An improved rim for a mouthpiece for a plurality of non-French horn labrosone brass musical instruments. The improved rim has a rim width having a predetermined width measurement as a smallest width dimension taken of an outer edge, a crown, and an inner edge of the improved rim, where the rim width can be a same width as a playing surface of the improved rim, where the playing surface is a width of the improved rim engaged by a musician's lips. Also provided are improved rims removably or permanently affixed to the mouthpiece.