Recent attention has been drawn to the existence of individual differences in correlated behaviour across contexts, animal 'personality' (Gosling 2001, Psychological Bulletin, 127, 45-86) and behavioural syndromes (Sih et al. 2004b, Quarterly Review of Biology, 79, 241-277). The causes of these patterns of behaviour are subjects of debate. Here, we present a very simple model of how adaptively managing noisy information, combined with differences in individual state, can lead to evolutionarily stable differences in how individuals respond to environmental cues. When information is very noisy, behavioural syndromes are most likely, but as long as there is some error, some types of individuals display the same behaviour in all contexts. In extreme cases, very few individuals display flexible behaviour, and different stable behavioural types dominate the population.