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 reassignments and find that boundary changes are ineffective in altering the socioeconomic composition of disadvantaged schools in highly segregated areas.