This is a board focused on mouthpiece work, but when diagnosing 
problems with warbling, for example, let's not forget that there are 
many factors that contribute to playability with the mouthpiece being 
extremely critical to that performance, of course.

Other considerations:

1)  Are all the pads on the instrument sealing well and are the keys 
well regulated?  If not, you've got work to do before hacking away at 
your mouthpiece.

2)  Is the neck tenon to body receiver a tight fit?  (You shouldn't 
have to turn that screw very much at all to get the neck to hold 
steady.)  If the neck is loose or you have to overtighten the screw, 
then you've got work to do before hacking away at your mouthpiece.

3)  Is the cork at the tip of the neck making positive contact with 
the inner bore of the mouthpiece?  It may be tight at the base of the 
mouthpiece further down the neck (giving the sensation that there's a 
tight fit), but that gap on the inside will create problems - 
particularly warbling in the lower range.  Putting some teflon tape 
on the tip to thicken it some will help diagnose if this is a problem.

There's other things to consider, but I just thought I'd post a few 
basics as a reminder that there's a few fundamentals that should be 
checked and addressed before lapping away at our treasured 
mouthpieces.