Two competing theories, the equality view and the priority view, might have in some cases similar recommendations about how to correct inequalities in health and healthcare, even if their conclusions are based on different arguments. In this paper, I discuss a typical case of health difference between socioeconomic categories and the way an egalitarian approaches this case. I refer to an egalitarian who tries to optimize the degree in which people enjoy a good health. His aim is to maximize the level where people have a nearly equal health state or avoid the equal maximal amount of suffering caused by illness. The egalitarian reasoning is balanced against the priority view. My argument makes the case for prioritarianism which, I believe, morally outweigh egalitarianism while offering a solution which cannot be but welcomed by the egalitarian. Several consequences for health policy are discussed.