Re: Jazz mouthpieces
Have the horn checked for air leaks. Often they bother more in the lower register than the upper one.
Secondly, maybe you don't have enough of the mouthpiece in your mouth (on the other hand, maybe too much). Experiment.
Make sure your bottom lip covers your teeth, and your top lip is firm but not too tight. Do not curl your top lip under your teeth. Don't bite!
Hope this helps!