Existing methods for studying individual differences in adults' mindreading often lack good psychometric characteristics. Moreover, it remains unclear, even in theory, how mindreading varies in adults who already possess an understanding of mental states. In this pre-registered study, it was hypothesised that adults vary in their motivation for mindreading and in the degree to which their answers on mindreading tasks are appropriate (context-sensitive). These factors are confounded in existing measures as they do not differentiate between the frequency of mental state terms (MST), indicative of motivation, and the quality of an explanation. Using an innovative scoring system, the current study examined whether individual differences in adult undergraduate psychology students' (N = 128) answer quality and / or quantity of explicit references to others' mental states on two open-ended response mindreading tasks were separable constructs, accounted for by mindreading motivation, and related differentially to measures previously linked with mindreading (e.g., religiosity, loneliness, social network size). A two-factor and one-factor model both provided acceptable fit. Neither model showed significant associations with mindreading motivation. However, a two-factor model (with MST and response appropriateness loading onto separate factors) provided greater explanatory power. Specifically, MST was positively associated with religiosity and response appropriateness was negatively associated with religiosity, whilst the one-factor solution did not predict any socially relevant outcomes. This provides some indication that mindreading quantity and mindreading quality may be distinguishable constructs in the structure of individual differences in mindreading.