**Exhibit 10.4**
**[Form of Waiver]**   [Name of Executive]            Dear                                         :  
     This letter (this “**Letter Agreement**”), dated as of _____, 2004, confirms theunderstanding 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 Agreementdated as of ____, 200___, a copy of which is attached hereto as **Exhibit A**(asamended, the “**Employment Agreement**”). Under the terms of the EmploymentAgreement, the Company is required to provide the Executive annual optiongrants under the Company’s 1996 Stock Option Plan with a value equal to [fiftypercent (50%)] of the Executive’s annual salary.
     2. For 2004, the Company desires to satisfy its obligations with respectto the grant of options to the Executive under the Employment Agreement byproviding fifty percent (50%) of the value required under the EmploymentAgreement in stock options under the Company’s 1996 Stock Option Plan (or asuccessor plan), with the remaining fifty percent (50%) of the value providedin restricted stock of the Company.
     3. By signing this Letter Agreement, the Executive hereby waives anybreach of the Employment Agreement by the Company resulting from the failure togrant the specified percentage of stock options under the 1996 Stock OptionPlan (or any successor plan), for 2004 only, under the Employment Agreement,and the Executive agrees to accept restricted stock of the Company in lieu offifty percent (50%) of the stock options required to be granted under theEmployment Agreement for 2004.
     4. The Company and the Executive agree that the waiver contained in thisLetter Agreement shall not be construed as a waiver of the Executive’s rightsto receive grants of options from the Company in any other year under the 1996Stock Option Plan (or any successor plan) strictly in compliance with the termsof the Employment Agreement. Moreover, the Company and the Executive agreethat this waiver shall not be construed as a waiver of any other past, presentor future breach of the Employment Agreement by the Company, nor shall thiswaiver be construed as affecting any rights or benefits to which the Executiveis entitled under the terms of the Employment Agreement, except with respect tothe specific subject matter described above.
**II. Miscellaneous**
     1. Except as expressly addressed in this Letter Agreement, the Company andthe Executive ratify and confirm all terms and conditions of the EmploymentAgreement as continuing in full force and effect.
     2. This Letter Agreement may not be amended or modified except in writingand this Letter Agreement will be governed by and construed in accordance withthe laws of the State of Texas.
     If the foregoing correctly sets forth the understanding and agreementbetween the Company and the Executive, please so indicate by signing in thespace provided for that purpose below, whereupon this Letter Agreement willconstitute a binding agreement effective as of the date first above written.
 

 
       **THE HOUSTON EXPLORATION COMPANY**    By:      Name:      Title:     
Agreed:
**THE EXECUTIVE:**     [Name of Executive]  
Page 2
 

 

**EXHIBIT A**
[Employment Agreement]