Schools can also differentiate by peer composition among other aspects. Different rules elite or private schools are subject to compared to public schools in admissions have been heavily debated because of their effects on student distribution. In many countries former group admit students earlier than the latter, which we call Sequential Admissions (SA). Furthermore, the former group can use academic criteria in admissions unlike the latter. We study the effect of these admission aspects on welfare and distribution. Our analysis has important distinguishing features. First, it includes private schools as well as public schools, whereas previous studies on admission rules focused on centralized public school allocation. Second, students can have preferences for peer composition at schools. This is an important factor that can determine sorting behavior which is not carefully studied before. First we theoretically study equilibria of the admission games complicated by the peer effects. Then we estimate a structural model using detailed high school applications data from Seoul to run counterfactual simulations. We show that SA can approximate centralized admission schemes well. This is important since complete centralization is known to increase welfare but hard to implement in many cases. Regarding admission criteria, we show that use of academic criteria in a subset of schools increases the desirability of these schools. The reason is that high performing students want to coordinate to study together and academic screening provides this. This suggests that, school choice has also a coordination aspect, it is not just an object allocation problem.