Despite efforts to increase the supply of donated organs for transplantation, organ shortages persist. We study the problem of organ wastage in a queueing-theoretic framework. We establish that self-interested individuals set their utilization levels more conservatively in equilibrium than the socially efficient level. To reduce the resulting gap, we offer an incentive mechanism that recompenses candidates returning to the waitlist for retransplantation, who have accepted a predefined set of organs, for giving up their position in the waitlist and show that it increases the equilibrium utilization of organs while also improving social welfare. Furthermore, the degree of improvement increases monotonically with the level of this nonmonetary compensation provided by the mechanism. In practice, this mechanism can be implemented by preserving some fraction of the waiting time previously accumulated by returning candidates. A detailed numerical study for the U.S. renal transplant system suggests that such an incentive helps significantly reduce the kidney discard rate (baseline: 17.4%). Depending on the strength of the population's response to the mechanism, the discard rate can be as low as 6.2% (strong response), 12.4% (moderate response), or 15.1% (weak response), which translates to 1,630, 724, or 338 more transplants per year, respectively. Although the average quality of transplanted kidneys deteriorates slightly, the resulting graft survival one-year posttransplant remains stable around 94.8% versus 95.0% for the baseline. We find that the optimal Kidney Donor Profile Index score cutoff, defining the set of incentivized kidneys, is around 85%, which coincides with the generally accepted definition of marginal kidneys in the medical community.