This study critically examined the previously reported partial independence between second language (L2) accentedness (degree to which L2 speech differs from the target variety) and comprehensibility (ease of understanding). In prior work, comprehensibility was linked to multiple linguistic dimensions of L2 speech (phonology, fluency, lexis, grammar) whereas accentedness was narrowly associated with L2 phonology. However, these findings stemmed from a single task (picture narrative), suggesting that task type could affect the particular linguistic measures distinguishing comprehensibility from accentedness. To address this limitation, speech ratings of 10 native listeners assessing 60 speakers of L2 English in three tasks (picture narrative, IELTS, TOEFL) were analyzed, targeting two global ratings (accentedness, comprehensibility) and 10 linguistic measures (segmental and word stress accuracy, intonation, rhythm, speech rate, grammatical accuracy and complexity, lexical richness and complexity, discourse richness). Linguistic distinctions between accentedness and comprehensibility were less pronounced in the cognitively complex task (TOEFL), with overlapping sets of phonology, lexis, and grammar variables contributing to listener ratings of accentedness and comprehensibility. This finding points to multifaceted, task-specific relationships between these two constructs.