THORNBURG MORTGAGE, INC.

Exhibit 10.4.3

THORNBURG MORTGAGE, INC.

AMENDMENT NO. 3

TO

AMENDED AND RESTATED

2002 LONG-TERM INCENTIVE PLAN

Dated as of January 25, 2005

Pursuant to Section 8.2 of the Amended and Restated 2002 Long-Term Incentive Plan (the “Plan”), the Board of Directors of Thornburg Mortgage, Inc. (the “Company”) hereby revises and amends the terms of the Plan as follows, effective January 25, 2005:

Section 3.6.1 of the Plan shall be amended by adding the following sentence at the end of the Section:

“The term of service on the Advisory Board and the term of continued participation in the incentive compensation distributions under the Plan under Section 3.6.2, shall be limited to a maximum of ten (10) years from the date of joining the Advisory Board.”

The Plan, as amended herein, is in all respects ratified and affirmed on behalf of the Company by its Board of Directors, including a majority of its non-employee Directors.

The Company has caused this Amendment No. 3 to the Plan to be executed in the name and on behalf of the Company by an officer of the Company thereunto duly authorized as of the date written above.