Should alcoholics compete equally for liver transplantation? The circumstances of liver transplantation are unique among organ transplantation because of the dire, absolute scarcity of donor livers and the predominance of one disease--alcohol-related end-stage liver disease--as the principal cause of liver failure. We propose that patients who develop end-stage liver disease through no fault of their own should have higher priority for receiving a liver transplant than those whose end-stage liver disease results from failure to obtain treatment for alcoholism. We base our proposal on considerations of fairness and on whether public support for liver transplantation can be maintained if, as a result of a first-come, first-served approach, patients with alcohol-related end-stage liver disease receive more than half the available donor livers. We conclude that since not all can live, priorities must be established for the use of scarce health care resources. 