The notion of complexity recurrently shows up in the context of language studies. From a Chomskyan/biolinguistic perspective, and given the uniform character of language acquisition, it has been assumed that all languages are equally complex or simple. However, the proper focus of Chomskyan linguistics is not natural languages, but the language faculty. Here, we discuss complexity in this domain, relying on Deacon's (2006) distinction between various levels of complexity. The discussion focuses on grammars of I(nternal)-languages and how these display traces of cumulative complexity (Deacon's third level) that go beyond the narrow confines of internalism. Focusing on instances of recent (sign) language emergence, and evidence from birdsongs, we argue that biolinguistics would be wrong to ignore what it can learn from how socio-cultural factors affect the linguistic phenotype.