The allocation of scarce health care resources such as flu treatment or organs for transplant presents stark problems of distributive justice. Persad, Wertheimer, and Emanuel have recently proposed a novel system for such allocation. Their "complete lives system" incorporates several principles, including ones that prescribe saving the most lives, preserving the most life-years, and giving priority to persons between 15 and 40 years old. This paper argues that the system lacks adequate moral foundations. Persad and colleagues' defense of giving priority to those between 15 and 40 leaves them open to the charge that they discriminate unfairly against children. Second, the paper contends that the complete lives system fails to provide meaningful practical guidance in central cases, since it contains no method for balancing its principles when they conflict. Finally, the paper proposes a new method for balancing principles of saving the most lives and maximizing life-years.