Proponents of epistocracy worry that high levels of voter ignorance can harm democracies. To combat such ignorance, they recommend allocating comparatively more political power to more politically knowledgeable citizens. In response, some recent critics of epistocracy contend that epistocratic institutions risk causing even more harm, since much evidence from political psychology indicates that more politically knowledgeable citizens are typically more biased, less open-minded, and more prone to motivated reasoning about political matters than their less knowledgeable counterparts. If so, perhaps epistocratic institutions will perform worse epistemically than corresponding democratic institutions. Call this 'the problem of epistocratic irrationality'. This paper argues that the problem of epistocratic irrationality can be overcome. First, I argue that critics of epistocracy have overlooked several complications regarding the psychological data they claim shows that more knowledgeable citizens are less politically rational. Second, I argue that appropriately designed epistocratic institutions could overcome the problem of epistocratic irrationality even if such critics have interpreted the data correctly. I first explore whether refined selection mechanisms could allow epistocrats to avoid empowering less rational citizens, before assessing the prospects of implementing only those epistocratic institutions with a solid track record of reliable performance.