Background: Teachers differ substantially in their instructional performance in the classroom. Thus, researchers and policymakers are interested in how these differences can be explained and how the instruction provided by low-performing teachers can be improved. Previous research has focused either on generic (cognitive ability and personality) or profession-specific (professional knowledge, beliefs, and motivation for teaching) teacher characteristics as predictors of instructional quality but their relative importance has not yet been tested. Aims: Hardly any studies have combined central generic and profession-specific variables in ascertaining their relative importance for instructional quality. In the present study, we seek to close this research gap. Samples: We investigated 209 German mathematics teachers and their 4,672 students attending grades 7-10 (13- to 16-year-old students). Methods: Teacher characteristics (cognitive ability, personality, professional knowledge, beliefs about, and enthusiasm for teaching) were assessed using standardized tests and self-report measures. Instructional quality (learning support, classroom disruptions, and cognitive activation) was rated by the students. Results: Using structural equation modelling, we found extraversion, enthusiasm for teaching, and pedagogical/psychological knowledge to be significant predictors of learning support (R[superscript 2] = 0.31) and conscientiousness and enthusiasm for teaching to be significant predictors of classroom discipline (R[superscript 2] = 0.21). We did not find significant predictors for cognitive activation. Conclusions: Our results indicate the relative significance of generic and profession-specific teacher variables for instructional quality. Overall, a substantial amount of variance in instructional quality is explained by teacher characteristics.