Faced with limited resources, medical providers and planners often ask bio-ethicists how to limit or ration the delivery of beneficial services in a or just way. What advice should we give them? To focus our thinking on the problems they face, I offer a friendly challenge to the field: solve the four rationing problems described here. We have generally ignored these problems because we think rationing an unusual phenomenon, associated with gas lines, butter coupons, or organ registries. But rationing is pervasive, not peripheral, since we simply cannot afford, for example, to educate, treat medically, or protect legally people in all the ways that their needs for these goods require or that accepted distributive principles seem to demand. Whenever we design institutions that distribute these goods, and whenever we operate those institutions, we are involved in rationing. Rationing decisions, both at the micro and macro levels, share three key features. First, the goods we often must provide--legal services, health care, educational benefits--are not sufficiently divisible (unlike money) to avoid unequal or lumpy distributions. Meeting the educational, health care, or legal needs of some people, for example, will mean that the requirements of others will go unsatisfied. Second, when we ration, we deny benefits to some individuals who can plausibly claim they are owed then in principle; losers as well as winners have plausible claims to have their needs met. Third, the general distributive principles appealed to by claimants as well as by rationers do not by themselves provide adequate reasons for choosing among claimants. They are too schematic; like my fair equality of opportunity account of just health care, they fail to yield specific solutions to these rationing problems. Solving these problems thus bridges the gap between principles of distributive justice and problems of institutional design. The Fair Choices/Best Outcomes Problem How much should we favor producing the best outcome until our limited resources? Like the other problems, the chances/best outcomes problem arises in both micro and macro contexts. Consider first its more familiar microrationing form: which of several equally needy individuals should get a scarce resource, such as a heart transplant? Suppose that Alice and Betty are the same age, have waited on queue the same length of time, and will each live only one week without a transplant. With the transplant, however, Alice is expected to live two years and Betty twenty. Who should get the transplant?[1] Giving priority to producing best outcomes, as in some point systems for awarding organs, would mean that Betty gets the organ and Alice dies (assuming persistent scarcity of organs, as Dan Brock notes).[2] But Alice might complain, Why should I give up my only chance at survival--and two years of survival is not insignificant--just because Betty has a chance to live longer? Alice demands a lottery that gives her an equal chance with Betty. To see the problem in its macroallocation version, suppose our health care budget allows us to introduce one of two treatments, T1 and T2, which can be given to comparable but different groups. Because T1 restores patients to a higher level of functioning than T2, it has a higher net benefit. We could produce the best outcomes by putting all our resources into T1; then patients treatable by T2 might, like Alice, complain that they are being asked to forgo any chance at a significant benefit. The problem has no satisfactory solution at either the intuitive or theoretical level. Few would agree with Alice, for example, if she had very little chance at survival; more would agree if her outcomes were only somewhat worse that Betty's. At the level of intuitions, there is much disagreement about when and how much to favor best outcomes, though we reject the extreme positions of giving full priority to chances or best outcomes. …