In a wide range of contexts from mate choice to foraging, animals are required to discriminate between alternative options on the basis of multiple cues. How should they best assess such complex multicomponent stimuli? Here, we construct a model to investigate this problem, focusing on a simple case where a ‘chooser’ faces a discrimination task involving two cues. These cues vary in their accuracy and in how costly they are to assess. As an example, we consider a mate-choice situation where females choose between males of differing quality. Our model predicts the following: (i) females should become less choosy as the cost of finding new males increases; (ii) females should prioritize cues differently depending on how choosy they are; (iii) females may sometimes prioritize less accurate cues; and (iv) which cues are most important depends on the abundance of desirable mates. These predictions are testable in mate–choice experiments where the costs of choice can be manipulated. Our findings are applicable to other discrimination tasks besides mate choice, for example a predator's choice between palatable and unpalatable prey, or an altruist's choice between kin and non–kin.