We investigate whether a policy that bases college admission on relative performance can modify the degree of racial or ethnic segregation in high schools by inducing students to relocate to schools with weaker competition. Theoretically, such school arbitrage will neutralize the admissions policy at the college level. It will result in partial desegregation of the high schools if flows are sufficiently unbiased. These predictions are supported by empirical evidence on the effects of the Texas Top Ten Percent Law, indicating that a policy intended to support diversity at the college level actually helped achieve it in the high schools.