Instances of strikingly accurate Batesian mimicry (in which a palatable prey organism closely resembles an aversive model) are often cited to illustrate the power of natural selection. Less attention has been paid to those mimics, such as many hoverfly (Syrphidae) mimics of wasps or bees, that resemble their models only poorly. Attempts to provide an adaptive explanation for imperfect mimicry have suggested that what seems a crude resemblance to human observers may appear a close match to predators, or that inaccurate mimics may bear a general resemblance to several different model species. I show here, however, that truly inaccurate mimicry of a single model organism may be favoured over perfect resemblance, by kin selection. Signal detection theory predicts that predators will modify their level of discrimination adaptively in response to the relative frequencies and similarity of models and mimics. If models are rare and/or weakly aversive, greater local similarity of mimics can thus lead to greater attack rates. Where individual mimics are related to others in their vicinity, kin selection will then oppose the evolution of accurate mimicry.