I had the honor of sitting next to Cat for two weeks when he played lead for Pearl Bailey/with Louis Bellson at the Sahara Hotel in Vegas when I worked there. Imagine a mouthpiece made out of butter. Lightly press your thumb down about a 16th of inch. This is what the cup, if you could call it that, looked like on Cat's mouthpiece. He was also very careful not to let too many people see it. Everytime he would have a rest, he would take it off the horn and put it in his coat pocket.
I have tested some shallow mouthpieces in my time. The shallowest was Chase's 6a4a model. Cat's was about 2/3rds smaller than that. I am sure I could not even get a sound on it. But it sure worked for him. Every night he would go out an play a screech solo, playing double c's and triple g;s. TRULY AMAZING, even after knowing about his small mouthpiece.
Where have all the giants gone?