This paper studies the roles of cognitive and non-cognitive characteristics in a standard Roemerian Inequality of Opportunity (IOP) model. Using Australian microdata, we model the effects of individuals’ backgrounds and their psychological traits on two adult income variables. We find that measurable psychological traits (intelligence, locus of control, big five personality traits) are slightly more important than background characteristics (such as race, gender, social class at birth) in explaining income disparities. However, the fraction of IOP confounded by psychological factors is small (11%–12%), which suggests that background inequalities do not meaningfully reflect differences in cognitive or non-cognitive ability.