On one important notion of irrelevance, evidence that is irrelevant in an inquiry may rationally be discarded, and attempts to obtain evidence amount to a waste of resources if they are directed at irrelevant evidence. The familiar Bayesian criterion of irrelevance, whatever its merits, is not adequate with respect to this notion. I show that a modification of the criterion due to Ken Gemes, though a significant improvement, still has highly implausible consequences. To make progress, I argue, we need to adopt a hyperintensional conception of content. I go on to formulate a better, hyperintensional criterion of irrelevance, drawing heavily on the framework of the truthmaker conception of propositions as recently developed by Kit Fine.