The reassignment of teachers to schools is a central issue in education policies. In several coun-tries, this assignment is managed by a central administration that faces a key constraint: ensuring that teachers obtain an assignment that they weakly prefer to their current position. To satisfy this constraint a variation on the Deferred Acceptance (DA) mechanism of Gale and Shapley (1962) has been proposed in the literature and used in practice—for example, in the assignment of French teachers to schools. We show that this mechanism fails to be eﬃcient in a strong sense: we can reassign teachers in a way that i) makes them better-oﬀ and ii) better fulﬁlls the administration’s objectives represented by the priority rankings of the schools. To address this weakness, we characterize the class of mechanisms that do not suﬀer from this eﬃciency loss and elicit a set of strategy-proof mechanisms within this class. To empirically assess the extent of potential gains associated with the adoption of our mechanisms, we use a rich dataset on teachers’ applications for transfers in France. These empirical results conﬁrm both the poor performance of the modiﬁed DA mechanism and the signiﬁcant improvements that our alternative mechanisms deliver in terms of teachers’ mobility and administration’s objectives.