I use a panel of higher education clearinghouse data to study the centralized assignment of applicants to Finnish polytechnics. Many top applicants remain completely unassigned each year. The same applicants' future applications reveal that many of them should have been admitted to a different program immediately. The application system, however, discourages applicants from applying to multiple programs within the same year, while at the same time leaving them in the dark on the set of programs willing to admit them. Improvements to the application system have the potential to substantially reduce reapplications, thereby shortening long queues into Finnish higher education.