stock specified in such
notice. Whenever the Company is required by this Section 6 to use its best
efforts to effect the registration of Restricted Stock, each of the procedures
and requirements of Section 4 (including but not limited to the requirement that
the Company notify all holders of Restricted Stock from whom notice has not been
received and all Founders and provide them with the opportunity to participate
in the offering) shall apply to such registration, provided, however, that the
requirements contained in the first sentence of Section 4(a) shall not apply to
any registration on Form S-3 which may be requested and obtained under this
Section 6. Notwithstanding anything to the contrary contained herein, no request
may be made under this Section 6 within one hundred eighty (180) days after the
effective date of a registration statement


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filed by the Company covering a firm commitment underwritten public offering in
which the holders of the Restricted Stock shall have been entitled to join
pursuant to Sections 4 or 5 in which there shall have been effectively
registered all shares of Restricted Stock as to which registration shall have
been requested, provided, further, that such 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 shareholders.

         7. REGISTRATION PROCEDURES. If and whenever the Company is required by
the provisions of Section 4, 5 or 6 to use its best efforts to effect the
registration of any shares of Registrable Stock under the Securities Act, the
Company will, as expeditiously as possible:

                  (a) Prepare and file with the Commission a registration
statement (which, in the case of an underwritten public offering pursuant to
Section 4, shall be on Form S-1 or other form of general applicability
satisfactory to the managing underwriter selected as therein provided) with
respect to such securities and use its best efforts to cause such registration
statement to become and remain effective for the period of the distribution
contemplated thereby (determined as hereinafter provided);

                  (b) Prepare and file with the Commission such amendments and
supplements to such registration statement and the prospectus used in connection
therewith as may be necessary to keep such registration statement effective for
the period specified in Paragraph (a) above and comply with the provisions of
the Securities Act with respect to the disposition of all Registrable Stock
covered by such registration statement in accordance with the sellers' intended
method of disposition set forth in such registration statement for such period;

                  (c) Furnish to each seller of Registrable Stock and to each
underwriter such number of copies of the registration statement and the
prospectus included therein (including each preliminary prospectus) as such
persons reasonably may request in order to facilitate the public sale or other
disposition of the Registrable Stock covered by such registration statement;

                  (d) Use its best efforts to register or qualify the
Registrable Stock covered by such registration statement under the securities or
"blue sky" laws of such jurisdictions as the sellers of Registrable Stock, or in
the case of an underwritten public offering, the managing underwriter reasonably
shall request, provided, however, that the Company shall not for any such
purpose be required to qualify generally to transact business as a foreign
corporation in any jurisdiction where it is not so qualified or to consent to
general service of process in any such jurisdiction;

                  (e) Use its best efforts to list the Registrable Stock covered
by such registration statement with any securities exchange on which the Common
Stock of the Company is then listed;

                  (f) Immediately notify each seller of Registrable Stock and
each underwriter under such registration statement, at any time when a
prospectus relating thereto is required to be delivered under the Securities
Act, of the happening of any event of which the Company has knowledge as a
result of which the prospectus contained in such registration statement, as then
in


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effect, includes an untrue statement of a material fact required to be stated
therein or necessary to make the statements therein not misleading in light of
the circumstances then existing;

                  (g) If the offering is underwritten and at the request of any
seller of Registrable Stock, use its best efforts to furnish on the date that
Registrable Stock is delivered to the underwriters for sale pursuant to such
registration: (i) an opinion dated such date of counsel representing the Company
for purposes of such registration, addressed to the underwriters and to such
seller, stating that such registration statement has become effective under the
Securities Act and that (A) to the best knowledge of such counsel, no stop order
suspending the effectiveness thereof has been issued and no proceedings for that
purpose have been instituted or are pending or contemplated under the Securities
Act, (B) the registration statement, the related prospectus and each amendment
or supplement thereof comply as to form in all material respects with the
requirements of the Securities Act (except that such counsel need not express
any opinion as to financial statements contained therein) and (C) to such other
effects as reasonably may be requested by counsel for the underwriters or by
such seller or its counsel and (ii) a letter dated such date from the
independent public accountants retained by the Company, addressed to the
underwriters and to such seller, stating that they are independent public
accountants within the meaning of the Securities Act and that, in the opinion of
such accountants, the financial statements of the Company included in the
registration statements or the prospectus, or any amendment or supplement
thereof, comply as to form in all material respects with the applicable
accounting requirements of the Securities Act, and such letter shall
additionally cover such other financial matters (including information as to the
period ending no more than five (5) business days prior to the date of such
letter) with respect to such registration as such underwriters reasonably may
request; and

                  (h) Make available for inspection by each seller of
Registrable Stock, any underwriter participating in any distribution pursuant to
such registration statement, and any attorney, accountant or other agent
retained by such seller or underwriter, all financial and other records,
pertinent corporate documents and properties of the Company, and cause the
Company's officers, directors and employees to supply all information reasonably
requested by such seller, underwriter, attorney, accountant or agent in
connection with such registration statement.

         For purposes of Sections 4 and 5, but excluding Section 6, the period
of distribution of Registrable Stock in a firm commitment underwritten public
offering shall be deemed to extend until each underwriter has completed the
distribution of all securities purchased by it, and the period of distribution
of Registrable Stock in any other registration shall be deemed to extend until
the earlier of the sale of all Registrable Stock covered thereby and one hundred
eighty (180) days after the effective date thereof.

         In connection with each registration hereunder, the sellers of
Registrable Stock will furnish to the Company in writing such information with
respect to themselves and the proposed distribution by them as reasonably shall
be necessary in order to assure compliance with federal and applicable state
securities laws.

         In connection with each registration pursuant to Sections 4, 5 or 6
covering an underwritten public offering, the Company and each seller agree to
enter into a written agreement with the managing underwriter selected in the
manner herein provided in such form


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and containing such provisions as are customary in the securities business for
such an arrangement between such underwriter and companies of the Company's size
and investment stature.

         8. EXPENSES. All expenses incurred by the Company in complying with
Sections 4, 5 or 6, including, without limitation, all registration and filing
fees, printing expenses, fees and disbursements of counsel and independent
public accountants for the Company, fees and expenses (including counsel fees)
incurred in connection with complying with state securities or "blue sky" laws,
fees of the National Association of Securities Dealers, Inc., transfer taxes,
fees of transfer agents and registrars, costs of insurance and fees and
disbursements of one counsel for the sellers of Registrable Stock (who shall be
selected by the selling holders of Restricted Stock), but excluding any Selling
Expenses, are called "Registration Expenses." All underwriting discounts and
selling commissions applicable to the sale of Registrable Stock are called
"Selling Expenses." The Company will pay all Registration Expenses in connection
with all registration statements under Sections 4, 5 or 6.

         Notwithstanding the foregoing, if a registration statement pursuant to
Sections 4 or 6 is withdrawn at the request of the stockholders requesting such
registration (other than as a result of information concerning the business or
financial condition of the Company which is made known to such holders after the
date on which such registration was requested) and if such requesting
stockholders elect not to have such registration counted as a registration
requested under Section 4, the requesting stockholders shall pay the
Registration Expenses of such registration pro rata in accordance with the
number of shares of Restricted Stock owned by them included in such registration
statement.

         9. INDEMNIFICATION AND CONTRIBUTION. (a) to the extent permitted by
law, the Company will indemnify and hold harmless each holder of Registrable
Stock (a "Holder"), any underwriter (as defined in the Securities Act) for such
Holder and each person, if any, who controls such Holder or underwriter within
the meaning of the Securities Act or the Exchange Act, against any losses,
claims, damages, or liabilities (joint or several) to which they may become
subject insofar as such losses, claims, damages or liabilities (or actions in
respect thereof) arise out of or are based upon any of the following statements,
omissions or violations (collectively a "Violation"): (i) any untrue statement
or alleged untrue statement of a material fact contained in such registration
statement, including any preliminary prospectus or final prospectus contained
therein or any amendment or supplements thereto, (ii) the omission or alleged
omission to state therein a material fact required to be stated therein, or
necessary to make the statements therein not misleading, or (iii) any violation
or alleged violation by the Company of the Securities Act, the Exchange Act
Securities, any state securities law or any rule or regulation promulgated under
the Securities Act, or the Exchange Act or any state securities law; and the
Company will pay to each such Holder, underwriter or controlling person, as
incurred, any legal or other expenses reasonably incurred by them in connection
with investigating or defending any such loss, claim, damage, liability, or
action; provided, however, that the indemnity agreement contained in this
Section 9(a) shall not apply to amounts paid in settlement of any such loss,
claim, damage, liability, or action if such settlement is effected without the
consent of the Company (which consent shall not be unreasonably withheld), nor
shall the Company be liable in any such case for any such loss, claim, damage,
liability, or action to the extent that it arises out of or is based upon a
violation which occurs in reliance upon and in


                                                                         Page 10
<PAGE>   11


conformity with written information furnished expressly for use in connection
with such registration by any such Holder, underwriter or controlling person.

                  (b) To the extent permitted by law, each selling Holder will
indemnify and hold harmless the Company, each of its directors, each of its
officers who has signed the registration statement, each person, if any, who
controls the Company within the meaning of the Securities Act, any underwriter,
any other Holder selling securities in such registration statement and any
controlling person of any such underwriter or other Holder, against any losses,
claims, damages, or liabilities (joint or several) to which any of the foregoing
persons may become subject, under the Securities Act, or the Exchange Act or
other federal or state law, insofar as such losses, claims, damages, or
liabilities (or actions in respect thereto) arise out of or are based upon any
Violation, in each case to the extent (and only to the extent) that such
Violation occurs in reliance upon and in conformity with written information
furnished by such Holder expressly for use in connection with such registration;
and each such Holder will pay, as incurred, any legal or other expenses
reasonably incurred by any person intended to be indemnified pursuant to this
Section 9(b), in connection with investigating or defending any such loss,
claim, damage, liability, or action; provided, however, that the indemnity
agreement contained in this Section 9(b) shall not apply to amounts paid in
settlement of any such loss, claim, damage, liability or action if such
settlement is effected without the consent of the Holder (which consent shall
not be unreasonably withheld); provided, that, in no event shall any indemnity
under this Section 9(n) exceed the gross proceeds from the offering received by
such Holder.

                  (c) Promptly after receipt by an indemnified party under this
Section 9 of notice of the commencement of any action (including any
governmental action), such indemnified party will, if a claim in respect thereof
is to be made against any indemnifying party under this Section 9, deliver to
the indemnifying party a written notice of the commencement thereof and the
indemnifying party shall have the right to participate in, and, to the extent
the indemnifying party so desires, jointly with any other indemnifying party
similarly noticed, to assume the defense thereof with counsel mutually
satisfactory to the parties; provided, however, that an indemnified party
(together with all other indemnified parties which may be represented without
conflict by one counsel) shall have the right to retain one separate counsel,
with the fees and expenses to be paid by the indemnifying party, if
representation of such indemnified party by that counsel retained by the
indemnifying party would be inappropriate due to actual or potential differing
interests between such indemnified party and any other party represented by such
counsel in such proceeding. The failure to deliver written notice to the
indemnifying party within a reasonable time of the commencement of any such
action, if prejudicial to its ability to defend such action, shall relieve such
indemnifying party of any liability to the indemnified party under this Section
9, but the omission so to deliver written notice to the indemnifying party will
not relieve it of any liability that it may have to any indemnified party
otherwise than under this Section 9.

                  (d) if the indemnification provided for in this Section 9 is
held by a court of competent jurisdiction to be unavailable to an indemnified
party with respect to any loss, liability, claim, damage, or expense referred to
therein, then the indemnifying party, in lieu of indemnifying such indemnified
party hereunder, shall contribute to the amount paid or payable by such
indemnified party as a result of such loss, liability, claim, damage, or expense
in such proportion as is appropriate to reflect the relative fault of the
indemnifying party on the one hand


                                                                         Page 11
<PAGE>   12


and of the indemnified party on the other in connection with the statements or
omissions that resulted in such loss, liability, claim, damage, or expense as
well as any other relevant equitable considerations. The relative fault of the
indemnifying party and of the indemnified party shall be determined by reference
to, among other things, whether the untrue or alleged untrue statement of a
material fact or the omission to state a material fact relates to information
supplied by the indemnifying party or by the indemnified party and the parties'
relative intent, knowledge, access to information, and opportunity to correct or
prevent such statement or omission.

                  (e) Notwithstanding the foregoing, to the extent that the
provisions on indemnification and contribution contained in the underwriting
agreement entered into in connection with the underwritten public offering are
in conflict with the foregoing provisions, the provisions in the underwriting
agreement shall control.

         10. CHANGES IN COMMON STOCK, NOTE WARRANT SHARES OR PREFERRED SHARES.
If, and as often as, there is any change in the Common Stock, the Note Warrant
Shares or the Preferred Shares by way of a stock split, stock dividend,
combination or reclassification, or through a merger, consolidation,
reorganization or recapitalization, or by any other means, appropriate
adjustment shall be made in the provisions hereof so that the rights and
privileges granted hereby shall continue with respect to the Common Stock, the
Note Warrant Shares or the Preferred Shares as so changed.

         11. RULE 144 REPORTING. With a view to making available the benefits of
certain rules and regulations of the Commission which may at any time permit the
sale of the Registrable Stock to the public without registration, at all times
after ninety (90) days after any registration statement covering a public
offering of securities of the Company under the Securities Act shall have become
effective, the Company agrees to:

                  (a) make and keep public information available, as those terms
are understood and defined in Rule 144 under the Securities Act;

                  (b) use its best efforts to file with the Commission in a
timely manner all reports and other documents required of the Company under the
Securities Act and the Exchange Act; and

                  (c) furnish to each holder of Registrable Stock forthwith upon
request a written statement by the Company as to its compliance with the
reporting requirements of such Rule 144 and of the Securities Act and the
Exchange Act, a copy of the most recent annual or quarterly report of the
Company, and such other reports and documents so filed by the Company as such
holder may reasonably request in availing itself of any rule or regulation of
the Commission allowing such holder to sell any Registrable Stock without
registration.

         12. REPRESENTATIONS AND WARRANTIES OF THE COMPANY. The Company
represents and warrants as follows:

                  (a) The execution, delivery and performance of this Agreement
by the Company have been duly authorized by all requisite corporate action and
will not violate any provision of the law, any order of any court or other
agency of government, the Certificate of Incorporation, as amended, or By-Laws,
as amended, of the Company or any provision of any


                                                                         Page 12
<PAGE>   13


indenture, agreement or other instrument to which it or any of its properties or
assets is bound, conflict with, result in a breach of or constitute (with due
notice or lapse of time or both) a default under any such indenture, agreement
or other instrument or result in the creation of imposition of any lien, charge
or encumbrance of any nature whatsoever upon any of the properties or assets of
the Company.

                  (b) This Agreement has been duly executed and delivered by the
Company and constitutes the legal, valid and binding obligation of the Company,
enforceable in accordance with its terms.

         13. MISCELLANEOUS.

                  (a) All covenants and agreements contained in this Agreement
by or on behalf of any of the parties hereto shall bind and inure to the benefit
of the respective successors and assigns of the Company, each of the Founders,
and each of the Investors (including without limitation transferees of any
Preferred Shares, Preferred Warrants, Preferred Warrant Shares, Note Warrants,
Note Warrant Shares or Restricted Stock), whether so expressed or not, provided,
however, that in the event the number of transferees becomes excessive, as
reasonably determined by the Company, the Company may request that the
transferees appoint a single representative to act on their behalf and to
receive all notices which any or all of them are entitled to receive pursuant to
this Agreement; and further provided that registration rights conferred herein
on the holders of Preferred Shares, Preferred Warrants, Preferred Warrant
Shares, Note Warrants, Note Warrant Shares or Restricted Stock shall only inure
to the benefit of a transferee of Preferred Shares, Preferred Warrants,
Preferred Warrant Shares, Note Warrants, Note Warrant Shares or Restricted Stock
if (i) there is transferred to such transferee at least 25% of the sum of the
total shares of Restricted Stock originally issued pursuant to the Series A
Purchase Agreement, Series B Purchase Agreement, Series C Purchase Agreement,
Bridge Note Purchase Agreement or Note Purchase Agreement, as the case may be,
to the direct or indirect transferor of such transferee or (ii) such transferee
is a partner, shareholder or affiliate of a party hereto. Successor, assigns and
transferees of Founders shall be bound by and entitled to benefit from this
Agreement only if such successor, assignee or transferee acquires shares of
Founders' Stock by (i) any transfer of Founders' Stock by a Founder by gift or
bequest or through inheritance to, or for the benefit of any member or members
of Founder's immediate family; (ii) any transfer of Founder's Stock by a Founder
to a trust in respect of which said Founder serves as a trustee, provided that
the trust instrument governing said trust shall provide that such Founder, as
trustee, shall retain sole and exclusive control over the voting and disposition
of said Founders' Stock until the termination of this Agreement; (iii) any sale
or transfer of Founders' Stock to the Company; or (iv) any sale or transfer of
Founders' Stock by a Founder to an affiliate or partner of such Founder.

                  (b) All notices, requests, consents and other communications
hereunder shall be in writing and shall be mailed return receipt requested,
postage prepaid or telecopied in the case of non-U.S. residents addressed as
follows:

                  If to the Company, a Founder or any Investor at the address of
such party as set forth on Schedule A or Schedule B to this Agreement;


                                                                         Page 13
<PAGE>   14
                  If to any subsequent holder of Preferred Shares, Preferred
Warrants, Preferred Warrant Shares, Note Warrants, Note Warrant Shares,
Restricted Shares or Founders' Stock to it at such address as may have been
furnished to the Company in writing by such holder;

                  or, in any case, at such other address or addresses as shall
have been furnished in writing to the Company (in the case of a holder of
Preferred Shares, Preferred Warrants, Note Warrants, Note Warrant Shares,
Restricted Stock or Founders' Stock) or to the holders of Registrable Stock (in
the case of the Company) in accordance with the provisions of this paragraph.

                  (c) This Agreement shall be governed by and construed in
accordance with the intentional laws of the State of Texas.

                  (d) This Agreement may not be amended or modified, and no
provision hereof may be waived, without the written consent of the Company and
the holders of at least sixty-six and two-thirds percent (66 2/3%) of the
outstanding shares of Restricted Stock; provided, however, that if and to the
extent that any such amendment, modification or waiver would disproportionately
negatively affect or be disproportionately detrimental to the interests or
rights of the Founders, such amendment, modification or waiver shall require the
prior approval of a majority of the holders of shares of Common Stock then held
by the Founders. Any amendment, modification or waiver by the holders of
sixty-six and two-thirds percent (66 2/3%) of the shares of Restricted Stock
shall be effective with respect to all holders of Restricted Stock. Any
amendment, modification or waiver by a majority of the holders of Common Stock
then held by the Founders shall be effective with respect to all Founders.

                  (e) [RESERVED.]

                  (f) The obligations of the Company to register shares of
Restricted Stock and Founders' Stock under Section 4, 5, or 6 shall terminate on
the earlier of: (i) the eighth anniversary of the date of this Agreement or (ii)
at such times as the holders of Registrable Stock may sell such shares pursuant
to Rule 144 without regard to Paragraph (k) thereof.

                  (g) Each holder of Registrable Stock who is a party to this
Agreement shall agree not to sell publicly any shares of Registrable Stock or
other shares of Common Stock (other than shares of Registrable Stock or other
shares of Common Stock being registered in such offering) without the consent of
such underwriters, until one hundred eight (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.
All persons entitled to registration rights with respect to shares of Common
Stock who are not parties to this Agreement, all other persons selling shares of
Common Stock in such offering and all executive officers and directors of the
Company shall have agreed not to sell publicly their Common Stock under
circumstances pursuant to the terms set forth in this Section 13(g).

                  (h) Notwithstanding the provisions of Section 7(a), the
Company's obligation to file a registration statement, or cause such
registration statement to become and remain


                                                                         Page 14
<PAGE>   15


effective, shall be suspended for a period not to exceed ninety (90) days in any
24-month period if there exists at the time material non-public information
relating to the Company which, in the reasonable opinion of the Company, should
not be disclosed or if at the time of any request to register Registrable Stock
pursuant to Section 4 or Section 6 the Company is engaged or has fixed plans to
engage within 30 days of the time of the request in a registered public offering
as to which holders of Registrable Stock may include Registrable Stock pursuant
to Section 5.

                  (i) Each holder of Registrable Stock included in any
registration shall furnish to the Company such information regarding such holder
and the distribution proposed by such holder as the Company may request in
writing and as shall be required in connection with any registration,
qualification or compliance referred to in this Agreement.

                  (j) The Company shall not grant to any third party any
registration rights more favorable than any of those contained herein, so long
as any of the registration rights under this Agreement remains in effect,
without the consent required by Section 13(d), and provided further, that no
consent of the Founders shall be required in such event withstanding Section
13(d) if such registration rights are granted in connection with a bona fide
financing of the Company.

                  (k) If any provision of this Agreement shall be held to be
illegal, invalid or unenforceable, such illegality, invalidity or
unenforceability shall attach only to such provision and shall not in any manner
affect or render illegal, invalid or unenforceable to any other provision of
this Agreement and this Agreement shall be carried out as if any such illegal,
invalid or unenforceable provision were not contained herein.

                  (l) This Agreement may be executed in two or more
counterparts, and by the parties hereto in separate counterparts each of which
when so executed shall be deemed an original and all of which taken together
shall constitute one and the same instrument. A facsimile transmission of a
signature hereto shall be deemed for all purposes to be an original signature.

                                    * * * * *


                                                                         Page 15
<PAGE>   16


         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first above-written.



         COMPANY:              ODYSSEY HEALTHCARE, INC.


                               By: /s/ Richard R. Burnham
                                  ----------------------------------------------
                                  Richard R. Burnham, President



         FOUNDERS:                 /s/ Richard R. Burnham
                               -------------------------------------------------
                               Richard R. Burnham


                                   /s/ David C. Gasmire
                               -------------------------------------------------
                               David C. Gasmire


                                   /s/ David S. Steffy
                               -------------------------------------------------
                               David L. Steffy


                                   /s/ David W. Cross
                               -------------------------------------------------
                               David W. Cross


                                   /s/ Robert H. Calland
                               -------------------------------------------------
                               Robert H. Calland


                               THREE ARCH PARTNERS, L.P.


                                   /s/ Mark Wan
                               -------------------------------------------------
                               By Three Arch Management, L.P.,
                               Its General Partner


                               THREE ARCH ASSOCIATES, L.P.


                                   /s/ Mark Wan
                               -------------------------------------------------
                               By Three Arch Management, L.P.,
                               Its General Partner
<PAGE>   17



INVESTORS:                     THREE ARCH PARTNERS, L.P.



                                   /s/ Mark Wan
                               ----------------------------------------------
                               By Three Arch Management, L.P.,
                               Its General Partner



                               THREE ARCH ASSOCIATES, L.P.



                                   /s/ Mark Wan
                               ----------------------------------------------
                               By Three Arch Management, L.P.,
                               Its General Partner



                               WEISS, PECK & GREER VENTURE
                                 ASSOCIATES III, L.P.,
                               By WPG Venture Partners III, L.P.,
                               General Partner



                               By  /s/ Ellen M. Feeney
                                  -------------------------------------------
                                 Ellen M. Feeney, General Partner



                               WPG ENTERPRISE FUND II, L.P.
                               By WPG Venture Partners III, L.P.,
                               General Partner



                               By  /s/ Ellen M. Feeney
                                  -------------------------------------------
                                 Ellen M. Feeney, General Partner



<PAGE>   18



                               OAK INVESTMENT PARTNERS VI,
                               LIMITED PARTNERSHIP


                               By  /s/ Ann Lamont
                                  ----------------------------------------------
                                  Ann Lamont, Managing Member of Oak
                                  Associates VI, LLC, the General Partner of Oak
                                  Investment Partners VI, Limited Partnership



                               OAK VI AFFILIATES FUND, LIMITED
                               PARTNERSHIP


                               By  /s/ Ann Lamont
                                  ----------------------------------------------
                                  Ann Lamont, Managing Member of Oak
                                  Associates VI, LLC, the General Partner of Oak
                                  Investment Partners VI, Limited Partnership



                               COLLINSON HOWE VENTURE
                               PARTNERS, INC.


                               By  /s/ Jeffrey J. Collinson
                                  ----------------------------------------------
                                  Jeffrey J. Collinson, President



                               HIGHLAND CAPITAL PARTNERS III
                               LIMITED PARTNERSHIP

                               By Highland Management Partners III
                               Limited Partnership, its General Partner


                               By  /s/ Wycliffe K. Grousbeck
                                  ----------------------------------------------
                                  General Partner


<PAGE>   19



                               HIGHLAND ENTREPRENEURS' FUND III
                               LIMITED PARTNERSHIP

                               By HEF III, LLC, its General Partner


                               By  /s/ Wycliffe K. Grousbeck
                                  ----------------------------------------------
                                  Wycliffe K. Grousbeck, Member


                               LIFE SCIENCE ENTREPRENEUR FUND


                               By  /s/ Brian C. Cunningham
                                  ----------------------------------------------
                                  Brian C. Cunningham, Administrative Partner


                                   /s/ Bradley J. Velie
                                  ----------------------------------------------
                                  Bradley J. Velie


                               CAPITAL RESOURCE LENDERS III, L.P.

                               By Capital Resource Partners III, L.L.C.
                                  Its General Partner


                               By  /s/ Alexander McGrath
                                  ----------------------------------------------


                               CRP INVESTMENT PARTNERS III, L.L.C.


                               By /s/ Alexander McGrath
                                  ----------------------------------------------