What qualities should admission criteria identify in applicants to teacher education programs in order to select those that should be admitted into the program from those applying? One approach to addressing this selection problem is to link the desired qualities of applicants to the desired qualities with which students in the program are to graduate. In this paper I, first, reconstruct in some detail an approach that puts at its centre a functional relationship between these two types of qualities. Then I discuss the challenges of this approach and offer a second approach to the admission problem that does not face the same kind of challenges. The second approach puts at its centre the linking of the selection problem to the design of the teacher education program itself.