I use a panel of higher education clearinghouse data to study the centralized assignment of applicants to Finnish polytechnics. I show that on a yearly basis, large numbers of top applicants unnecessarily remain unassigned to any program. There are programs which rejected applicants would find acceptable, but the assignment mechanism both discourages applicants from applying, and stops programs from admitting those who do. A mechanism which would admit each year's most eligible applicants has the potential to substantially reduce re-applications, thereby shortening the long queues into Finnish higher education.