Sexual dimorphism is pronounced in Myrmarachne, a large genus of ant-like jumping spiders (Salticidae) and one of the major animal groups in which Batesian mimicry of ants has evolved. Although adult females and juveniles of both sexes are distinctly ant-like in appearance, Myrmarachne males have elongated chelicerae that might appear to detract from their resemblance to ants. Experimental findings suggest that the Myrmarachne male's solution is to adopt compound mimicry (i.e. the male's model seems to be not simply an ant worker but a combination of an ant and something carried in the ant's mandibles: an ‘encumbered ant’). By becoming a mimic of a particular subset of worker ants, Myrmarachne males may have retained their Batesian-mimicry defence against ant-averse predators, but at the price of receiving the unwanted attention of predators for which encumbered ants are preferred prey. Two salticid species were used as predators in the experiments. Portia fimbriata is known to choose other salticids as preferred prey and to avoid unencumbered ants and their mimics (Myrmarachne females). In experiments reported here, P. fimbriata avoided encumbered ants and Myrmarachne males. Ants are the preferred prey of Chalcotropis gulosa. In our experiments, C. gulosa chose safer encumbered ants in preference to more dangerous unencumbered ants, chose Myrmarachne males more often than Myrmarachne females and showed no evidence of distinguishing between Myrmarachne males and encumbered ants. The cost of reconciling sexual dimorphism with Batesian mimicry appears to be that Myrmarachne males attract the unwanted attention of specialist predators of their compound model.