Luck Egalitarianism is an influential view, or, more accurately, a broad family of views. What these views have in common is the idea that distributive justice is sensitive to responsibility in the sense that inequality is unjust if the worse off person is not responsible for her position. In this paper, we consider the main ways to interpret the luck egalitarian idea and argue that none of them escapes the following dilemma: If LE is reducible to or reflects a familiar consideration or considerations, such as desert, priority for the worse off, or utility, or a simple balance of such familiar considerations, it is theoretically redundant and misleading; whereas if it is a distinct principle, which is not reducible to (a balance of) familiar considerations, it is false.