Intelligibility has been widely regarded as an appropriate goal for second language pronunciation teaching. Yet there is no universally accepted definition of intelligibility, nor any field-wide consensus on the best way to measure it. Further, there is little empirical evidence to suggest which pronunciation features are crucial for intelligibility to guide teachers in their instructional choices. This mixed-methods study examines whether intelligibility is an appropriate criterion for assessing pronunciation proficiency in the academic domain. Speech samples of eight non-native English speaking graduate students were elicited using the Test of Spoken English, a standardized test often used to screen international teaching assistants (ITAs). Results of a fine-grained analysis of the speech samples combined with intelligibility ratings of 18 undergraduate science students suggest that intelligibility, though an adequate assessment criterion, is a necessary but not a sufficient condition for international graduate students to instruct undergraduate courses as teaching assistants.