The literature on assignment mechanisms largely focuses on efficiency based on agents' preferences, though policymakers may prioritize different goals. In assigning teachers to classrooms, a school district might prioritize student learning but must also consider teacher welfare. This paper studies the potential gains in student test scores from alternative within-district assignments of teachers to classrooms, using novel administrative data on teacher and school principal decisions from the district's internal transfer system (ITS) and student test scores under the observed assignments. To credibly predict student test scores under unrealized assignments, we jointly model student achievement and teacher and principal decisions, accounting for potential selection of teachers on test score gains. We estimate the variation in teachers' comparative advantage in producing learning to be one-ninth the magnitude of the variation in their general effectiveness. Further, teachers dislike comparative advantage–based assignments. Assignment of teachers to classrooms to maximize learning under the constraint of not reducing any assigned teacher's welfare would raise the average test score by 7% of a standard deviation (SD) relative to that under the observed assignment, with this effect driven mostly by assignment of teachers with higher general effectiveness to larger classrooms rather than by harnessing teachers' comparative advantage.