Although the literature on assignment mechanisms emphasizes the importance of efficiency based on agents’ preferences, policymakers may want to achieve different goals. For instance, school districts may want to affect student learning outcomes but must take teacher welfare into account when assigning teachers to students in classrooms and schools. This paper studies both the potential efficiency and equity test-score gains from within-district reassignment of teachers to classrooms using novel data that allows us to observe decisions of both teachers and principals in the teacher internal transfer process, and test-scores of students from the observed assignments. We jointly model student achievement and teacher and school principal decisions to account for potential selection on test score gains and to predict teacher effectiveness in unobserved matches. Teachers, but not principals, are averse to assignment based on the teachers’ comparative advantage. Estimates from counterfactual assignments of teachers to classrooms imply that, under a constraint not to reduce any retained teacher’s welfare, average student test scores could rise by 7% of a standard deviation. Although both high and low achievers would experience average gains under this counterfactual, gains would be larger for high-achieving students.