Transplant center oversight—conducted through costly flagging based on survival rates—is intended to improve outcomes. However, it has faced challenges because centers strategically select patients (and organs) to improve their reported outcomes. We study the optimal flagging policy using a mechanism-design model in which heterogeneous centers can improve their survival rates by investing, selecting patients, or both. We find that (a) the optimal mechanism never flags intrinsically good-enough center types, and (b) under the optimal mechanism, intrinsically worse centers select patients, while intrinsically better centers underinvest. These results apply to the regulation of charter schools and development banks.