A recurrent statement when implementation of international orders or recommendations in individual cases is considered is the belief that greater specificity of the measures helps compliance. Our research project examined a number of decisions adopted by some of the UN treaty bodies, and the regional human rights commissions and courts, in Africa, the Americas and Europe, and attempted to trace the extent to which the reparations ordered by the supranational bodies were implemented by the state authorities. This article focuses primarily on the reparations ordered by the Inter-American, African and UN systems and attempts to define specificity, emphasizing that it refers to a constant process of refining and clarifying the meaning of different forms of reparation. Specificity is then ‘unpacked’ in terms of the content of the reparation, deadlines imposed, who is responsible and who is a victim, and how the decision is reasoned. In so doing, the article maintains that specificity must also be considered vis-à-vis the degree of discretion that is given (or not) to states to act on orders or recommendations given by supranational bodies in individual cases. We conclude that a more nuanced approach to specificity versus ambiguity is needed, tailored to each reparation, each state and each case.