Research on intelligence and competence has developed widely independent of each other. The present paper aims at relating these traditions and at integrating the dominant models to fill gaps in the respective theories. We test the structural models derived from this integration in a series of confirmatory factor analyses and a latent moderated structural equations approach using teachers as an example. The data reveal that both fluid intelligence ("gf") and domain-specific knowledge affect teachers' ability to solve the domain-specific items. Teachers' academic self-concept related to mathematics explains individual differences beyond "gf." An interaction effect between "gf" and self-concept exists for teachers' pedagogical content and general pedagogical knowledge, but not for their mathematics knowledge. This finding indicates that a positive self-concept cannot compensate for a lack of "gf," but it supports the acquisition of domain-specific knowledge in case of high "gf," probably because it facilitates overcoming challenges.