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 new schools. We simulate school assignment policies and find that boundary changes that reassign areas to a highly disadvantaged school are ineffective at altering the socioeconomic composition at the disadvantaged school.