<PAGE>

                                                                   EXHIBIT 10.12

                               NETEZZA CORPORATION

                               Amendment No. 1 to
              Third Amended and Restated Investor Rights Agreement

     This Amendment No. 1, dated as of June 14, 2005, amends the Third Amended
and Restated Investor Rights Agreement dated as of December 22, 2004 among
Netezza Corporation, a Delaware corporation (the "Company'), the Founders and
the Purchasers (the "Investor Rights Agreement"). Capitalized terms not defined
herein shall have the meanings ascribed to them in the Investor Rights
Agreement.

     WHEREAS, the Company is issuing Warrants to Purchase Stock to each of
Silicon Valley Bank and Gold Hill Venture Lending 03, L.P.; and

     WHEREAS, such Warrants to Purchase Stock provide for the grant by the
Company to Silicon Valley Bank and Gold Hill Lending 03, L.P. of certain
registration rights with respect to the shares issuable upon exercise of such
Warrants to Purchase Stock;

     NOW, THEREFORE, in consideration of the execution of the Loan and Security
Agreement among the Company, Silicon Valley Bank and Gold Hill Venture Lending
03, L.P. and other good and valuable consideration, the receipt and sufficiency
of which are hereby acknowledged, the undersigned parties to this Amendment No.
1 hereby agree as follows:

     1. Section 1 of the Investor Rights Agreement is hereby amended as follows:

          (a) In clause (vi) of the definition of "Shares", the term "SVB
Shares" is hereby deleted and the term "Warrant Shares" is hereby substituted
therefor.

          (b) In the definition of "Stockholders", the term "Silicon Valley
Bank" is hereby deleted and the term "Lenders" is hereby substituted therefor.

          (c) The defined term "SVB Shares" is hereby deleted and the following
defined term is added in substitution therefor.

     "Warrant Shares" means (i) the shares of Series A Convertible Preferred
Stock issuable upon exercise of a Warrant to Purchase Stock dated August 27,
2001 issued by the Company to Silicon Valley Bank, (ii) the shares of Series B
Convertible Preferred Stock issuable upon exercise of a Warrant to Purchase
Stock dated September 24, 2002 issued by the Company to Silicon Valley Bank,
(iii) the shares of Series D Convertible Preferred Stock issuable upon exercise
of a Warrant to Purchase Stock dated June 14, 2005 issued by the Company to
Silicon Valley Bank and (iv) the shares of Series D Convertible Preferred Stock
issuable upon exercise of a Warrant to Purchase Stock dated June 14, 2005 issued
by the Company to Gold Hill Venture Lending 03, L.P. (such Warrants to purchase
stock are collectively referred to herein as the "Lender Warrants").

          (d) The following defined term is hereby added to Section 1:

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          "Lenders" means Silicon Valley Bank and Gold Hill Venture Lending 03,
L.P. and their permitted assigns under the Lender Warrants.

     2. Section 2.1(a) of the Investor Rights Agreement is hereby amended by (a)
deleting the term "Silicon Valley Bank" from the first sentence thereof and
inserting the term "Lenders" in substitution therefor and (b) deleting the term
"SVB Shares" from the first sentence thereof and inserting the term "Warrant
Shares" in substitution therefor.

     3. Section 3.1(g) is hereby amended by deleting clause (v) and inserting
the following in substitution therefor:

          "(v) the shares of Preferred Stock issuable upon exercise of the
Lender Warrants;"

     4. Exhibit A to the Investor Rights Agreement is hereby amended by adding
the following name and address thereto:

          Gold Hill Venture Lending 03, L.P.
          One Newton Executive Park
          Suite 306
          Newton, MA 02462

     This Amendment No. 1 has been executed as of the date first written above.

                                        COMPANY:

                                        NETEZZA CORPORATION


                                        By: /s/ Patrick J. Scannell, Jr.
                                            ------------------------------------
                                        Name: Patrick J. Scannell, Jr.
                                        Title: Senior Vice President, Chief
                                               Financial Officer and Treasurer


                                        PURCHASERS:

                                        MATRIX PARTNERS VI, L.P.

                                        By: Matrix VI Management Co., L.L.C.,
                                            its General Partner


                                        By: /s/ David Skok
                                            ------------------------------------
                                        Name: David Skok
                                              Managing Member


                                       -2-

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                                        MATRIX VI PARALLEL PARTNERSHIP-A, L.P.

                                        By: Matrix VI Management Co., L.L.C.,
                                            its General Partner


                                        By: /s/ David Skok
                                            ------------------------------------
                                        Name: David Skok
                                              Managing Member


                                        MATRIX VI PARALLEL PARTNERSHIP-B, L.P.

                                        By: Matrix VI Management Co., L.L.C.,
                                            its General Partner


                                        By: /s/ David Skok
                                            ------------------------------------
                                        Name: David Skok
                                              Managing Member


                                        WESTON & CO. VI LLC, as Nominee

                                        By: Matrix Partners Management Services,
                                            L.P.
                                            Sole Member

                                        By: Matrix Partners Management Services
                                            GP, LLC,
                                            its General Partner


                                        By: /s/ David Skok
                                            ------------------------------------
                                        Name: David Skok
                                              Authorized Member


                                       -3-

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                                        CHARLES RIVER PARTNERSHIP XI, LP

                                        By: Charles River XI GP, LP
                                            Its General Partner

                                            By: Charles River XI GP, LLC
                                            Its: General Partner


                                            By: /s/ Ted R. Dintersmith
                                                --------------------------------
                                                Authorized Manager

                                        Address: 1000 Winter Street, Suite 3300
                                                 Watham, MA 02451


                                        CHARLES RIVER FRIENDS XI-A, LP

                                        By: Charles River XI GP, LLC
                                            Its: General Partner


                                            By: /s/ Ted R. Dintersmith
                                                --------------------------------
                                                Authorized Manager

                                        Address: 1000 Winter Street, Suite 3300
                                                 Watham, MA 02451


                                        CHARLES RIVER FRIENDS XI-B, LP

                                        By: Charles River XI GP, LLC
                                            Its: General Partner


                                            By: /s/ Ted R. Dintersmith
                                                --------------------------------
                                                Authorized Manager

                                        Address: 1000 Winter Street, Suite 3300
                                                 Watham, MA 02451


                                        BATTERY VENTURES VI, L.P.

                                        By: Battery Partners VI, LLC


                                        By: /s/ Oliver D. Curme
                                            ------------------------------------
                                            Member Manager
                                            Oliver D. Curme


                                       -4-

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                                        BATTERY INVESTMENT PARTNERS VI, LLC


                                        By: /s/ Oliver D. Curme
                                            ------------------------------------
                                            Member Manager
                                            Oliver D. Curme

                                        Sequoia Capital X
                                        Sequoia Technology Partners X
                                        Sequoia Capital X Principals Fund

                                        By: SC X Management, L.L.C.
                                            A Delaware Limited Liability Company
                                            General Partner of Each


                                        By: /s/ [Illegible]
                                            ------------------------------------
                                            Managing Member


                                        MERITECH CAPITAL PARTNERS II L.P.

                                        By: Meritech Capital Associates II
                                            L.L.C.
                                            its General Partner

                                        By: Meritech Management Associates II
                                            L.L.C.
                                            a managing member


                                        By: /s/ Michael B. Gordon
                                            ------------------------------------
                                            Michael B. Gordon, a managing member


                                        MERITECH CAPITAL AFFILIATES II L.P.

                                        By: Meritech Capital Associates II
                                            L.L.C.
                                            its General Partner

                                        By: Meritech Management Associates II
                                            L.L.C.
                                            a managing member


                                        By: /s/ Michael B. Gordon
                                            ------------------------------------
                                            Michael B. Gordon, a managing member


                                       -5-

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                                        MCP ENTREPRENEUR PARTNERS II L.P.

                                        By: Meritech Capital Associates II
                                            L.L.C.
                                            its General Partner

                                        By: Meritech Management Associates II
                                            L.L.C.
                                            a managing member


                                        By: /s/ Michael B. Gordon
                                            ------------------------------------
                                            Michael B. Gordon, a managing member


                                        SILICON VALLEY BANCSHARES


                                        By:
                                            ------------------------------------
                                        Name:
                                              ----------------------------------
                                        Title:
                                               ---------------------------------


                                        GOLD HILL VENTURE LENDING 03, L.P.


                                        By: /s/ David Fischer
                                            ------------------------------------
                                        Name: David Fischer
                                        Title: Managing Director


                                       -6-