Smoking, drinking too much alcohol, overconsuming unhealthy food and drink, underconsuming healthy food and drink, and not taking enough exercise: these all cause not only ill-health but health inequalities. Taxation and regulation might not only make people healthier, they might reduce the health inequalities. Since health inequalities are often thought to be unjust, it may appear obvious that social justice supports taxation and regulation. But it is not obvious as I try to show in discussing the relation between social justice, health, welfare, and the rather mysterious value of health equity. My positive thesis is that social justice can supplement paternalism. Bearing in mind that any paternalistic policy is likely to be good for some people and bad for others, social justice can help swing the case for paternalist policies that especially benefit the worst off. My negative thesis is that social justice is ONLY a supplement to paternalism. A public health intervention could make the worst off healthier and yet worse off in welfare; if it would, social justice would speak against such an intervention.