Exhibit 10.4

AMENDMENT TO EMPLOYMENT AGREEMENT

This FIRST AMENDMENT TO EMPLOYMENT AGREEMENT (“Amendment”) dated as of January
30, 2007 is between Clayton Holdings, Inc., a Delaware corporation with its
principal place of business located at 2 Corporate Drive, Shelton, CT 06484 (the
“Employer”), and Steven L. Cohen (the “Employee”).

WHEREAS, the Employee is currently employed as the Senior Vice President —
General Counsel of the Employer under an Employment Agreement dated December 21,
2004 with an effective date of January 31, 2005 (the “Agreement”); and

WHEREAS, the Board of Directors of Employer has authorized new bonus and change
of control arrangements in respect of Employee, and the parties hereto consider
it appropriate that the Agreement be amended to reflect such arrangements;

NOW, THERFORE, the Employer and the Employee agree to the following amendments
to the Agreement.  Capitalized terms used in this Amendment that are not
otherwise defined shall have the same meanings as in the Agreement.

1. Section IV. of the Agreement is hereby amended by deleting the second and
third paragraphs in their entirety and replacing them with the following:

“Notwithstanding the “at will” nature of this Agreement and Employee’s
employment hereunder, if Employee’s employment under this Agreement is
terminated for any reason other than (i) by Employer for Cause (as that term is
defined in Section I(b)), (ii) as a result of Employee’s voluntary termination
other than for Good Reason (as that term is defined herein), or (iii) due to
Employee’s death or disability, Employer shall provide to Employee the
Termination Benefits (as that term is defined below).

The “Termination Benefits” shall include continuation of salary at a rate equal
to one hundred percent (100 %) of Employee’s Base Salary as in effect at the
date of termination for a period of twelve (12) months following the date of
termination (payment shall be subject to withholding under applicable law and
shall be made in periodic installments in accordance with the Employer’s payroll
policies), unless such termination is within eighteen (18) months after the
consummation of a Change of Control (as that term is defined herein) in which
case the Employer will pay to Employee, within fifteen (15) days after the
termination of his employment, in one lump-sum payment the sum of (y) eighteen
(18) months of Base Salary and (z) one hundred fifty percent (150%) of
Employee’s target incentive bonus for the year in which the termination of
employment occurs.”

2. Section IV. of the Agreement is further amended by deleting the sixth
paragraph and replacing it with the following:

“For purposes of this Agreement, a “Change of Control” shall mean the occurrence
of any of the following: (A) the consummation of a merger or consolidation of
the Employer with or into an entity unaffiliated with the Employer prior to the
effective date of such merger or consolidation or any other corporate
reorganization, if more than fifty percent (50%) of the combined voting power of
the continuing or surviving entity’s securities outstanding immediately after
such merger, consolidation or other reorganization is owned by a person who in
the aggregate owned less than twenty-five percent (25%) of the Employer’s
combined voting power represented by the outstanding securities of the Employer
immediately prior to such merger, consolidation or other reorganization; (B) the
sale, transfer or other disposition of all or substantially all of the assets of
the Employer; (C) a change in the composition of the Board of Directors of the
Employer (the “Board”), resulting in fewer than one-half of its members either
having been (i) members of the Board on the date which was twenty-four (24)
months immediately prior to the date of the event that may constitute a Change
of Control (the “Original Members”), or (ii) elected or nominated for election
to the Board with the affirmative votes of at least a majority of the aggregate
of the

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Original Members who were on the Board at the time of the election or nomination
and the members whose election or nomination was previously so approved; or (D)
any transaction as a result of which any person becomes the “Beneficial Owner”
(as defined in Rule 13d-3 under the Securities Exchange Act of 1934, as
amended), directly or indirectly, of securities of the Employer representing
more than fifty percent (50%) of the total voting power represented by the
Employer’s then outstanding voting securities.  For purposes of the immediately
preceding subsection (D), the term “Person” shall have the same meaning as when
used in section 13(d) and 14(d) of the Securities Exchange Act of 1934, as
amended, but shall exclude: (i) a trustee or other fiduciary holding securities
under an employee benefit plan of the Employer or a subsidiary thereof; (ii) a
corporation owned directly or indirectly by the stockholders of the Employer in
substantially the same proportions as their ownership of the common stock of the
Employer; and (iii) the Employer.  For purposes of this Agreement, “Good Reason”
shall mean the occurrence of any of the following events: (A) a reduction in
Employee’s annual Base Salary; (B) a material diminution of Employee’s duties or
job function as the Senior Vice President — General Counsel of the Employer or
otherwise normally expected of or assigned to a person holding the position of
Senior Vice President — General Counsel at a business of Employer’s size, nature
and industry; or (C) the relocation of the offices at which Employee is
principally employed to any other location which increases Employee’s commute by
more than fifty (50) miles from the current location of such offices.

3. Section V of the Agreement is hereby deleted in its entirety and replaced
with the following:

“V.          INCENTIVE COMPENSATION:

In addition to Base Salary, Employee shall be eligible to receive an annual
incentive bonus. The Employer, at its discretion, shall determine the exact
amount of such bonus based on a combination of Employer and Employee performance
goals, criteria and targets established by the Employer’s Board of Directors or
a committee thereof.”

[Remainder of Page Intentionally Left Blank]

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IN WITNESS WHEREOF, the Employee and Employer have executed this Amendment as of
the date set forth above.

 

EMPLOYEE:

 

 

 

 

 

/s/ Steven L. Cohen

 

Steven L. Cohen

 

 

 

 

 

EMPLOYER:

 

 

 

CLAYTON HOLDINGS, INC.

 

 

 

 

 

/s/ Frank P. Filipps

 

Frank P. Filipps

 

Chief Executive Officer

 

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