Several decades ago I went to a brass "clinic" with a noted mouthpiece maker. The man had supplied many jazz greats with mouthpieces. As well as a veritable "Who's Who" of commercial lead players.
While sifting through his mouthpiece collection the man had me spend most of my playing time in the lower register. He had me tongue bell tones way down to Low F#.
"Why are you getting that puny sound down there"?
He would say. Yelled at me in fact. Then he taught me a set of breathing exercises that I still use and promote today. When i finally got my Low G to open up he said:
"There's your G above High C". He replied. Meaning that a solid, readable High G was contingent upon a musical and powerful Low G.
What I was doing was learning to loosen the center of my embouchure and place the playing burden on the outer facial muscles. Playing the horn in a very loose or "weak" position. At least that was/is the way it felt.
Over the years i learned that the way to make a shallow/small mouthpiece work best is to set for a Low G and work the register higher. In fact (as a piece of advice that may help someone) whenever you try a mouthpiece even shallower consider setting in a somewhat weaker setting than the larger piece.
"Setting weaker" is probably a concept better understood than explained. You'll know what i mean when you get there. Another way of understanding this mysterious idea is to evaluate how your development on a shallow piece improves.
When trying a super shallow piece for the first time always reserve judgment on it. Wait until late in the gig and see if it opens up. Or wait until a few weeks pass before making a final determination as to it's usefulness.
On my most recent change to a very very shallow piece I found that it took a couple years before I could use it all night. In the early days it wouldn't open up until the last set. So i was better off playing only a medium shallow piece through most of the gig. But by and by my muscles learned to synchronize better and I can now use the thing from start to finish. In fact i think i could even learn to play something even smaller. That's a real change from my first impression. From a novelty piece to my main tool. I may not want to go as shallow as Cat did but am not ruling it out. Cat's two pieces:
Conversely when playing a deeper mouthpiece I must set a tad firmer all throughout the registers. Puckering more too. To gain more support for the upper register. The bigger piece requires more physical work to accomplish the same high tones.
What trumpet players may not realize is that the cup volume on your really shallow pieces may be less than half that of the large one. That the Schilke 5a4a say may hold far less cup volume than the Schilke 14. So in a way the change from 14 to 5a4a is not far removed from switching from a trombone mouthpiece to a trumpet mouthpiece.
In fact the ability to double on trombone i find similar to switching from "legit' to screamer piece. Or in comparison:
Mack Truck to F-150 (trombone mouthpiece to standard trumpet piece)
F-150 to Mini Cooper (standard trumpet piece to screamer).
When we go from trombone to trumpet we play in a tessitura an octave higher. Going from most standard mouthpieces designed for symphonic or legit to screamer we move yet another octave of our tessitura.
Going from Schilke 14 to 5a4a effectively changing to an instrument more suited to play the next higher octave.
*"Clinic" in quotes as we were the only two people there. Much of the session involved massive consumption of warm beer...