Game theoretical models of signalling, based on Zahavi's handicap principle, suggest that signal intensity is likely to vary continuously in relation to the quality or need of the signaller. In reality, by contrast, signals are often discrete, `all-or-nothing' events that are more stereotyped than non-signal movements. Where there is variation in the form of a display, it frequently involves just a few, distinct levels of intensity. Here, I present an evolutionarily stable strategy (ESS) signalling model that incorporates perceptual error, an inevitable feature of real signalling systems that has been ignored in all but a few previous studies. Numerical analysis of the model reveals that the introduction of perceptual error leads, under a wide range of conditions, to the evolution of discrete, 'all-or-nothing' signals. The handicap principle thus provides a strategic explanation for the typical intensity of animal displays.