Exhibit 99.1

STAR GAS PARTNERS, L.P.

AMENDED AND RESTATED MANAGEMENT INCENTIVE COMPENSATION PLAN

Dated as of July 19, 2012

WHEREAS, on July 20, 2006 the Board of Directors (the “Board”) of Kestrel Heat, LLC, a Delaware limited liability company (“Kestrel”), the general partner of Star Gar Partners, L.P., a Delaware limited partnership (the “Partnership”), adopted a Management Incentive Compensation Plan (the “Plan”) to reward key management employees of the Partnership and its direct and indirect subsidiaries; and

WHEREAS, on July 19, 2012, the Board approved certain amendments to the Plan; and

NOW, THEREFORE, as amended, the Plan is hereby amended and restated in its entirety to read as follows:

The purpose of the Plan is:

(a) To (i) reward key management employees of Star Gas Partners, L.P., a Delaware limited partnership and of its direct and indirect subsidiaries (the “Partnership”) for their positive accomplishments since Kestrel Heat LLC (“Kestrel”) became the general partner of the Partnership in 2006 and (ii) as an incentive to work as a team to improve the profits of the Partnership in the future; and

(b) To enable the Partnership to retain high quality management employees and encourage them to devote their full careers to the Partnership.

To enable the Partnership to fund benefits under the Plan, Kestrel has agreed to permanently and irrevocably forego receipt of 50% of all distributions to which it would become entitled in excess of minimum quarterly distributions with respect to its general partnership interest and the Partnership Agreement has been amended to effect this agreement. Kestrel has also agreed to contribute to the Partnership, as a contribution to capital, an amount equal to the Gains Interest payable to Participants by the Partnership.

“Board of Directors” means the Board of Directors of Kestrel.

“Gains Interest” means an amount equal to 50% of the cash and non-cash proceeds which Kestrel shall receive from (i) the sale of all or part of its General Partnership Units (as defined in the Partnership Agreement), (ii) any consideration paid to Kestrel by the Partnership with respect to its general partnership interest whether in replacement of or in addition to the consideration required to be paid on the date hereof (iii) any additional security issued to Kestrel with respect to or in exchange for any existing right or in addition to any existing right to the extent that Kestrel will pay less than fair market value and (iii) liquidating distributions paid to Kestrel pursuant to Section 14.4(c) of the Partnership Agreement or any successor section, less in each such case expenses and applicable taxes.

“Incentive Distributions” shall mean all amounts distributable to Kestrel with respect to its General Partnership Units pursuant to subsections 5.4(iv) and (v) of the Partnership Agreement prior to reduction to fund benefits payable to Participants pursuant to the Plan.

“Kestrel” shall have the meaning assigned in Section 2.

“Participant” means those employees listed on Schedule A.

“Partnership” shall have the meaning assigned to it in Section 1.

“Partnership Agreement” means the Second Amended and Restated Agreement of Limited Partnership of Star Gas Partners, L.P., as amended from time to time.

“Percentage Share” means the interest of a Participant determined by dividing the number of Points allocated to such Participant by the total number of Points allocated to all Participants, each determined as of the date of determination. Points which are forfeited will be deemed to be outstanding for purposes of this calculation.

“Plan” means this Management Incentive Compensation Plan.

“Plan Benefits” means collectively the Gains Interest and Incentive Distributors.

“Plan Year” shall mean the 12 month period ended September 30.

“Points” means the number of points allocated to a Participant as set forth on Schedule A hereto. No additional points may be issued.

2

“Vested Percentage Interest” means a Participant’s vested interest in the Plan Benefits as determined pursuant to Section 7.

“Vested Share” shall mean a member’s Percentage Share of the Plan Benefits times his Vested Percentage Interest.

Only the Participants and the beneficiaries of a deceased Participant will participate in the Plan.

Within 7 days after receipt by the Partnership of any Plan Benefits the Partnership shall distribute to each Participant who was a Participant on the date such Plan Benefits were received an amount in cash equal to his Vested Share of the Plan Benefits determined as of such date.

A Participant’s vested percentage of his or her Plan Benefits will be 100% during the time a Participant is an employee or consultant for the Partnership. Following the termination of employment, a Participant’s vested percentage shall be equal to 20% for each full or partial year of employment or consultation with the Partnership starting with the fiscal year ended September 30, 2012 (33 1/3% in the case of Daniel P. Donovan).

Notwithstanding the foregoing, Participant’s Vested Percentage Interest shall be forfeited (and deemed to be zero) if such Participant shall become an employee of, or a consultant or advisor to, an entity engaged in the retail distribution of heating oil, propane and related services offered by the Partnership (“Restricted Activities”) in states served by the Partnership on the date such employment, consultancy or advisory services commence. This provision will not prohibit a Participant from becoming employed by or consulting with an entity less that 10% of whose revenues are derived from Restricted Activities, provided that the Participant is not directly or indirectly engaged in any of the Restricted Activities on behalf of such entity.

3

(a) Each Participant shall be paid the amount to which he or she becomes entitled as provided in Section 5. In the event of a Participant’s death prior to such payment, a Participant’s Payment will be paid to the Participant’s designated beneficiary as soon as practicable following the Participant’s date of death.

(b) A Participant shall have the right to designate a beneficiary for any benefits payable under the Plan following his or her death on a form supplied by the Partnership. In the absence of the Participant’s designation or if the designated beneficiary has predeceased the Participant, the designated beneficiary shall be the Participant’s spouse, or if no spouse to whom he or she is legally married then survives him or her, then the beneficiary shall be the Participant’s estate.

(c) Any beneficiary entitled to receive any portion of the Plan Benefits of a deceased Participant shall succeed to all rights of such deceased Participant, including the right to designate a beneficiary on his or her death.

(d) If a Participant is deceased but no beneficiary has been determined to be entitled to his or her Plan Benefits, then such Plan Benefits shall be retained by Kestrel.

(a) The Plan shall be administered by the Partnership’s Chief Financial Officer under the direction of the Board of Directors, or by such other officer as the Board of Directors may from time to time direct.

(b) The Board of Directors shall have the final decision making authority on each aspect of the Plan.

4

No amendment, modification or repeal of the Plan or any processes hereof shall in any manner terminate, reduce or impair the rights of any Participant without the prior written consent of such Participant, or beneficiary, if applicable.

(a) The Chief Financial Officer shall be responsible for determining all claims for benefits under this Agreement by a Participant or his or her spouse or estate or other beneficiaries (“Claimant”). Within ninety (90) days after receiving a claim (or within up to one hundred eighty (180) days, where special circumstances require an extension of time for processing the claim, if the claimant is so notified, including notification of the reason for the delay), the Chief Financial Officer shall notify the Claimant of its decision in writing. If the decision is adverse to the claimant, the Chief Financial Officer shall advise him or her of the specific reasons for the denial, the specific Plan provisions on which the denial is based, of any additional information which he or she must provide to perfect his or her claim, and of his or her right to request a review of the decision and the manner in which such request must be made.

(b) A claimant may request a review of an adverse decision by written request to the Board of Directors made within sixty (60) days (or within one hundred twenty (120) days were special circumstances require an extension of time for processing the claim, if the claimant is so notified) after receipt of the decision. The claimant, or his or her duly authorized representative, may review pertinent documents and submit written issues and comments. Within sixty (60) days after receiving a request for review, the Board of Directors shall notify the claimant in writing of (i) its decision, (ii) the reasons therefore, and (iii) the Plan provisions upon which it is based.

(c) The decision (“Decision”) of the Chief Financial Officer or the Board of Directors, if applicable, shall be final and binding on a Claimant except as to objections specified in writing by the Claimant and delivered to the Partnership within 10 business days after the Decision has been received by the Claimant.

5

This Plan is unfunded and shall at all times remain unfunded. The obligations of the Partnership with respect to the benefits payable hereunder shall (i) be limited to the amounts received from Kestrel and (ii) be paid out of the Partnership’s general assets and shall not be secured. To the extent that any person acquires a right to receive payments from the Partnership under this Plan, such right shall be no greater than the right of any unsecured general creditor of the Partnership.

If the Board of Directors shall find that any person to whom payment is payable under this Plan is unable to care for his affairs because of illness or accident, or is a minor, any payment due (unless a prior claim therefore shall have been made by a duly appointed guardian, committee or other legal representative) may be paid to the spouse, a child, parent, or brother or sister, or to any person deemed by the Board of Directors to have incurred expense for such person otherwise entitled to payment, in such manner and proportions as the Board of Directors may determine. Any such payment shall be a complete discharge of the liabilities of Kestrel under this Plan.

Nothing contained herein shall be construed as conferring upon any employee the right to continue in the employ of the Partnership as an executive or in any other capacity or to interfere with the Partnership’s right to discharge him or her at any time for any reason whatsoever.

In case any provision of this Plan shall be illegal or invalid for any reason, said illegality or invalidity shall not affect the remaining parts hereof, but this Plan shall be construed and enforced as if such illegal and invalid provision never existed.

The Partnership shall have the right to make such provisions as it deems necessary or appropriate to satisfy any obligations it may have to withhold federal, state or local income, employment or other taxes incurred by reason of payments pursuant to this Plan.

6

This Plan shall be binding upon and inure to the benefit of the Partnership, its successors and assigns and the Participants and their heirs, executors, administrators and legal representatives.

Except as provided herein, the benefits payable under this Plan shall not be subject to anticipation, alienation, sale, transfer, assignment, pledge, encumbrance, attachment, garnishment, execution or levy of any kind, by creditors of the Participant or the Participant’s spouse or estate as beneficiary hereunder, and any attempt to cause any benefits to be so subjected shall not be recognized.

This Plan shall be construed in accordance with and governed by the law of the State of New York except to the extent preempted by the Employee Retirement Income Security Act of 1974, as amended.

(a) This Plan is intended to comply with Section 409A of the Internal Revenue Code of 1986, as amended (“Section 409A”) and shall be construed and operated accordingly. It is the intention of the Partnership that payments or benefits payable under the Plan not be subject to the additional tax or interest imposed pursuant to Section 409A and the Plan shall be construed and operated accordingly. To the extent any payments or benefits are or could become subject to additional tax or interest under Section 409A, Participant agrees to cooperate with the Partnership to amend the Plan with the goal of giving Participant the economic benefits described herein in a manner that does not result in such additional tax or interest being imposed; provided, however, that the Partnership is under no obligation to do so to the extent that the Partnership would incur any additional cost or expense and provided further that the Partnership does not guarantee or warrant that such amendment, if any, will have the result of preventing the imposition of such additional tax or, interest. Participant shall, at the request of the Partnership, take any reasonable action (or refrain from taking any action), required to comply with any correction procedure promulgated pursuant to Section 409A.

7

(b) If at the time of separation from service, a Participant is a “specified employee” as defined in Section 409A of the Code, then

8