Exhibit 3.1

Execution Version

AMENDMENT NO. 1 TO THE AMENDED AND RESTATED

AGREEMENT OF LIMITED PARTNERSHIP OF

INERGY HOLDINGS, L.P.

This AMENDMENT NO. 1 TO THE AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP OF INERGY HOLDINGS, L.P. (this “Amendment”), dated as of November 3, 2010, is entered into and effectuated by Inergy Holdings GP, LLC, in its capacity as general partner (the “General Partner”) of Inergy Holdings, L.P. (the “Partnership”), pursuant to authority granted to it in Sections 5.6 and 13.1(g) of the Amended and Restated Agreement of Limited Partnership of Inergy Holdings, L.P., dated as of June 24, 2005 (the “Holdings Partnership Agreement”). Capitalized terms used but not defined herein have the meanings ascribed to them in the Holdings Partnership Agreement.

WHEREAS, Section 5.6(a) of the Holdings Partnership Agreement provides that the Partnership may issue additional Partnership Securities for any Partnership purpose at any time and from time to time to such Persons for such consideration and on such terms and conditions as the General Partner shall determine, all without the approval of any Limited Partners;

WHEREAS, Section 5.6(b) of the Holdings Partnership Agreement provides that the Partnership Interest authorized to be issued by the Partnership pursuant to Section 5.6(a) may be issued in one or more classes, or one or more series of any such classes, with such designations, preferences, rights, powers and duties (which may be senior to existing classes and series of Partnership Securities), as shall be fixed by the General Partner;

WHEREAS, Section 13.1(g) of the Holdings Partnership Agreement provides that the General Partner, without the approval of any Partner, may amend any provision of the Holdings Partnership Agreement to reflect an amendment that the General Partner determines to be necessary or appropriate in connection with the authorization of issuance of any class or series of Partnership Securities pursuant to Section 5.6 of the Holdings Partnership Agreement; and

WHEREAS, the General Partner deems it advisable and in the best interest of the Partnership to effectuate this Amendment to provide for (i) the creation of a new class of Units to be designated as Nonparticipating Limited Partner Units and to fix the preferences and the relative participating, optional and other special rights, powers and duties pertaining to the Nonparticipating Limited Partner Units, and (ii) such other matters as are provided herein.

NOW, THEREFORE, it is hereby agreed as follows:

A. Amendment. The Holdings Partnership Agreement is hereby amended as follows:

1. Section 1.1 is hereby amended to add the following definition:

“Nonparticipating Limited Partner Units” means a Partnership Security representing a fractional part of the Interests of all Limited Partners, and having the rights and obligations specified with respect to the Nonparticipating Limited Partner Units in this Agreement.

2. Section 1.1 is hereby amended by amending and restating the following definitions:

“Capital Account” means the capital account maintained for a Limited Partner pursuant to Section 5.5. The “Capital Account” of a Limited Partner in respect of a Common Unit, Nonparticipating Limited Partner Unit or any other Interest shall be the amount that such Capital Account would be if such Common Unit, Nonparticipating Limited Partner Unit or other Interest were the only interest in the Partnership held by such Limited Partner from and after the date on which such Common Unit, Nonparticipating Limited Partner Unit or other Interest was first issued.

“Limited Partner Interest” means the ownership interest of a Limited Partner in the Partnership, which may be evidenced by Common Units, Nonparticipating Limited Partner Units or other Partnership Securities or a combination thereof or interest therein, and includes any and all benefits to which such Limited Partner is entitled as provided in this Agreement, together with all obligations of such Limited Partner to comply with the terms and provisions of this Agreement.

“Partnership Security” means any class or series of equity interest in the Partnership (but excluding any options, rights, warrants and appreciation rights relating to an equity interest in the Partnership), including without limitation, Common Units and Nonparticipating Limited Partner Units, which are separate classes of Limited Partner Interests.

“Unit” means a Partnership Security that is designated as a “Unit” and shall include Common Units and Nonparticipating Limited Partner Units.

3. Section 1.1 is hereby amended by adding the following sentence at the end of the definition of “Common Unit”:

“The term “Common Unit” does not refer to a Nonparticipating Limited Partner Unit.”

4. Article V is hereby amended to add a new Section 5.12 creating a new series of Units as follows:

Section 5.12 Establishment of Nonparticipating Limited Partner Units.

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(a) General. The General Partner hereby designates and creates a series of Units to be designated as “Nonparticipating Limited Partner Units” and consisting of a total of 1,000 Nonparticipating Limited Partner Units, and fixes the designations, preferences and relative, participating, optional or other special rights, powers and duties of holders of the Nonparticipating Limited Partner Units as set forth in this Section 5.12.

(b) Allocations. Except as may be required to properly maintain Capital Accounts pursuant to Section 704(b) of the Code, no items of Partnership income, gain, loss, deduction and credit under Section 6.1(a) and Section 6.1(b) shall be allocated to the Nonparticipating Limited Partner Units;

(c) Distributions of Available Cash from Operating Surplus and Distributions of Available Cash from Capital Surplus. Notwithstanding anything to the contrary in Section 6.4 or Section 6.5, no Nonparticipating Limited Partner Unit shall have the right to share in any distributions made to the Unitholders pursuant to Section 6.4 or Section 6.5;

(d) Capital Accounts. The initial Capital Account balance associated with each Nonparticipating Limited Partner Unit shall equal $1.00.

(g) Voting Rights. The Nonparticipating Limited Partner Units shall not be entitled to vote on any matters coming before the Partners for a vote.

(h) No Certificates. The Nonparticipating Limited Partner Units will not be evidenced by certificates.

(i) Registrar and Transfer Agent. The Partnership will act as the registrar and transfer agent of the Nonparticipating Limited Partner Units.

6. Section 6.3 is hereby amended by adding the following final sentence:

“Notwithstanding anything to the contrary in this Agreement, no distributions shall be made pursuant to this Section 6.3 in respect of any Nonparticipating Limited Partner Unit.”

B. Agreement in Effect. Except as hereby amended, the Holdings Partnership Agreement shall remain in full force and effect.

C. Applicable Law. This Amendment shall be construed in accordance with and governed by the laws of the State of Delaware, without regard to principles of conflicts of laws.

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D. Invalidity of Provisions. If any provisions of this Amendment are or become invalid, illegal or unenforceable in any respect, the validity, legality and enforceability of the remaining provisions contained herein shall not be affected thereby.

(Signature Page Follows)

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IN WITNESS WHEREOF, this Amendment has been executed as of the date first written above.

Signature Page to Amendment No. 1 to the Amended and Restated

Agreement of Limited Partnership of Inergy Holdings, L.P.