Individuals in capitalist societies are increasingly exposed to market risks. Luck egalitarian theories, which advocate neutralizing the influence of luck on distribution, fail to cope with this problem, because they focus on the wrong kinds of distributive constraints. Rules of distributive justice can specify (1) acceptable procedures for allocating goods, (2) the range of acceptable variations in distributive outcomes, or (3) which individuals should have which goods, according to individual characteristics such as desert or need. Desert-catering luck egalitarians offer rules of the third type. Their theories fail because considerations of market efficiency, freedom, and dignity undermine the claims of desert to inform standards of justice for society as a whole. Responsibility-catering luck egalitarians offer rules of the first type. Their theories fail because such rules don’t constrain the downside risks of market choices. To solve this problem, we need rules of the second type, which allow market forces, and hence luck, to influence distributive outcomes, but only within an acceptable egalitarian range. The ideal of equality in social relations helps us devise acceptable constraints at the top, bottom, and middle of the income range.