The concept of responsibility plays a crucial part in the debate between proponents of democratic equality, like Rawls, and defenders of luck egalitarianism, such as Dworkin. In this paper it is argued that the two theories can be combined, and that they should be combined to achieve a theory of justice that puts personal responsibility in its proper place. The concept of justice requires two different conceptions. The two theories can be combined because they deal with different problems of justice. They ought to be combined because, first, luck egalitarianism needs a theory of background justice, and second, a theory of justice must supply an answer to the question of just individual allocations, something that is not provided by democratic equality. Democratic equality and luck egalitarianism solve each other’s problems. The combined theory will lead to allocations of goods that respect both the difference principle and the envy test.