When should multiple traits on Batesian mimics be selected to resemble corresponding traits on model species? Here, we explore two possibilities. First, features of equal salience to predators may be used to categorize prey, selecting for multicomponent mimicry. Second, if different predators use single yet different traits to categorize prey, multicomponent mimicry may still be selected. We studied how blue tits categorized rewarding and unrewarding artificial prey items that are differentiated by a combination of two color dimensions. Many birds used both color dimensions to make decisions, and overall, the population selected for multicomponent mimicry. However, a subset of birds used one color or another to make decisions; among this subset, multicomponent mimicry was also favored. The cost of sampling did not affect selection. Our results suggest that multicomponent warning signals may be selected when traits are equally salient to individual predators, or when communities of predators focus on different traits to discriminate between prey.