This paper examines the possible relationship between proposed social determinants of morphological 'complexity' and how this contributes to linguistic diversity, specifically via the typological nature of the sign languages of deaf communities. We sketch how the notion of morphological complexity, as defined by Trudgill (2011), applies to sign languages. Using these criteria, sign languages appear to be languages with low to moderate levels of morphological complexity. This may partly reflect the influence of key social characteristics of communities on the typological nature of languages. Although many deaf communities are relatively small and may involve dense social networks (both social characteristics that Trudgill claimed may lend themselves to morphological 'complexification'), the picture is complicated by the highly variable nature of the sign language acquisition for most deaf people, and the ongoing contact between native signers, hearing non-native signers, and those deaf individuals who only acquire sign languages in later childhood and early adulthood. These are all factors that may work against the emergence of morphological complexification. The relationship between linguistic typology and these key social factors may lead to a better understanding of the nature of sign language grammar. This perspective stands in contrast to other work where sign languages are sometimes presented as having complex morphology despite being young languages (e.g., Aronoff et al., 2005); in some descriptions, the social determinants of morphological complexity have not received much attention, nor has the notion of complexity itself been specifically explored.