Should teachers have complete autonomy over teaching methods and practices, or should some aspects of their practice be determined by school or government policy? We address this question using repeated (value-added) maths test scores linked to rich survey data from the TALIS video study. With the possible exception of inexperienced teachers, we generally find no relationship between teacher autonomy and pupil outcomes (test scores, maths self-efficacy or interest in maths). In partial contrast with our findings for pupil outcomes, teachers with very low levels of autonomy are more likely to report reduced job satisfaction. It may hence be that some level of restriction on teacher autonomy is justified, especially among inexperienced teachers, particularly when it represents only partial control of teachers' approaches in the classroom and is done to introduce evidence-based methods.