Form of waiver to employment agreement

Exhibit 10.4

[Form of Waiver]

     This letter (this “Letter Agreement”), dated as of _____, 2004, confirms the understanding between The Houston Exploration Company, a Delaware corporation (the “Company”), and ____(the “Executive”), as follows:

I. Employment Agreement

          1. The Company and the Executive have entered into an Employment Agreement dated as of ____, 200___, a copy of which is attached hereto as Exhibit A (as amended, the “Employment Agreement”). Under the terms of the Employment Agreement, the Company is required to provide the Executive annual option grants under the Company’s 1996 Stock Option Plan with a value equal to [fifty percent (50%)] of the Executive’s annual salary.

     2. For 2004, the Company desires to satisfy its obligations with respect to the grant of options to the Executive under the Employment Agreement by providing fifty percent (50%) of the value required under the Employment Agreement in stock options under the Company’s 1996 Stock Option Plan (or a successor plan), with the remaining fifty percent (50%) of the value provided in restricted stock of the Company.

     3. By signing this Letter Agreement, the Executive hereby waives any breach of the Employment Agreement by the Company resulting from the failure to grant the specified percentage of stock options under the 1996 Stock Option Plan (or any successor plan), for 2004 only, under the Employment Agreement, and the Executive agrees to accept restricted stock of the Company in lieu of fifty percent (50%) of the stock options required to be granted under the Employment Agreement for 2004.

     4. The Company and the Executive agree that the waiver contained in this Letter Agreement shall not be construed as a waiver of the Executive’s rights to receive grants of options from the Company in any other year under the 1996 Stock Option Plan (or any successor plan) strictly in compliance with the terms of the Employment Agreement. Moreover, the Company and the Executive agree that this waiver shall not be construed as a waiver of any other past, present or future breach of the Employment Agreement by the Company, nor shall this waiver be construed as affecting any rights or benefits to which the Executive is entitled under the terms of the Employment Agreement, except with respect to the specific subject matter described above.

II. Miscellaneous

     1. Except as expressly addressed in this Letter Agreement, the Company and the Executive ratify and confirm all terms and conditions of the Employment Agreement as continuing in full force and effect.

     2. This Letter Agreement may not be amended or modified except in writing and this Letter Agreement will be governed by and construed in accordance with the laws of the State of Texas.

     If the foregoing correctly sets forth the understanding and agreement between the Company and the Executive, please so indicate by signing in the space provided for that purpose below, whereupon this Letter Agreement will constitute a binding agreement effective as of the date first above written.

Agreed:

THE EXECUTIVE:

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EXHIBIT A

[Employment Agreement]