We present a theory of how a rational, profit-maximizing firm would respond to pressure for gender pay equity by strategically distributing raises to reduce the pay gap between its female and male employees at minimum cost. Using formal analysis and pay data from a real employer, we show that (1) employees in low-paying jobs and whose pay-related observables are similar to those of men at the firm are most likely to get raises; (2) counterintuitively, some men may get raises, and giving raises to certain women would increase the pay gap; and (3) a firm can reduce the gender pay gap as measured by a much larger percentage than the overall increase in pay to women at the firm. We also identify the conditions under which a firm could “explain away” a gender pay gap using other pay-related observables, such as job category, as well as the conditions under which this strategy would backfire. Our paper helps explain some empirical puzzles, such as the tendency for some men to get raises after gender equity pay reviews, and yields a rich set of implications for empirical research and practice.