International criminal tribunals (ICTs) are epistemic engines in the sense that they find (or claim to find) factual truths about such past events that qualify as genocide, crimes against humanity and war crimes. The value of this kind of knowledge would seem to be beyond dispute. Yet, in general the truth-finding aspect of ICTs plays only a very limited role in the often heated debates about their legitimacy. Furthermore, those who actually do address the issue seem widely divided as to whether critiques of the epistemic function of ICTs in fact constitute, in Andreas Føllesdal’s words, one of ‘the challenges that can plausibly be raised against them’ – and if so, in what ways. In this paper, I address the first of these questions asking whether truth-finding should at all be considered a desideratum for ICTs. To this end, I discuss the widespread claim that it should not because the legal truth found in ICT judgements is in fact sui generis; i.e. something categorically different from ordinary truth because exclusively tied to and determined by the legal process as defined in accordance with ideals of due process/fair trial. I argue that this position is ill-founded. Properly understood, truth in law is intimately connected to ordinary truth. Truth-finding capacity therefore does belong in legitimacy debates as a challenge that can plausibly be raised against them. This, in turn makes it relevant, in future research, to map, analyse and interrelate the various critiques that have been launched against the actual truth conduciveness of ICTs.