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I like the PT88 but prefer the Laskey rim. I'm about to have a 30G rim put on a PT88. In my opinion, the 88 is a better mouthpiece for my equipment but (again, my opinion) I have never liked the PT rims. . .

I was talking to Ivan about getting a screw rim for his Bayamo but evidently they're not quite there yet (at least in my price range).

I'm sure this goes without saying but, it really depends on your preferences and the tuba you are playing. . .

I will second a vote for trying the Caver by GW. I liked the Bayamo but like you desired more of the high overtones and the caver did the trick. I will say that the laskey 30g is also an outstanding mpc and would think it will produce the results you desire over the pt88

I've tried going to other mouthpieces, buying several, but always seemed to go back to my trusty PT-88. I'm pretty content now, but who knows a couple of months from now. I guess I'll never learn.