Exhibit 3.3

FIRST AMENDMENT

TO

LIMITED LIABILITY COMPANY AGREEMENT

OF

INERGY HOLDINGS GP, LLC

This First Amendment to Limited Liability Company Agreement of Inergy Holdings GP, LLC (this “Amendment”) is made and entered into as of November 5, 2010, between John J. Sherman, Trustee of the John J. Sherman Revocable Trust dated May 4, 1994 (the “Sherman Trust”) and Inergy Holdings GP, LLC, a Delaware limited liability company (the “Company”).

On April 14, 2005, the Sherman Trust, William C. Gautreaux, Trustee of the William C. Gautreaux Revocable Trust Under Trust Indenture dated March 8, 2004 (the “Gautreaux Trust”), Carl A. Hughes, Trustee of the Carl A. Hughes Revocable Trust Under Trust Indenture dated September 13, 2002 (the “Hughes Trust”), Paul E. McLaughlin (“McLaughlin”), Andrew Atterbury (“Atterbury”), David G. Dehaemers, Jr. (“Dehaemers”), Phillip L. Elbert (“Elbert”) and R. Brooks Sherman, Jr. (“Brooks Sherman”) entered into a Limited Liability Company Agreement of Inergy Holdings GP, LLC (the “Original LLC Agreement”).

The Company is the general partner of Inergy Holdings, L.P., a Delaware limited partnership previously known as Inergy Holdings, LLC (“Inergy Holdings”).

On September 3, 2010, Inergy Holdings, Inergy, L.P. (“NRGY”) and certain of their affiliates entered into a First Amended and Restated Agreement and Plan of Merger (the “Agreement and Plan of Merger Agreement”). On the date hereof, which is the closing date of the transactions contemplated by the Agreement and Plan of Merger (the “Merger Closing Date”), holders of Inergy Holdings common units have the right to receive 0.77 common units of NRGY in exchange for each common unit of Inergy Holdings.

The Sherman Trust is the only Voting Member (as defined in the Original LLC Agreement) and, pursuant to Section 11.8 of the Original LLC Agreement, has the power to amend the Original LLC Agreement in the manner provided herein.

Accordingly, the parties agree as follows:

1. Capitalized terms not otherwise defined in this Amendment have the meanings given to such terms in the Original LLC Agreement.

2. Attached is a revised Schedule A as of the date hereof.

3. The term “Holdings Common Units” is hereby replaced throughout the Original LLC Agreement with the term “NRGY Common Units”, which has the following definition:

“NRGY Common Units” means, collectively, (i) common units representing limited partner interests in NRGY and (ii) Class B units representing limited partner interests in NRGY.

4. The term “Holdings Ownership Percentage” is hereby amended by deleting the current definition in the Original LLC Agreement in its entirety and by inserting, in lieu thereof, the following definition:

“Holdings Ownership Percentage” means, with respect to a Member at a particular time, a percentage equal to (i) the aggregate number of issued and outstanding Original Common Units owned by such Member and such Member’s Controlled Persons at such time divided by (ii) the aggregate number of issued and outstanding Original Common Units owned by all Members and all of their respective Controlled Persons at such time.

5. The term “Original Holdings Common Units” is hereby replaced throughout the Original LLC Agreement with the term “Original Common Units”, which has the following definition:

“Original Common Units” means those specific NRGY Common Units that were previously Original Holdings Common Units (as defined in the Original LLC Agreement) and that are owned by the Members on the Merger Closing Date, as adjusted thereafter as a result of any dividend or distribution payable in securities (other than any Class B units representing limited partner interests in NRGY that are issued in kind as a distribution after the Merger Closing Date), split, reclassification, recharacterization or similar event (including any conversion of Class B units representing limited partner interests in NRGY into common units representing limited partner interests in NRGY) with respect to NRGY Common Units generally or with respect to any class of NRGY Common Units. Prior to the Merger Closing Date, the number of Original Common Units was 38,986,661. As of the Merger Closing Date, the number and type of Original Common Units is 18,451,161 common units representing limited partner interests in NRGY and 11,568,560 Class B units representing limited partner interests in NRGY. The ownership breakdown of each Original Common Unit (both pre-Merger and post-Merger) is set forth on Schedule B. If a dispute later arises as to whether any particular NRGY Common Units are Original Common Units, the burden will be on the Member holding such NRGY Common Units (whether held by the Member or his or its Controlled Persons) to show that they are Original Common Units, and the Voting Members will make all decisions as to whether any particular NRGY Common Units are Original Common Units. From time to time, the president or the Voting Members may request an affidavit from each Member certifying in writing the ownership by the Member and his or its Controlled Persons of Original Common Units (broken down by class of NRGY Common Unit) and the manner in which they are held (unit certificate number, segregated account held in street name, etc.) and, in the case of Controlled Persons, all documentation reasonably requested in order to confirm that the purported Controlled Person is actually a Controlled Person. In the absence of a written waiver by the Voting Members, failure to fully or timely respond to such request will result in all NRGY Common Units held by the non-responding Member or his or its Controlled Persons ceasing to be Original Common Units.

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6. Section 5.3 of the Original LLC Agreement is hereby amended by deleting Section 5.3 in its entirety and by inserting, in lieu thereof, the following:

5.3 Determination of Voting Members.

(a) As long as the Sherman Entities own, in the aggregate, more than 33.0% of the issued and outstanding Original Common Units owned, in the aggregate, by all of the Members and their Controlled Persons, the Sherman Trust (or, if the Sherman Trust is no longer a Member, such other Member as may be appointed by the Sherman Entities) will be the only Voting Member and all other Members will be Non-Voting Members.

(b) If, at any time, the Sherman Entities own, in the aggregate, 33.0% or less of the Original Common Units owned by all of the Members and their Controlled Persons, then all of the Members (including the Sherman Entities that are Members) will each become Voting Members and will at all times thereafter remain Voting Members until such time as the Sherman Entities again own, in the aggregate, more than 33.0% of the Original Common Units owned by all of the Members.

7. Section 6.1(b) of the Original LLC Agreement is hereby amended by deleting Section 6.1(b) in its entirety and by inserting, in lieu thereof, the following:

(b) Number, Tenure and Qualifications. The Board of Directors will consist of one Director. Sherman is hereby appointed as the Director. Sherman will serve at the pleasure of the Voting Members and will hold office until a successor has been elected and qualified or until his death, resignation or removal.

8. Section 6.1(e) of the Original LLC Agreement is hereby amended by deleting Section 6.1(e) in its entirety and by inserting, in lieu thereof, the following:

(e) Special Meetings. Special meetings of the Board of Directors may be called by or at the request of the president or any Director. The Person authorized to call special meetings of the Board of Directors may fix any place as the place for holding any special meeting of the Board of Directors called by them.

9. Section 6.1(j) of the Original LLC Agreement is hereby amended by deleting Section 6.1(j) in its entirety and by inserting, in lieu thereof, the following:

(j) No Committees. The Board of Directors may not establish committees.

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10. Section 6.1(k) of the Original LLC Agreement is hereby amended by deleting Section 6.1(k) in its entirety and by inserting, in lieu thereof, the following:

(k) Informal Action. Any action required to be taken at a meeting of the Board of Directors, or any other action that may be taken at a meeting of the Board of Directors, may be taken without a meeting if a consent in writing, setting forth the actions so taken, is signed by a majority of the Directors.

11. Section 9.9 of the Original LLC Agreement is hereby amended by deleting Section 9.9 in its entirety and by inserting, in lieu thereof, the following:

9.9 Purchase of Interest Upon Sale of NRGY Common Units. If, at any time, a Member (other than the sole remaining Member of the Company) and such Member’s Controlled Persons own, in the aggregate, less than 0.5% of the number of issued and outstanding NRGY Common Units owned, beneficially and of record, by all Members and their Controlled Persons (such event, a “Reduction Event”), then the Company will have the option to redeem all (but not less than all) of such Member’s Interest for an amount equal to such Member’s Capital Account balance as of the last day of the month in which the Reduction Event occurred, with the closing of such redemption to take place within 30 days following the last day of such month. The restrictions contained in Section 9.2 will not apply to Transfers under this Section 9.9.

12. Except as amended herein, the Original LLC Agreement will remain in full force and effect, and references in the Original LLC Agreement to “Agreement”, “hereof”, “herein” and words of similar impact are deemed to be a reference to the Original LLC Agreement as amended by this Amendment.

The parties have entered into this Amendment as of the date set forth in the introductory clause.

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SCHEDULE A

SCHEDULE OF PERCENTAGE INTERESTS

(November 5, 2010)

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SCHEDULE B

ORIGINAL COMMON UNITS

(November 5, 2010)

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