The present study provides a preliminary empirical test of [Chamorro-Premuzic, T., & Furnham, A. (2004). A possible model to understand the personality-intelligence interface. "British Journal of Psychology," 95, 249-264], [Chamorro-Premuzic, T., & Furnham, A. (2006a). Intellectual competence and the intelligent personality: A third way in differential psychology. "Review of General Psychology," 10, 251-267]) model of intellectual competence, which conceptualized an integrative framework for understanding the ability and non-ability determinants of academic performance (AP). Specifically, we set out to test whether Neuroticism and Extraversion affect self-assessed intelligence (SAI); whether SAI mediates the effects of Neuroticism and Extraversion on AP; and whether Openness (positively) and Conscientiousness (negatively) mediate the effects of gf on crystallized ability (gc) and AP. Sex differences were also examined. Using structural equation modelling and analyzing 4-year longitudinal data from a sample of 473 UK university students (316 men and 157 women), wide support was found for the model. Theoretical and applied implications are discussed in relation to the non-ability and ability determinants of individual differences in educational achievement. (Contains 2 figures and 2 tables.)