Because of a shortage of transplantable livers and hearts, the transplant community has had to decide-by who gets an organ--who lives or dies. Despite this shortage, whether one has previously received a transplant is not used as a criterion to distribute organs. The existing allocation system distributes 10% to 20% of available hearts and livers to retransplant patients. This article examines three differences between primary transplantation and retransplantation that may affect the priority that retransplant candidates should receive in vying for organs: (1) the special obligations that transplant teams have not to abandon patients on whom they have already performed a transplant, (2) the fairness of allowing individuals to get multiple transplants while some die awaiting their first, and (3) the difference in efficacy between primary transplantation and retransplantation. Only this last difference holds up to critical analysis. Our moral duty to direct scarce, lifesaving resources to those likely to benefit from them, suggests that, all other things equal, primary transplant candidates should receive priority because their mortality after transplantation is lower. Consistency also demands that previous transplant history be taken into account, as we already allocate organs according to ABO blood group matching, a factor that affects transplant outcome approximately the same amount as a previous transplantation. We therefore conclude that the system should be revised so that primary transplant candidates have a better chance of receiving organs than retransplant candidates.