According to Luck egalitarians, fairness requires us to bring it about that nobody is worse off than others where this results from brute bad luck, but not where they choose or deserve to be so. In this paper, I consider one type of brute bad luck that appears paradigmatic of what a Luck Egalitarian ought to be most concerned about, namely that suffered by people who are born to badly off parents and are less well off as a result. However, when we consider what is supposedly unfair about this kind of unequal brute luck, luck egalitarians face a dilemma. According to the standard account of luck egalitarianism, differential brute luck is unfair because of its effects on the distribution of goods. Yet, where some parents are worse off because they have chosen to be imprudent, it may be impossible to neutralize these effects without creating a distribution that seems at least as unfair. This, I argue, is problematic for luck egalitarianism. I, therefore, explore two alternative views that can avoid this problem. On the first of these, proposed by Shlomi Segall, the distributional effects of unequal brute luck are unfair only when they make a situation more unequal, but not when they make it more equal. On the second, it is the unequal brute luck itself, rather than its distributional effects, that is unfair. I conclude with some considerations in favour of this second view, while accepting that both are valid responses to the problem I describe.