Research on intelligibility in international encounters has long focused on issues of pronunciation to the detriment of factors such as linguistic co-text and extralinguistic context, which are comparatively well-studied variables in intelligibility research concerning L1 listeners. This paper seeks to expand the scope of international intelligibility research in this respect by reporting on a large-scale study involving 423 nonnative listeners at different proficiency levels, who transcribed words spoken with another nonnative accent under four conditions that varied in the availability of syntactic, semantic, and schematic cues. The results suggest that co-text and context as well as listening proficiency are crucial variables that ought to receive greater attention in research on international intelligibility. The pedagogical implications of these findings are addressed as well.