AMENDMENT TO RIGHTS AGREEMENT

Exhibit 4.1

Execution Version

AMENDMENT TO RIGHTS AGREEMENT

     THIS AMENDMENT (the “Rights Amendment”) is entered into as of the 9th day of July 2007, by and between Graphic Packaging Corporation, a Delaware corporation (f/k/a Riverwood Holding, Inc.) (the “Corporation”), and Wells Fargo Bank, National Association (f/k/a Wells Fargo Bank Minnesota, National Association), as Rights Agent (the “Rights Agent”), in order to amend the terms of that certain Rights Agreement dated as of August 7, 2003, by and between the Corporation and the Rights Agent (the “Rights Agreement”).

     WHEREAS, the Corporation, Bluegrass Container Holdings, LLC, a Delaware limited liability Company (“BCH”), TPG Bluegrass IV, LP, a Delaware limited partnership (“TPG IV”), TPG Bluegrass IV-AIV 2, LP, a Delaware limited partnership (“TPG IV-AIV”), TPG Bluegrass V, LP, a Delaware limited partnership (“TPG V”), TPG Bluegrass V-AIV 2, LP, a Delaware limited partnership (“TPG V-AIV”), Field Holdings, Inc., a Delaware corporation (“Field Holdings”), TPG FOF V-A, L.P., a Delaware limited partnership (“FOF V-A”), TPG FOF V-B, L.P., a Delaware limited partnership (“FOF V-B”), BCH Management LLC, a Delaware limited liability company (together with TPG IV, TPG IV-AIV, TPG V, TPG V-AIV, Field Holdings FOF V-A, FOF V-B and each owner of BCH equity interests joining the Transaction Agreement (as hereinafter defined) as a Seller pursuant to Section 5.13 of the Transaction Agreement, the “Sellers”), New Giant Corporation, a Delaware corporation (“Newco”), and Giant Merger Sub, Inc., a Delaware corporation (“Merger Sub”) propose to enter into a Transaction Agreement and Agreement and Plan of Merger, dated as of July 9, 2007 (the “Transaction Agreement”) pursuant to which Merger Sub will be merged with and into the Corporation (the “Merger”) and each Seller will contribute to Newco the BCH equity interests owned by each such Seller in exchange for the issuance by Newco to each such Seller of common stock of Newco (the “Exchange”);

     WHEREAS, BCH, the Corporation and certain stockholders of the Corporation, in connection with the Transaction Agreement, are entering into a Voting Agreement, dated as of July 9, 2007 (the “Voting Agreement”);

     WHEREAS, the Board of Directors of the Corporation has determined, in connection with the proposed execution of the Transaction Agreement and the Voting Agreement, that it is desirable to amend the Rights Agreement to exempt the Transaction Agreement, the Voting Agreement, and the transactions contemplated thereby, including, without limitation, the Merger and the Exchange, from the application of the Rights Agreement as set forth in this Rights Amendment;

     WHEREAS, as of the time immediately prior to the execution of this Rights Amendment, no Person has become an Acquiring Person;

     WHEREAS, Section 27 of the Rights Agreement provides that prior to a Stock Acquisition Time, the Corporation may, and the Rights Agent shall if the Corporation so directs, supplement or amend any provision of the Rights Agreement in any respect whatsoever or desirable without the approval of any other person or persons, subject to certain limitations provided therein;

     WHEREAS, Section 27 of the Rights Agreement provides that any supplement or amendment to the Rights Agreement becomes effective immediately upon execution by the Corporation, whether or not executed by the Rights Agent, so long as it does not amend the Rights Agreement in a manner adverse to the Rights Agent; and

     WHEREAS, the Corporation desires to amend the Rights Agreement as set forth herein and hereby directs the Rights Agent to execute this Rights Amendment.

     NOW, THEREFORE, in consideration of the premises and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto do hereby agree as follows:

     SECTION 1. AMENDMENTS TO THE RIGHTS AGREEMENT. The Rights Agreement is hereby amended as follows:

          1.1. New Definitions. Section 1 of the Rights Agreement is hereby amended by inserting the following subsections at the end of Section 1:

“(aaa) “Transaction Agreement” shall mean the Transaction Agreement and Agreement and Plan of Merger dated as of July 9, 2007 (as it may be amended or supplemented from time to time), by and among the Corporation, Bluegrass Container Holdings, LLC, a Delaware limited liability Company, TPG Bluegrass IV, LP, a Delaware limited partnership, TPG Bluegrass IV-AIV 2, LP, a Delaware limited partnership, TPG Bluegrass V, LP, a Delaware limited partnership, TPG Bluegrass V-AIV 2, LP, a Delaware limited partnership, Field Holdings, Inc., a Delaware corporation, TPG FOF V-A, L.P., a Delaware limited partnership, TPG FOF V-B, L.P., a Delaware limited partnership, BCH Management, LLC, a Delaware limited liability company, New Giant Corporation, a Delaware corporation, and Giant Merger Sub, Inc., a Delaware corporation.”

“(bbb) “Merger” shall have the meaning set forth in the Transaction Agreement.”

“(ccc) “Exchange” shall have the meaning set forth in the Transaction Agreement.”

“(ddd) “Exempted Transaction” shall have the meaning set forth in Section 1(a)(vi) of this Agreement.”

“(eee) “BCH Parties” shall mean Bluegrass Container Holdings, LLC, a Delaware limited liability Company, TPG Bluegrass IV, LP, a Delaware limited partnership, TPG Bluegrass IV-AIV 2, LP, a Delaware limited partnership, TPG Bluegrass V, LP, a Delaware limited partnership, TPG Bluegrass V-AIV 2, LP, a Delaware limited partnership, Field Holdings, Inc., a Delaware corporation, TPG FOF V-A, L.P., a Delaware limited partnership, TPG FOF V-B, L.P., a Delaware limited partnership, BCH Management, LLC, a Delaware limited liability company and each owner of BCH equity interests joining the Transaction Agreement as a Seller pursuant to Section 5.13 of the Transaction Agreement.”

“(fff) “Newco” shall have the meaning set forth in the Transaction Agreement.”

“(ggg) “Merger Sub” shall have the meaning set forth in the Transaction Agreement.”

“(hhh) “Voting Agreement” shall mean the Voting Agreement dated as of July 9, 2007 (as it may be amended or supplemented from time to time), by and among Bluegrass Container Holdings, LLC, the Corporation and certain stockholders of the Corporation.”

          1.2. Amendment to Definition of “Acquiring Person”. Section 1(a) of the Rights Agreement is hereby amended by inserting the following subclause (vi) at the end of Section 1(a):

“(vi) Notwithstanding anything in this Agreement to the contrary, none of the BCH Parties, their Subsidiaries, Affiliates or Associates, including Newco or Merger Sub, is, nor shall any of them be deemed to be, an Acquiring Person solely by reason of (A) the approval, amendment, adoption, execution, delivery or performance of the Transaction Agreement, (B) the approval or consummation of the Merger or the Exchange, (C) the approval or consummation of any other transaction contemplated by the Transaction Agreement, (D) the approval, amendment, adoption, execution, delivery or performance of the Voting Agreement or (E) the announcement of any of the foregoing, it being the purpose of the Corporation in adopting this amendment to the Agreement that neither the execution of the Transaction Agreement or Voting Agreement by any of the parties nor the consummation of the transactions contemplated thereby shall in any respect give rise to any provisions of the Agreement becoming effective. Each event described in this subclause (vi) is referred to herein as an “Exempted Transaction.”

          1.3. Amendment to Definition of “Beneficial Owner”. Section 1(f) of the Rights Agreement shall be amended by inserting the following subclause (v) at the end of Section 1(f):

“(v) Notwithstanding anything in this Section 1(f) to the contrary, none of the BCH Parties, their Subsidiaries, Affiliates or Associates, including Newco and Merger Sub, shall be deemed a Beneficial Owner of, or to beneficially own, any securities solely by virtue of or as a result of any Exempted Transaction.”

          1.4. Amendment to Definition of “Stock Acquisition Time”. Section 1(uu) of the Rights Agreement shall be amended by inserting the following sentence at the end of Section 1(uu):

“Notwithstanding the foregoing or any provision to the contrary in this Agreement, a Stock Acquisition Time shall not occur or be deemed to have occurred by virtue of or as a result of any Exempted Transaction.”

          1.5. Amendment to Section 3(a). Section 3(a) of the Rights Agreement shall be amended by inserting the following sentence at the end of Section 3(a):

“Notwithstanding the foregoing or any provision to the contrary in this Agreement, a Distribution Date shall not occur or be deemed to have occurred in connection with, by virtue of or as a result of any Exempted Transaction.”

          1.6. Amendment to Section 7(a). Clause (i) of Section 7(a) of the Rights Agreement shall be amended and restated in its entirety to read as follows:

“(i) the earlier of (A) the Close of Business on August 8, 2013 or (B) immediately prior to the Effective Time (as defined in the Transaction Agreement and of which the Corporation will give the Rights Agent twenty four (24) hours notice), but only if such Effective Time shall occur (the earlier of (A) and (B) being herein referred to as the “Final Expiration Date”)”.

          1.7. Amendment to Section 8. Section 8 of the Rights Agreement shall be amended by deleting the last two sentences of Section 8 and by inserting the following three sentences at the end of Section 8:

“Subject to applicable law and regulation, the Rights Agent shall maintain (i) in a retrievable database electronic records of all cancelled or destroyed stock certificates

which have been canceled or destroyed by the Rights Agent. The Rights Agent shall maintain such electronic records or physical records for the time period required by applicable law and regulation. Upon written request of the Corporation (and at the expense of the Corporation), the Rights Agent shall provide to the Corporation or its designee copies of such electronic records or physical records relating to rights certificates cancelled or destroyed by the Rights Agent.”

          1.8. Amendment to Section 11(a)(ii). Section 11(a)(ii) of the Rights Agreement shall be amended by inserting the following sentence at the end of Section 11(a)(ii):

“Notwithstanding the foregoing or any provision to the contrary in this Agreement, a Section 11(a)(ii) Event shall not occur or be deemed to have occurred in connection with, by virtue of or as a result of any Exempted Transaction.”

          1.9. Amendment to Section 13(a). Section 13(a) of the Rights Agreement shall be amended by inserting the following sentence at the end of Section 13(a):

“Notwithstanding the foregoing or any provision to the contrary in this Agreement, a Section 13 Event shall not occur or be deemed to have occurred, in connection with, by virtue of or as a result of any Exempted Transaction.”

          1.10. Amendment to Section 13(b). Section 13(b) of the Rights Agreement shall be amended by inserting the following sentence at the end of Section 13(b):

“Notwithstanding the foregoing or any provision to the contrary in this Agreement, none of the BCH Parties, their Subsidiaries, Affiliates or Associates, including Newco or Merger Sub, is, nor shall any of them be deemed to be, a Principal Party in connection with, by virtue of or as a result of any Exempted Transaction.”

          1.11. Addition of Section 35. A new Section 35 is hereby added to the end of the Agreement, which new Section 35 shall read in its entirety as follows:

“Section 35. Termination. On the Final Expiration Date, (a) this Agreement shall be terminated and be without any further force or effect, (b) none of the parties to this Agreement will have any rights, obligations or liabilities hereunder and (c) the holders of the Rights shall not be entitled to any benefits, rights or other interests under this Agreement, including, without limitation, the right to purchase or otherwise acquire Preferred Stock or any other securities of the Corporation.”

     SECTION 2. DIRECTION TO RIGHTS AGENT. The Corporation hereby directs Wells Fargo Bank, National Association, in its capacity as Rights Agent and in accordance with the terms of Section 27 of the Rights Agreement, to execute this Rights Amendment.

     SECTION 3. EFFECTIVENESS AND CONTINUED EFFECTIVENESS. Except as specifically supplemented and amended, changed or modified in Section 1 above, the Rights Agreement shall be unaffected by this Rights Amendment and remain in full force and effect in accordance with its terms; provided, however, that if for any reason the Transaction Agreement is terminated or the transactions contemplated thereby are abandoned, then this Rights Amendment shall be of no further force and effect and the Rights Agreement shall remain exactly the same as it existed immediately prior to execution of this Amendment. Subject to the foregoing provisions of this Section 3, this Rights

Amendment shall become effective upon execution by the Corporation and shall be deemed to be in full force and effect prior to the execution of the Transaction Agreement and Voting Agreement.

     SECTION 4. DEFINITIONS. All terms defined in the Rights Agreement that are used herein shall have the meanings defined in the Rights Agreement, unless specifically defined otherwise herein. The term “Agreement” as used in the Rights Agreement shall mean the Rights Agreement, as amended by this Rights Amendment, or as it may from time to time be amended in the future by one or more other written amendment or modification agreements entered into pursuant to the applicable provisions of the Rights Agreement.

     SECTION 5. GOVERNING LAW. This Rights Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts to be made and performed entirely within such State. The parties agree that all actions and proceedings arising out of this Rights Amendment or any of the transactions contemplated hereby in connection with the rights and obligations of the Rights Agent shall be brought in the courts of the State of Delaware or the United States District Court for the District of Delaware (each, a “Delaware Court”) and that, in connection with any such action or proceeding relating to the rights and obligations of the Rights Agent, the parties submit to the jurisdiction of, and venue in, such Delaware Court. Each of the parties hereto irrevocably waives any right to a trial by jury in any action, proceeding or counterclaim arising out of this Rights Amendment or the transactions contemplated hereby.

     SECTION 6. COUNTERPARTS. This Rights Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

     SECTION 7. DESCRIPTIVE HEADINGS. Descriptive headings of the several Sections of this Rights Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

     SECTION 8. COMPLIANCE WITH RIGHTS AGREEMENT. By execution of this Rights Amendment by the undersigned officer of the Corporation, the Corporation hereby certifies that this Rights Amendment complies with Section 27 of the Rights Agreement.

     SECTION 9. SEVERABILITY. If any term, provision, covenant or restriction of this Rights Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Rights Amendment, and of the Rights Agreement, shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

     SECTION 10. WAIVER OF NOTICE. By executing this Rights Amendment, the Corporation and the Rights Agent hereby waive any notice requirement under the Rights Agreement pertaining to the matters addressed herein.

[SIGNATURES ON FOLLOWING PAGE]

     IN WITNESS WHEREOF, the parties hereto have caused this Rights Amendment to be duly executed as of the date first above written.

[Signature Page to Amendment to Rights Agreement]