AMENDMENT NO. 2
TO
THE HOUSTON EXPLORATION COMPANY
EXECUTIVE DEFERRED COMPENSATION PLAN

     The Houston Exploration Company (the Sponsor) wishes to amend The Houston Exploration Company Executive Deferred Compensation Plan (the Plan) to            freeze the Plan as of December 31, 2004 with respect to the value of participants vested Plan accounts as of December 31, 2004 and any deemed earnings or losses thereon accruing after December 31, 2004. The purpose of this Amendment is to permit Plan participants to enjoy a grandfathering exemption from section 409A of the Internal Revenue Code of 1986, as amended, as provided under the American Jobs Creation Act of 2004 and the authoritative guidance issued thereunder (AJCA). No modification, whether in the form of a Plan amendment, the exercise of any discretionary authority under the Plan, or otherwise, may be made to the Plan which constitutes a material modification under AJCA, and any attempt to do so will be void and without effect.

     Accordingly, effective December 31, 2004, the Plan is amended as follows: