Exhibit 4.1

EXECUTION COPY

THIRD SUPPLEMENTAL INDENTURE

THIRD SUPPLEMENTAL INDENTURE (this “Third Supplemental Indenture”) dated as of May 8, 2012, among VERSO PAPER HOLDINGS LLC, a Delaware limited liability company (the “Company”), VERSO PAPER INC., a Delaware corporation (together with the Company, the “Issuers”), the GUARANTORS party thereto (the “Guarantors”), and WILMINGTON TRUST COMPANY, as trustee under the Indenture referred to below (the “Trustee”).

WITNESSETH

WHEREAS, the Issuers and the Guarantors have heretofore executed and delivered to the Trustee an indenture (the “Original Indenture”), dated as of August 1, 2006, providing for the issuance of the Issuers’ Second Priority Senior Secured Floating Rate Notes due 2014 (the “Securities”), initially in the aggregate principal amount of $250,000,000, as amended and supplemented by the First Supplemental Indenture (the “First Supplemental Indenture”), dated as of May 30, 2009, among the Issuers, the new guarantors named therein and the Trustee, and as further amended and supplemented by the Second Supplemental Indenture (the “Second Supplemental Indenture”), dated as of January 10, 2011, among the Issuers, the new guarantor named therein and the Trustee (the Original Indenture, as amended and supplemented by the First Supplemental Indenture and the Second Supplemental Indenture, the “Indenture”);

WHEREAS, Section 9.02(a) of the Indenture provides that the Issuers, the Guarantors and the Trustee may amend the Indenture with respect to each series of Securities with the written consent of the Holders of at least a majority in principal amount of the Securities of such series then outstanding voting as a single class (including consents obtained in connection with a tender offer or exchange offer for the Securities) (the “General Requisite Consents”);

WHEREAS, Sections 9.02(a) and 11.04(a)(4) of the Indenture allow the release of Liens on property that constitutes all of the Collateral securing the obligations under the Securities (the “Collateral Release”) with the consent of the Holders of at least two-thirds in aggregate principal amount of the outstanding Securities (the “Collateral Release Requisite Consents” and, together with the General Requisite Consents, the “Requisite Consents”);

WHEREAS, the Issuers distributed a confidential offering memorandum and consent solicitation dated March 28, 2012, as supplemented by the news release issued on April 11, 2012, as supplemented by Supplement No. 1 dated April 25, 2012 and as further supplemented by Supplement No. 2 dated May 7, 2012 (as amended and supplemented, the “Offering Memorandum”), in order to, among other things, subject to the terms and conditions set forth in the Offering Memorandum, solicit consents (the “Consents”) from Holders to certain amendments to the Indenture and the Securities (the “Proposed Amendments”);

WHEREAS, the Holders of 92.61% in principal amount of the outstanding Securities have validly tendered Consents and not validly withdrawn their Consents to the adoption of the Proposed Amendments;

WHEREAS, having received the Requisite Consents from the outstanding Securities, pursuant to Section 9.02(a) of the Indenture, the Issuers, the Guarantors and the Trustee desire to amend the Indenture;

WHEREAS, the Issuers, the Guarantors and the Trustee are authorized to execute and deliver this Third Supplemental Indenture;

WHEREAS, the Issuers have complied with all conditions precedent provided for in the Indenture relating to this Third Supplemental Indenture; and

WHEREAS, the Issuers have requested that the Trustee execute and deliver this Third Supplemental Indenture.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Issuers, the Guarantors and the Trustee mutually covenant and agree for the equal and ratable benefit of the Holders of the Securities as follows:

1. Defined Terms. Capitalized terms used but not otherwise defined herein shall have the meaning assigned to them in the Indenture. The words “herein,” “hereof” and “hereby” and other words of similar import used in this Third Supplemental Indenture refer to this Third Supplemental Indenture as a whole and not to any particular section hereof.

2. Effectiveness. This Third Supplemental Indenture shall become effective immediately upon its execution and delivery by the Issuers, the Guarantors and the Trustee; provided that the amendments to the Indenture set forth herein shall not be operative until all of the Securities that have been tendered and accepted for payment have been paid for in accordance with the terms of the Offering Memorandum.

3. Amendment. The Indenture is hereby amended by deleting the following Sections or clauses of the Indenture and all references and definitions related thereto in their entirety, except to the extent otherwise provided below, and these Sections and clauses shall be of no further force and effect, and the words “[INTENTIONALLY DELETED]” shall be inserted, in each case, in place of the deleted text:

Section 4.02 (Reports and Other Information)

Section 4.03 (Limitation on Incurrence of Indebtedness and Issuance of Disqualified Stock and Preferred Stock)

Section 4.04 (Limitation on Restricted Payments)

2

Section 4.05 (Dividend and Other Payment Restrictions Affecting Subsidiaries)

Section 4.06 (Asset Sales)

Section 4.07 (Transactions with Affiliates)

Section 4.08 (Change of Control)

Section 4.09 (Compliance Certificate)

Section 4.10 (Further Instruments and Acts)

Section 4.11 (Future Guarantors)

Section 4.12 (Liens)

Section 4.13 (Impairment of Security Interest)

Section 4.15 (Limitation on Business Activities of Finance Co.)

Section 4.16 (Further Assurances; Collateral Inspections and Reports; Costs and Indemnification)

Clauses (a)(iii), (a)(iv), (a)(vi) and (b)(ii) of Section 5.01 (When Company May Merge or Transfer Assets)

Clauses (c), (d), (e), (f) and (g) of Section 6.01 (Events of Default)

Section 6.12 (Waiver of Stay or Extension Laws)

Clauses (a)(ii), (a)(iii), (a)(iv), (a)(v), (a)(vi), (a)(vii) and (a)(viii) of Section 8.02 (Conditions to Defeasance)

4. Approval of Amendments to, Restatements of or Termination of Certain Security Documents. Notwithstanding anything to the contrary, any amendments to, restatements of, or termination of, as applicable, the Security Documents and any related documents, including, but not limited to, any acknowledgements, side-letters, joinders and other agreements, in order to effectuate all of the transactions contemplated by the Collateral Release shall be permitted under the Indenture.

5. Ratification of Indenture; Supplemental Indentures Part of Indenture. Except as expressly amended hereby, the Indenture is in all respects ratified and confirmed and all the terms, conditions and provisions thereof shall remain in full force and effect. This Third Supplemental Indenture shall form a part of the Indenture for all purposes, and every holder of Securities heretofore or hereafter authenticated and delivered shall be bound hereby.

3

6. Governing Law. THIS THIRD SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

7. Trustee Makes No Representation. The Trustee makes no representation as to the validity or sufficiency of this Third Supplemental Indenture.

8. Counterparts. The parties may sign any number of copies of this Third Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement.

9. Effect of Headings. The Section headings herein are for convenience only and shall not effect the construction thereof.

[Remainder of page intentionally left blank]

4

IN WITNESS WHEREOF, the parties have caused this Third Supplemental Indenture to be duly executed as of the date first written above.

GUARANTORS:

VERSO PAPER LLC

VERSO ANDROSCOGGIN LLC

VERSO BUCKSPORT LLC

VERSO SARTELL LLC

VERSO QUINNESEC LLC

VERSO MAINE ENERGY LLC

VERSO FIBER FARM LLC

VERSO QUINNESEC REP HOLDING INC.

NEXTIER SOLUTIONS CORPORATION

[Signature Page to Supplemental Indenture]

5

[Signature Page to Supplemental Indenture]

6