I don't know what you mean by a "new parameter", so I can only make guesses.
Is this delayed service call the first call after the application is deployed, or the server starting up? If that's the case, then you're probably hitting issues with initial loading of classes or static data. If this is the case, and it's really important to get this first request working faster, then it might be worth having a servlet init method that just sends a dummy request to the web service that exercises all the critical paths, which will do the initial class and data loading.
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