I reconsider and enhance a somewhat neglected argument within the domains of reparations for slavery and black reparations. That argument is for compensating present-day descendants of enslaved persons for wrongs done to their genetic ancestors, based on the inheritance of rights to compensation. After highlighting some of its virtues, some questions for it on which I remain agnostic, and some outright problems, I offer three desiderata for an elaboration of the argument: stronger African American claims, meaningful connection, and material-structural sensitivity. To satisfy these without ad-hocness, I motivate seven ‘hierarchies of connection’ between heir and predecessor via a series of thought-experiments involving ordinary inheritance of an estate. Moreover, I suggest that the elaborated version of the inheritance argument might be harder for good-faith political conservatives to dismiss than other pro-reparations arguments. Finally, I address an objection by modifying my view about the kind of right that will be held by descendants of enslaved persons if the argument succeeds.