Research on sources of individual difference in parental Infant-Directed Speech (IDS) is limited and there is a particular lack of research on fathers’ compared to mothers’ speech. This study examined the predictive relations between infant characteristics and variability in paternal lexical diversity (LD) in dyadic free play with two-year-olds (M = 24.1 months, SD = 1.39, 35 girls). Ten minutes of interaction for sixty-four father–infant dyads were transcribed and multiple regression analyses were performed to examine the effects of a set of distal and proximal sources of infant influence on paternal LD. Fathers’ LD was predicted only by infant language, both standardised language scores and dynamic language measures, and was not predicted by infant age, gender, executive function, or temperament. Findings are discussed in the light of the complex interplay of factors contributing to variability in IDS and the infant's linguistic environment.