This article distinguishes historical ills and historical injustices. It conceives of the latter as legalised natural crimes, committed by morally competent agents. A natural crime consists in the deliberate violation of a natural right. 'Legalised' means that the natural crime must be prescribed, permitted or tolerated by the legal system. I advocate an approach which assesses moral competence on the basis of an exposedness criterion, that is: a historical agent must not be blamed for failing to see the right moral reasons if his epoch and social world is utterly unacquainted with these reasons. However, an appropriate application of the exposedness criterion should take social factors and psychological mechanisms into account that obstruct access to the right reasons. I state a number of factors that seem to be auspicious for the development of moral competence.