What is the efficacy of redrawing school attendance boundaries as a desegregation policy? To provide causal evidence on this question we employ novel data with unprecedented detail on the universe of Danish children and exploit changes in attendance boundaries over time. Households defy reassignments to schools with lower socioeconomic status. There is a strong social gradient in defiance, as resourceful households are more sensitive to the student composition of schools. We simulate the efficacy of desegregation policies and find that in areas with large levels of segregation, behavioral responses of households almost completely offset the intended effects of boundary changes.