Choosing a school is one of the most important decisions parents make regarding their children’s human capital, yet application constraints can make observed choices an imperfect measure of what parents value. We study preferences for school effectiveness and peer quality in the centralized secondary school market of Barbados, where admissions are based on a one-shot exam and parents face a binding cap on the number of schools they can list. Exploiting a policy reform that further tightened this cap, we show that parents respond by 'skipping the impossible': omitting the most selective schools from their applications, with little change in equilibrium assignments. We then estimate preferences for school effectiveness, measured by impacts on test scores and adult wages, and peer quality under alternative behavioral assumptions. Under the truth-telling assumption that applications reveal parents’ most preferred schools, we find no evidence that parents value school effectiveness conditional on peer quality. In contrast, under market-stability assumptions that allow parents to omit desirable but seemingly unattainable schools, we find that parents value both school effectiveness and peer quality. The difference arises because the most selective schools are also the most effective. Thus, approaches that interpret omitted schools as less preferred than ranked ones can understate parental demand for school effectiveness.