Many believe that it is morally wrong to give lower priority for a liver transplant to alcoholics with end-stage liver disease than to patients whose disease is not alcohol-related. Presumably, alcoholism is a disease that results from factors beyond one's control and therefore one cannot be causally or morally responsible for alcoholism or the liver failure that results from it. Moreover, giving lower priority to alcoholics unfairly singles them out for the moral vice of heavy drinking. I argue that the etiology of alcoholism may involve enough control for the alcoholic to be responsible for his condition and accordingly have a weaker claim to receive a new liver than someone who acquires the disease through no fault of his own. In addition, I show why it is more plausible to reframe the question of priority in terms of control and responsibility rather than virtue and vice. Given that medical resources like livers are scarce, some people may justifiably be given lower priority than others in receiving these resources.