We consider why imperfect deceptive mimics can persist when it appears to be in the predator's interest to discriminate finely between mimics and their models. One theory is that a receiver will accept being duped if the model and mimic overlap in appearance and the relative costs of attacking the model are high. However, a more fundamental explanation for the difficulty of discrimination is not based on perceptual uncertainty, but simply based on a lack of information. In particular, predators in the process of learning may cease sampling imperfect mimics entirely because the immediate pay-off and future value of information is low, allowing such mimics to persist. This outcome will be particularly likely when the model is relatively costly to attack and/or the discriminative rules the predator has to learn are complex. Information limitations neatly explain why predators tend to adopt discriminative rules based on single traits (such as stripe colour), rather than on combinations of traits (such as stripe order). They also explain why predators utilize certain salient discriminative traits while ignoring equally informative ones (a phenomenon known as overshadowing), and why imperfect mimics may be more common in phenotypically diverse prey communities.This article is part of the themed issue 'Animal coloration: production, perception, function and application'.