EX-10.29.B: FIRST AMENDMENT TO THE SUPPLEMENT

Exhibit 10.29(b)

FIRST AMENDMENT TO THE SERIES 2005-1 SUPPLEMENT

          This FIRST AMENDMENT (this “Amendment”), dated as of December 23, 2005, amends the Series 2005-1 Supplement (the “Series 2005-1 Supplement”), dated as of February 25, 2005, as amended by the First Amendment thereto, dated as of June 3, 2004, and is between CENDANT RENTAL CAR FUNDING (AESOP) LLC (formerly known as AESOP Funding II L.L.C.), a special purpose limited liability company established under the laws of Delaware (“CRCF”), THE BANK OF NEW YORK, a New York banking corporation, as trustee (in such capacity, the “Trustee”) and as agent for the benefit of the Series 2005-1 Noteholders, each Series 2005-1 Interest Rate Swap Counterparty and the Surety Provider (in such capacity, the “Series 2005-1 Agent”), to the Second Amended and Restated Base Indenture, dated as of June 3, 2004, between CRCF and the Trustee (as amended, modified or supplemented from time to time, exclusive of Supplements creating a new Series of Notes, the “Base Indenture”). All capitalized terms used herein and not otherwise defined herein shall have the respective meanings provided therefor in the Definitions List attached as Schedule I to the Base Indenture (as amended through the date hereof) or the Series 2005-1 Supplement, as applicable.

W I T N E S S E T H:

          WHEREAS, pursuant to Section 12.2(i) of the Base Indenture, an amendment to any Supplement which amends the applicable amount of Enhancement requires the consent of CRCF, the Trustee and each affected Noteholder of the applicable Series of Notes;

          WHEREAS, pursuant to Section 6.11 of the Series 2005-1 Supplement, the Surety Provider is deemed to be the sole holder of the Series 2005-1 Notes for the purpose of giving all consents, waivers and approvals under the Series 2005-1 Supplement and the Base Indenture on behalf of the Series 2005-1 Notes;

          WHEREAS, the parties desire to amend the Series 2005-1 Supplement (1) to increase the Series 2005-1 Required Enhancement Percentage when an Event of Bankruptcy has occurred with respect to a Manufacturer of Program Vehicles, (2) to modify certain Series 2005-1 Maximum Manufacturer Amounts and (3) to make conforming changes; and

          WHEREAS, CRCF has requested the Trustee, the Series 2005-1 Agent and each Noteholder to, and, upon this Amendment becoming effective, CRCF, the Trustee, the Series 2005-1 Agent and the Surety Provider voting as the sole Noteholder have agreed to, amend certain provisions of the Series 2005-1 Supplement as set forth herein;

          NOW, THEREFORE, it is agreed:

          1. Article I(b) of the Series 2005-1 Supplement is hereby amended to include the following definitions in appropriate alphabetical order:

     “Series 2005-1 Bankrupt Manufacturer Vehicle Percentage” means, as of any date of determination, a fraction, expressed as a percentage, (i) the numerator of which is the aggregate Net Book Value of all Program Vehicles manufactured by a Bankrupt Manufacturer and leased under the AESOP I Operating Lease as of such date and (ii) the denominator of which is the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease as of such date; provided that, solely for the purposes of clause (i) of this definition, if a Bankrupt Manufacturer is the debtor in Chapter 11 Proceedings, until the thirtieth (30th) calendar day following commencement of such Chapter 11 Proceedings, the Net Book Value of all Program Vehicles Manufactured by such Bankrupt Manufacturer shall be deemed to be zero.

     “Series 2005-1 Required Incremental Bankrupt Manufacturer Rate” means (i) as of any date following the occurrence of an Event of Bankruptcy with respect to a Manufacturer of Program Vehicles, the excess of (A) the Series 2005-1 Required Non-Program Enhancement Percentage as of such date over (B) the Series 2005-1 Required Program Enhancement Rate and (ii) as of any other date of determination, zero.

          2. Each of the following defined terms, as set forth in Article I(b) of the Series 2005-1 Supplement, is hereby amended and restated in its entirety as follows:

     “Series 2005-1 Maximum Aggregate Kia/Isuzu/Subaru/Hyundai/Suzuki Amount” means, as of any day, with respect to Kia, Isuzu, Subaru, Hyundai and Suzuki, in the aggregate, an amount equal to 20% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day.

     “Series 2005-1 Maximum Non-Program Vehicle Percentage” means, as of any date of determination, 40%; provided that the Series 2005-1 Maximum Non-Program Vehicle Percentage as of any date of determination shall be increased by a fraction, expressed as a percentage, the numerator of which is the aggregate Net Book Value of all Redesignated Vehicles manufactured by each Bankrupt Manufacturer and each other Manufacturer with respect to which a Manufacturer Event of Default has occurred and leased as of such date under the AESOP I Operating Lease or the Finance Lease as of such date and the denominator of which is the aggregate Net Book Value of all Vehicles leased under the Leases as of such date.

     “Series 2005-1 Maximum Manufacturer Amount” means, as of any day, any of the Series 2005-1 Maximum Mitsubishi Amount, the Series 2005-1 Maximum Individual Kia/Isuzu/Subaru Amount, the Series 2005-1 Maximum Individual Hyundai/Suzuki Amount or the Series 2005-1 Maximum Aggregate Kia/Isuzu/Subaru/Hyundai/Suzuki Amount.

     “Series 2005-1 Required Enhancement Amount” means, as of any date of determination, the sum of (i) the product of the Series 2005-1 Required Enhancement Percentage as of such date and the Series 2005-1 Invested Amount as of such date, (ii) the Series 2005-1 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the Non-Program Vehicle Amount as of such date over the Series 2005-1 Maximum Non-Program Vehicle Amount

as of such date, (iii) the Series 2005-1 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the aggregate Net Book Value of all Vehicles manufactured by Mitsubishi and leased under the Leases as of such date over the Series 2005-1 Maximum Mitsubishi Amount as of such date, (iv) the Series 2005-1 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the aggregate Net Book Value of all Vehicles manufactured by Kia, Isuzu or Subaru, individually, and leased under the Leases as of such date over the Series 2005-1 Maximum Individual Kia/Isuzu/Subaru Amount as of such date, (v) the Series 2005-1 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the aggregate Net Book Value of all Vehicles manufactured by Hyundai or Suzuki, individually, and leased under the Leases as of such date over the Series 2005-1 Maximum Individual Hyundai/Suzuki Amount as of such date, (vi) the Series 2005-1 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the aggregate Net Book Value of all Vehicles manufactured by Kia, Isuzu, Subaru, Hyundai or Suzuki, in the aggregate, and leased under the Leases as of such date over the Series 2005-1 Maximum Aggregate Kia/Isuzu/Subaru/Hyundai/Suzuki Amount as of such date, (vii) the Series 2005-1 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the Specified States Amount as of such date over the Series 2005-1 Maximum Specified States Amount as of such date, (viii) the Series 2005-1 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the Non-Eligible Manufacturer Amount as of such date over the Series 2005-1 Maximum Non-Eligible Manufacturer Amount as of such date and (ix) the Series 2005-1 Percentage of any Aggregate Adjustment Amount.

“Series 2005-1 Required Enhancement Percentage” means, as of any date of determination, the sum of (i) the product of (A) the Series 2005-1 Required Program Enhancement Rate as of such date and (B) the Series 2005-1 Program Vehicle Percentage as of such date, (ii) the product of (A) the Series 2005-1 Required Non-Program Enhancement Percentage as of such date and (B) the Series 2005-1 Non-Program Vehicle Percentage as of such date, and (iii) the product of (A) the Series 2005-1 Required Incremental Bankrupt Manufacturer Rate as of such date and (B) the Series 2005-1 Bankrupt Manufacturer Vehicle Percentage as of such date.

          3. Article I(b) of the Series 2005-1 Supplement is hereby amended by deleting the definition “Series 2005-1 Maximum Individual Kia/Isuzu/Subaru/Hyundai/Suzuki Amount” and inserting the following definitions in appropriate alphabetical order:

     “Series 2005-1 Maximum Individual Kia/Isuzu/Subaru Amount” means, as of any day, with respect to Kia, Isuzu or Subaru, individually, an amount equal to 5% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day.

     “Series 2005-1 Maximum Individual Hyundai/Suzuki Amount” means, as of any day, with respect to Hyundai or Suzuki, individually, an amount equal to 7.5% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day.

          4. This Amendment is limited as specified and, except as expressly stated herein, shall not constitute a modification, acceptance or waiver of any other provision of the Series 2005-1 Supplement.

          5. This Amendment shall become effective as of the date (the “Amendment Effective Date”) on which each of the following have occurred: (i) each of the parties hereto shall have executed and delivered this Amendment to the Trustee, (ii) the Rating Agency Consent Condition shall have been satisfied with respect to this Amendment, (iii) all certificates and opinions of counsel required under the Base Indenture shall have been delivered to the Trustee and (iv) the Surety Provider, as the Requisite Noteholders, shall have consented hereto.

          6. From and after the Amendment Effective Date, all references to the Series 2005-1 Supplement shall be deemed to be references to the Series 2005-1 Supplement as amended hereby.

          7. This Amendment may be executed in separate counterparts by the parties hereto, each of which when so executed and delivered shall be an original but all of which shall together constitute one and the same instrument.

          8. THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES HEREUNDER SHALL BE CONSTRUED IN ACCORDANCE WITH AND GOVERNED BY THE LAWS OF THE STATE OF NEW YORK.

          IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed by their respective duly authorized officers as of the date above first written.