This paper offers a critique of recent attempts, by George Sher and others to justify compensation to be paid to descendants of deceased victims of past wrongs. This recent attempt (the ‘continuing injustice argument’) is important as it endeavours to avoid some well-known critiques of previous attempts, such as the non-identity problem. Furthermore, this new attempt is grounded in individual rights, without invoking a more controversial collectivist assumption. The first step in this critique is to differentiate between compensation and restitution. Once this important distinction is clear, an examination of several factors follows: the importance of the passage of time vis-à-vis claims for compensation and/or restitution (and especially the passing away of the original victims and wrongdoers), the responsibility of the would be payers, the responsibility of the descendants of the victims, the welfare level of the descendants of the victims, information-related issues, and several additional factors. The conclusion is that once we take into account the distinction between compensation and restitution, and the additional factors mentioned, the case for compensation and/or restitution under the ‘continuing injustice argument’, is highly limited.