Many large urban school districts are rethinking their personnel management strategies, often giving increased control to schools in the hiring of teachers, reducing, for example, the importance of seniority. If school hiring authorities are able to make good decisions about whom to hire, these reforms have the potential to benefit schools and students. Prior research on teacher transfers uses career history data, identifying the school in which a teacher teaches in each year. When such data are used to see which teachers transfer, it is unclear the extent to which the patterns are driven by teacher preferences or school preferences, because the matching of teachers to schools is a two-sided choice. This study uses applications-to-transfer data to examine separately which teachers apply for transfer and which get hired and, in so doing, differentiates teacher from school preferences. Holding all else equal, we find that teachers with better pre-service qualifications (certification exam scores, college competitiveness) are more likely to apply for transfer, while teachers whose students demonstrate higher achievement growth are less likely. On the other hand, schools prefer to hire "higher quality" teachers across measures that signal quality. The results suggest that not only do more effective teachers prefer to stay in their schools but that schools are able to identify and hire the best candidates when given the opportunity. (Contains 4 figures, 31 footnotes, and 11 tables.)