The Common European Framework of Reference has stimulated research on the relation between linguistic competence and communicative competence. Such studies have often used linguistic measures from the Complexity-Accuracy-Fluency (CAF) paradigm to objectively tap into the linguistic competence of language learners; others have used Processability Theory. This study contributes to this research by measuring grammatical accuracy and complexity, in terms of both CAF and level of processability, in learners of second language Swedish taking a speaking proficiency test. The results show that a higher level of processability primarily enables learners to use a more complex, rather than a more accurate, language. Nevertheless, assessors focus primarily on accuracy. This raises questions about the reliability of communicative language testing, and the article argues for a more psycholinguistic and experimental approach to language testing.