NightHawk Radiology Holdings, Inc. Board Member Appointment and Compensation Letter Agreement with Ernie Ludy

Exhibit 10.24

May 24, 2006

Mr. Ernie Ludy

3030 Bridgeway, Suite 204

Sausalito, CA 94965

Dear Ernie:

On behalf of NightHawk Radiology Holdings, Inc. (the “Company”), I am extremely pleased to invite you to become a member of the Company’s Board of Directors (the “Board”). It is our belief that your skills, expertise and knowledge will prove helpful to the progress of the Company.

In connection with your service as director, you will receive an initial grant of restricted stock units (the “Initial Grant”) equal to approximately $200,000, with the actual number of restricted stock units to be determined on the date of grant based upon the closing trading price of the Company’s common stock. The Initial Grant will be made pursuant to the Company’s 2006 Equity Incentive Plan (the “Plan”) with the shares vesting fully on the one year anniversary of the date of the Initial Grant. Beginning at the annual meeting of the Company’s Board held in connection with the Company’s 2007 annual stockholder meeting, and at each annual meeting thereafter during your service on the Board, you may also receive an additional grant of restricted stock units in an amount currently anticipated to be equal to approximately $120,000, the actual number of restricted stock units to be determined at the time of the grant (the “Annual Grant”).

The Initial Grant and the Annual Grant will be subject to the terms and conditions of the Plan and the Restricted Stock Unit Agreement evidencing the Initial Grant and the Annual Grant.

In addition to the grants described above, you will also receive cash compensation in the amount of $4,000 per quarter during your service as a Board member and an additional $1,000 for each board or committee meeting attended in person ($500 for meetings attended by telephone). Finally, you shall also be reimbursed for all reasonable expenses incurred by you in connection with your services to the Company. All expense reimbursements will be in accordance with established Company policies.

Our Board meetings are generally held quarterly and we would hope that your schedule would permit you to attend all of the meetings. In addition, there may be telephonic calls to address special projects that arise from time to time.

In addition to your service on the Board, as one of the Company’s “independent” directors, the Company will require your service on the Board’s Audit Committee.

In accepting this offer, you are representing to us that (i) you do not know of any conflict that would restrict you from becoming a director of the Company and (ii) you will not provide the Company with any documents, records or other confidential information belonging to any other parties. Nothing in this offer or the Restricted Stock Agreement(s) should be construed to interfere with or otherwise restrict in any way the rights of the Company and the Company’s stockholders to remove any individual from the Board at any time in accordance with the provisions of applicable law.

May 24, 2006

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We hope that you find the foregoing terms acceptable. You may indicate your agreement with these terms and accept this offer by signing and dating both the enclosed duplicate and original letter and returning them to me.

We are looking forward to having you join us at the Company. We believe that your enthusiasm and past experience will be an asset to the Company and that you will have a positive impact on the organization. If you have any questions, please call me at (208)  ###-###-####.

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