Intelligibility is the widely agreed-upon goal for teaching spoken language. Its opposite, nativeness, is now rarely put forth by teachers or researchers as a worthwhile goal, though it remains vibrant in pronunciation instruction. This chapter contrasts and compares the implications of teaching for nativeness and teaching for intelligibility. Teaching for nativeness means that learners have to completely match a native speaker’s production of all pronunciation targets, segmental and suprasegmental, in order to have achieved proper pronunciation in a foreign language. There is no need to prioritize one sound or feature over another. All are necessary. An intelligibility-based approach, on the other hand, requires making some sounds priorities because some errors have a relatively large effect on understanding and others a relatively small effect. Exactly what an intelligibility-based approach should look like is not always clear because the intelligibility principle must be context-sensitive and interlocutor-sensitive, and thus a number of recommendations are compared. This chapter argues that priorities mean not only selectivity, but also helping learners pronounce well, as well as teaching those same learners to understand others.