I combine novel data on job applications and hiring decisions for the universe of public sector jobs in Brazil and a natural experiment that decreased discretion in hiring to analyze how screening determines gender application and hiring gaps. I find that hiring practices have crucial gender equity consequences for selection and sorting, and not all approaches to reduce discretion have the same implications. Limiting discretion in existing tools or adding new impartial tools reduces the gender hiring gap by a third. However, policies that eliminate subjective tools like interviews are ineffective, suggesting employers should carefully weigh bias-information trade-offs.