FIRST AMENDMENT TO THE ODYSSEY HEALTHCARE, INC. 2001 EQUITY-BASED COMPENSATION PLAN

Exhibit 10.1

FIRST AMENDMENT TO THE

      THIS FIRST AMENDMENT is made effective as of May 5, 2005 (the “Effective Date”) by Odyssey Healthcare, Inc., a Delaware corporation (the “Company”).

WITNESSETH:

      WHEREAS, the Company sponsors the Odyssey Healthcare, Inc. 2001 Equity-Based Compensation Plan (the “Plan”) for the benefit of its eligible employees and their beneficiaries;

      WHEREAS, pursuant to Section 10(c) of the Plan the Board of Directors of the Company (the “Board”) may amend or alter the Plan without the consent of stockholders or participants, provided that, any such amendment or alteration, including any increase in any share limitation, shall be subject to the approval of the Company’s stockholders not later than the annual meeting next following such Board action if such stockholder approval is required by any federal or state law or regulation or the rules of The NASDAQ Stock Market, and the Board may otherwise, in its discretion, determine to submit other such changes to the Plan to stockholders for approval; provided further that, without the consent of an affected participant, no such Board action may materially and adversely affect the rights of any participant under any previously granted and outstanding award;

      WHEREAS, pursuant to Section 2(g)(ii) of the Plan, a change in control of the Company may result from a transition in the members of the Board;

      WHEREAS, the Board believes it is in the best interest of the Company to revise the criteria for determining when a transition in the members of the Board constitutes a change in control of the Company;

      WHEREAS, pursuant to Section 4(a) of the Plan, the total number of shares of the Company’s Common Stock (“Stock”) reserved and available for delivery in connection with awards under the Plan shall not exceed the lesser of 225,000,000 shares of Stock (as adjusted for previous Stock dividends) or ten percent (10%) of the total number of shares of Stock outstanding, assuming the exercise of all outstanding options, warrants or other rights to purchase Stock and assuming the conversion or exchange or exercise of all other securities convertible into Stock;

      WHEREAS, the Board believes it is in the best interest of the Company to increase the total number of shares of Stock reserved and available for issuance under the Plan, from inception, to a total of 6,149,778;

      WHEREAS, Section 5 of the Plan provides that in each fiscal year during any part of which the Plan is in effect, individuals who may subject the Company to the deduction limitations provided in section 162(m) of the Internal Revenue Code of 1986, as amended (the

“Code”) may not be granted awards relating to more than 225,000,000 shares of Stock (as adjusted for previous Stock dividends);

      WHEREAS, the Board believes it is in the best interest of the Company to provide that in each fiscal year of the Company, during any part of which the Plan is in effect, individuals who may subject the Company to the deduction limitations provided in section 162(m) of the Code may not be granted awards relating to more than 1,300,000 shares of Stock or, in the case of awards the value of which is not directly related to the value of the Stock, awards the value of which at the time of payment exceeds $3,000,000;

      WHEREAS, the Plan provides several business criteria on which the grant and/or settlement of awards may be based if (1) the Company’s Compensation Committee (the “Committee”) determines that an award to any participant should be so conditioned or (2) the Committee determines that an award granted to an officer of the Company, who may subject the Company to the deduction limitations of section 162(m) of the Code, should qualify as “performance-based compensation” for purposes of section 162(m) of the Code;

      WHEREAS, the Board believes it is in the best interest of the Company to allow the stockholders of the Company to reapprove the business criteria on which the grant and/or settlement of awards may be based;

      WHEREAS, Sections 9(c), 9(e) and 10(c) of the Plan provide collectively that upon a change in control of the Company, the Committee shall have certain powers to modify awards which include the power to (1) accelerate the vesting schedule associated with any awards, (2) require the mandatory surrender of options for cash consideration, and (3) make any other such revisions to awards as the Committee deems appropriate; and

      WHEREAS, the Board believes it is in the best interest of the Company to provide that upon a change in control of the Company, the Committee shall fully accelerate the vesting schedule associated with all awards and either require the mandatory surrender of options for cash consideration or provide that the fully vested options shall be exercisable for a given period and shall thereafter expire.

      NOW, THEREFORE, the Plan is hereby amended as follows:

      1. Section 2(g)(ii) is hereby amended in its entirety, effective on the Effective Date, to read as follows:

            (iii) A majority of the members of the Board is replaced during any 12-month period by directors whose appointment or election is not endorsed by a majority of the members constituting the Board prior to the date of the appointment or election;

      2. Section 4(a) is hereby amended in its entirety, effective on the Effective Date, to read as follows:

            (a) Overall Number of Shares Available for Delivery. Subject to adjustment in a manner consistent with any adjustment made pursuant to Section 9, the total number of shares of Stock reserved and available for delivery in connection with Awards under this Plan, from inception, is 6,149,778.

      3. Section 5 is hereby amended in its entirety, effective on the Effective Date, to read as follows:

            5. Eligibility; Per Person Award Limitations. Awards may be granted under this Plan only to Eligible Persons. In each fiscal year during any part of which this Plan is in effect, a Covered Employee may not be granted Awards relating to more than 1,300,000 shares of Stock, subject to adjustment in a manner consistent with any adjustment made pursuant to Section 9, and in the case of Awards the value of which is not directly related to the value of the Stock, Awards the value of which at the time of payment exceeds $3,000,000.

      4. Section 8(b) of the Plan shall continue to read in its current state.

      5. Section 9(c) is hereby amended in its entirety, effective on the Effective Date, to read as follows:

            (c) Corporate Restructuring. If the Company recapitalizes, reclassifies its capital stock, or otherwise changes its capital structure (a “recapitalization”), the number and class of shares of Stock covered by an Option theretofore granted shall be adjusted so that such Option shall thereafter cover the number and class of shares of stock and securities to which the holder would have been entitled pursuant to the terms of the recapitalization if, immediately prior to the recapitalization, the holder had been the holder of record of the number of shares of Stock then covered by such Option and the share limitations provided in Sections 4 and 5 shall be adjusted in a manner consistent with the recapitalization. Upon a Change in Control the Committee, shall fully accelerate the forfeiture provisions associated with all outstanding Awards and, acting in its sole discretion without the consent or approval of any holder, effect one of the following alternatives with respect to Options: (1) accelerate the time at which all Options then outstanding may be exercised so that such Options may be exercised in full for a limited period of time on or before a specified date (before or after such Change in Control) fixed by the Committee, after which specified date all unexercised Options and all rights of holders thereunder shall terminate, or (2) require the mandatory surrender to the Company of all of the outstanding Options held by such holders (irrespective of whether such Options are then exercisable under the provisions of this Plan) as of a date, before such Change in Control, specified by the Committee, in which event the Committee shall thereupon cancel such Options and pay to each holder an amount of cash per share equal to the excess, if any, of the amount calculated in Section 9(d) (the “Change in Control Price”) of the shares subject to such Option over the exercise price(s) under such Options for such shares.

      NOW, THEREFORE, be it further provided that, except as provided above, the Plan shall continue to read in its current state.

      IN WITNESS WHEREOF, this First Amendment has been executed by a duly authorized officer of the Company as of the date set forth in the introductory paragraph and effective as set forth herein.