The answer, quite frankly, is no. They do not. Particularly when you're used to larger mouthpieces, switching to a small one can (at least in the short term)
Milashius Mouthpieces 5G Review
Yamaha Mouthpieces
Comparison: Trumpet Mouthpieces - Shaping Tone & Enhancing Range
Trumpet Mouthpiece Sizes, Shapes and Features
Review: Trumpet Mouthpiece - Yamaha 11B4 - good for beginners?
How to design YOUR OWN Trumpet Mouthpieces with Vennture
JET-TONE Original Studio Model B, Trumpet Mouthpiece Review
4/35) Beginning Trumpet - Mouthpiece
Mouthpiece Selection Guide
Trumpet Mouthpiece Comparison
Mouthpiece (brass) - Simple English Wikipedia, the free encyclopedia
Comparison: Trumpet Mouthpieces - Shaping Tone & Enhancing Range
OZWINDS - How To Choose a Trumpet Mouthpiece
Mouthpiece Selection Guide
Jet-Tone Trumpet, Cornet & Flugelhorn Mouthpieces