Proponents of school choice argue that it improves educational outcomes by allowing parents to self-select into schools that are most effective for their children. Contrary to these arguments, empirical evidence suggests that parents may not incorporate school effectiveness or match quality when choosing schools. The findings potentially impugn proponents' effectiveness arguments of choice-based assignment. We develop novel solutions that restore effectiveness by maximizing match quality subject to stability constraints. Maximization algorithms are provided for both small and large school districts. Simulations reveal substantial match quality gains from our solutions compared to the celebrated Deferred Acceptance mechanism with a random tie-breaker. Our methodology can be used to optimize for other policy objectives in school choice or other priority-based matching problems.