Mouthpieces for brass wind musical instruments are shaped so the physical length of a mouthpiece body (40, 50, 60, 70, & 80) is inversely-proportional to the volumetric size of a corresponding cup-chamber (42, 52, 62, 72, & 82). Methods for constructing separate sets of such mouthpieces for each kind of brass wind instrument are disclosed. Other embodiments include variations like multi-section components and alternative backbore shapes.