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Theories of statistical discrimination predict that removing information will increase, rather than decrease, disparities across demographic groups. However, using a large dataset of more than 700,000 initial salary offers made to job candidates in the United States between 2017 and 2020, I find that the removal of past salary information reduced, rather than widened, gender disparities in pay. To unpack this theoretical puzzle, I conduct two dozen in-depth interviews with hiring managers and compensation experts. The qualitative findings reveal an alternative framework for how offers are set: not as a direct function of perceived quality, but as a function of perceived leverage--that is, candidates’ outside options and bargaining power. I then test this leverage-based model by empirically demonstrating a positive relationship between leverage and offers, a relationship that is magnified when past salary information is removed. I conclude by discussing how understanding offer-setting advances research on gender inequality, labor markets, and organizations.