Amendment No. 1 to Override Agreement

Exhibit 10.1

Amendment No. 1 to

Override Agreement

This Amendment No. 1 to Override Agreement dated as of March 27, 2008 (the “Amendment”) is by and among Thornburg Mortgage Inc. (“TMI”), Thornburg Mortgage Hedging Strategies, Inc. (“TMHS” and, together with TMI, “TMA”) and each entity designated on the signature pages hereto as a “Counterparty” (each a “Counterparty” and, collectively, the “Counterparties”). Unless otherwise defined herein, capitalized terms shall have the meaning given to them in that certain Override Agreement dated as of March 17, 2008 (the “Override Agreement”) by and among TMI, TMHS and the Counterparties.

RECITALS

WHEREAS, TMA and the Counterparties desire to amend the Override Agreement;

NOW, THEREFORE, in consideration of good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties agree as follows:

AGREEMENT

1. Amendment to the Override Agreement.

(a) Section 1(c) of the Override Agreement is hereby amended by deleting “or” at the end of clause (vi), replacing the period at the end of clause (vii) with “; or”, and adding the following clause (viii):

“(vii) TMA breaches its covenant in the last sentence of Section 3 of Amendment No. 1 to Override Agreement dated as of March 27, 2008.”

(b) Section 3(a) of the Override Agreement is hereby amended and restated to read in its entirety as follows:

“on or before March 28, 2008, to obtain commitments to raise at least $1 billion of new capital (the “Capital Raise”) and to receive net proceeds of at least $948 million of the Capital Raise;”

(c) The phrase “promptly upon (and in any event no later than the next business day after) receipt of the net proceeds of the Capital Raise” in Section 3(b) of the Override Agreement is hereby replaced with the phrase “on March 31, 2008”.

(d) Section 3(g) of the Override Agreement is hereby amended and restated to read in its entirety as follows:

“promptly upon receipt of any required legal and regulatory approvals, including any approval from the New York Stock Exchange and any shareholders approval, and completion of the Capital Raise, to issue to the Counterparties such number of “penny” warrants for TMI common stock that (after each of a shareholders’ vote authorizing an increase in the number of authorized shares of common stock of TMI (the “Vote”) and the completion of self-tenders for preferred stock of TMI (the “Tender”)) will constitute at least 4.04% of common stock of TMI on a fully diluted basis, provided that the Counterparties shall exercise such warrants promptly and shall vote at any shareholders’ meeting occurring on or before June 15, 2008 any common stock of TMI owned by them in favor of a proposal to increase the number of authorized shares of common stock of TMI. Subject to receipt of regulatory approvals, TMA shall issue 46,960,000 million of such warrants to the Counterparties no later than April 11, 2008, and the remaining such warrants promptly after each of the Vote and the Tender. Each such warrant will be exercisable for a period of 5 years at an exercise price of $0.01 per share of common stock of TMI and have terms substantially similar to the terms of warrants granted to investors participating in the Capital Raise. Warrants will be allocated to each Counterparty in proportion to the percentages set forth on Schedule IV;”

(e) Schedule I of the Override Agreement is hereby amended to add the following sentence immediately before the subheading “Repo Balances and Margin Call Amounts”:

“Notwithstanding anything to the contrary in this Agreement, solely for purposes of Sections 2(a), 2(b), 3(d) and any security agreement or other document or instrument giving effect to Section 3(d), the Bear Stearns auction rate swap with a call date of July 25, 2008 and a notional amount on March 27, 2008 of $409,077,000 shall be a Financing Agreement (and shall be secured to the same extent as all other Financing Agreements).”

(f) Schedule IV of the Override Agreement is hereby amended and restated to read in its entirety as set forth on Exhibit A hereto.

2. Waiver.

(a) The Counterparties hereby waive the requirement of Section 3(a) of the Override Agreement as in effect prior to the execution of this Amendment (the “Original Override Agreement”) with respect to the failure timely to obtain the commitments and to receive the net proceeds as required by such Section 3(a) of the Original Override Agreement, and agree that no Override Termination Event will be deemed to have occurred as a result of such failure.

(b) The Counterparties hereby waive any and all Override Termination Events pursuant to Section 1(c)(vii) of the Override Agreement arising solely as a result of the Change in Control resulting from the transactions contemplated by the Capital Raise and described (subject to non-material variations) in the term sheet included as Exhibit 10.1 to the Current Report on Form 8-K filed with the Securities and Exchange Commission on March 24, 2008, and agree that no such Override Termination Event will be deemed to have occurred as a result of any such Change in Control.

(c) The waiver granted pursuant to Section 2(b) hereof shall terminate at 5:00 p.m. (New York City time) on March 28, 2008 if TMA shall not have received prior to such time net proceeds of at least $948 million of the Capital Raise.

(d) Except as expressly provided in this Section 2 of this Amendment, the execution, delivery and effectiveness of this Amendment will not: (a) limit, impair, constitute a waiver of or otherwise affect any right, power or remedy of any Counterparty under the Override Agreement, the Original Override Agreement or the related Financing Agreements or any document or instrument relating to the foregoing; or (b) constitute a waiver of any provision in the Override Agreement, the Original Override Agreement or any Financing Agreement.

3. Acknowledgement. The Counterparties acknowledge that TMA will grant a security interest in any rights to payment of interest with respect to the assets subject to the Override Agreement to the extent (and only to the extent) that such interest is required to be remitted (after, without limitation, application of any portion thereof as may be permitted (i) pursuant to the Override Agreement, any Financing Agreement, any security agreement or other document, instrument and agreement executed by TMA or any of its affiliates in connection with any of the foregoing or (ii) by setoff, netting or other similar provisions of any agreement that is not a Financing Agreement between a Counterparty or an affiliate and TMI or an affiliate) to TMA pursuant to the last sentence of Section 2(f) of the Override Agreement or (if the Override Agreement has terminated) any of the Financing Agreements (the “Payment Rights”), notwithstanding any restrictions in those agreements on the transfer of the Payment Rights, in reliance on Uniform Commercial Code §§ 9-406(d) and 9-408(a). The Counterparties consent to the grant of such security interest. TMA agrees to substitute for such security interest on or before April 7, 2008 a security interest in a deposit account or a security account to which the Counterparties will be instructed irrevocably to make any such payments.

4. Conditions to Effectiveness. This Amendment shall be effective as of the date hereof only if, on or before March 31, 2008, (a) TMA completes the Capital Raise to raise at least $1,000,000,000 of new capital and to receive net cash proceeds of at least $948,000,000, (b) TMA pays $50,000,000 in the aggregate to Royal Bank of Scotland plc and Greenwich Capital Markets Inc. and $10,000,000 in the aggregate to Credit Suisse International in respect of their exposure under the Auction Swaps and (c) TMA pays no more than $10,000,000 to Citigroup Global Markets Limited in respect of the prior reduction in TMA’s Payment Obligations by at least $500,000,000.

5. Miscellaneous.

(a) On and after the date of this Amendment, each reference in the Override Agreement to “this Agreement,” “hereunder,” “hereof,” “herein” or words of like import, shall mean and be a reference to the Override Agreement as amended by this Amendment.

(b) Except as specifically amended above, the Override Agreement is and shall continue to be in full force and effect and is hereby ratified and confirmed in all respects.

(c) This Amendment may be executed in any number of counterparts and by different parties in separate counterparts, each of which taken together shall constitute one and the same original.

(d) This Amendment shall be governed by and construed in accordance with the laws of the State of New York, without reference to the choice of law doctrine of such state.

<Signature Pages Follow>

IN WITNESS WHEREOF, this Amendment No. 1 to the Override Agreement is agreed and accepted as of the day and year first above written.