Saxophonists have different expectations from the saxophone mouthpiece, as it significantly affects the playability and the sound of the instrument. A mass personalization paradigm provides unique products to cater to their needs, using the flexibility of additive manufacturing. The lack of quantitative knowledge on mouthpiece design hinders the personalization attempts. This study aims to lay out how design parameters affect mouthpiece characteristics. Twenty-seven 3D-printed mouthpieces with varying design parameters are used in conjunction with an artificial blowing machine, to determine the acoustical relevance of the various mouthpiece designs on four selected mouthpiece features. The influence of the design parameters is evaluated statistically and via a case study with five saxophonists. The analysis shows that seven out of nine parameters tested affect the mouthpiece characteristics by relatively different amounts. A user study demonstrates that saxophonists confirm the results in 7 of 10 cases, and they prefer personalized mouthpieces in 4 of 5 cases. The results present a key contribution to the understanding of mouthpiece design. The findings provide valuable insights for new mouthpiece design and mouthpiece personalization.