The optimal functioning of centralized allocation systems is undermined by the presence of institutions operating off-platform--a feature common to virtually all real-world implementations. These off-platform options generate justified envy, as students may reject their centralized assignment in favor of an outside offer, leaving vacant seats in programs that others would have preferred to their current match. We examine whether sequential assignment procedures can mitigate this inefficiency: they allow students to delay their enrollment decision to potentially receive a better offer later, at the cost of waiting before knowing their final admission outcome. To quantify this trade-off, we estimate a dynamic model of application and acceptance decisions using rich administrative data from the French college admission system, which include rank-ordered lists and waiting decisions. We find that waiting costs are large. Yet, by improving students' assignment outcomes relative to a standard single-round system, the sequential mechanism decreases the share of students who leave the higher education system without a degree by 5.4% and leads to large welfare gains.