A critical limiting factor for adaptive teaching is the availability of diagnostic tools that allow reliable and valid assessments of students' domain-specific skills in a way that produces detailed information for planning subsequent instructional strategies. The present study demonstrates how Cognitive Diagnosis Models (CDM) can deliver fine-grained diagnostic information on students' skills in dealing with domain-specific tasks, using introductory accounting as an exemplary field of application. Based on data from a sample of 773 students from secondary business schools in Austria, statistical analyses that incorporated several criteria for evaluating model fit corroborate theoretical assumptions on distinct skills as "multiple" dimensions of accounting competence. Moreover, they illustrate that CDMs allow not only to quantify the shares of students who have mastered or still lack each accounting skill but also to identify "individual skill profiles," which can serve as reliable classification criteria to distinguish homogeneous or heterogeneous ability groups among the learners. We conclude by discussing the practical implications of different diagnostic information obtained from CDM outputs for generic strategies of adaptive teaching, again with an illustrative focus on introductory accounting instruction.