Many schools and districts have considerable discretion when hiring teachers, yet little is known about how that discretion should be used. Using data from a new teacher screening system in the Los Angeles Unified School District (LAUSD), we find that performance during screening, and especially performance on specific screening assessments, is significantly and meaningfully predictive of hired teachers' evaluation outcomes, contributions to student achievement, attendance, and mobility. However, applicants' performance on individual components of the screening process are differentially predictive of different teacher outcomes, highlighting challenges and potential trade-offs faced by districts during screening.