Batesian mimics-benign species that predators avoid because they resemble a dangerous species-often vary geographically in resemblance to their model. Such geographical variation in mimic-model resemblance may reflect geographical variation in model abundance. Natural selection should favour even poor mimics where their model is common, but only good mimics where their model is rare. We tested these predictions in a snake-mimicry complex where the geographical range of the mimic extends beyond that of its model. Mimics on the edge of their model's range (where the model was rare) resembled the model more closely than did mimics in the centre of their model's range (where the model was common). When free-ranging natural predators on the edge of the model's range were given a choice of attacking replicas of good or poor mimics, they avoided only good mimics. By contrast, those in the centre of the model's range attacked good and poor mimics equally frequently. Generally, although poor mimics may persist in areas where their model is common, only the best mimics should occur in areas where their model is rare. Thus, counter-intuitively, the best mimics may occur on the edge of their model's range.