With diminishing returns to the peer group, it is optimal social policy to mix children in schools. We consider what happens when, contrary to the outcome being determined by a social planner, schools and children are free to seek each other out: with some caveats, this leads to perfect segregation by child quality. It is shown that this is the worst possible outcome. We show also that a competitive system produces the optimal allocation of children to schools. Proof of the Proposition is appended. (Contains 2 figures and 5 notes.)