In two experiments, participants had to switch regularly between two cognitive strategies of a different complexity in the context of a numerosity judgement task. Expt 1 comprised bivalent stimuli (i.e. allowing the application of the two strategies), whereas Expt 2 involved univalent stimuli (i.e. allowing the application of only one strategy). Both experiments revealed that switching between strategies entailed a cognitive cost that was reflected in longer response times on switch compared to non-switch trials but not in reduced accuracy. The size of this switch cost did not differ as a function of strategy complexity but tended to diminish as a strategy became more appropriate for solving a particular problem. We discuss the extent to which current theories of task switching can account for these findings.