Switzerland features strong socio-economic segregation and no formal school choice, making residential relocation the only channel through which parents can access preferred schools. Identifying how parents value school attributes is therefore essential but challenging, given that choices bundle multiple characteristics. We address this by conducting a discrete choice experiment with nearly 2,700 parents with school-aged children, allowing us to estimate willingness to pay (WTP) for individual and combined school attributes. We find that a substantial minority of parents value academic quality so highly that their preferences are effectively price-insensitive. Among price-sensitive parents, academic quality remains central, but they also exhibit positive WTP for schools with fewer students with special educational needs and fewer non-native-speaking peers. Interaction effects are strong: WTP for reductions in special-needs peers is highest if the school is among the academically strongest. Accounting for attribute interactions further reveals marked heterogeneity, with parents clustering into seven distinct preference types.