Theoretical models frequently assume that the rate at which a searching predator encounters prey increases linearly with prey density. In a recent experiment using great tits searching for winter moth caterpillars, the time to find the first prey item did not decline as quickly with density as the standard theory assumes. Using a spatial simulation model, we show that prey aggregation and/or spatially correlated searching behaviour by the predator can generate a range of relationships, including results that are qualitatively similar to those found in the great tit experiment. We suggest that further experiments are required to determine whether the explanation proposed here is correct, and that theoretical work is needed to determine how this behaviour is likely to influence the ecological and evolutionary dynamics of predator-prey communities.