Free school choice has often been argued to be a tide that lifts school quality through increased competition. This paper analyzes the underlying assumption that school quality is an important choice criterion for parents. Using a large and representative data set of over 15,000 Dutch primary school starters we estimate models of school demand that incorporate heterogeneity in school preferences. Our results show that traditional measures for school quality matter, but other characteristics, such as school denomination and educational philosophy, are more important predictors of choice. Preferences for these school characteristics are strongly heterogeneous across parents.