If an accessory stimulus regularly precedes a critical stimulus at a fixed inter‐stimulus interval then the shorter the interval the lower the threshold for the critical stimulus. Three hypotheses which might explain this are discussed, and two experiments described. Experiment 1 shows that varying the intensity of an accessory stimulus does not affect the extent of the threshold fall it produces. Experiment 2 confirmed a prediction that randomizing inter‐stimulus intervals over a small range would allow the threshold to fall as the mean inter‐stimulus interval decreased at long mean intervals but not at short ones. Taken with earlier results, these experiments indicate that the subject lowers his threshold during a range of time about the end of the inter‐stimulus interval in which he expects that the stimulus may occur. It is also shown that the extent of the fall in threshold is inversely proportional to the length of this range of expectation, and that the latter appears to be directly proportional to the duration of the inter‐stimulus interval.This variation in threshold level is considered in terms of the model of the threshold provided by signal detectability theory. It is shown that the threshold falls are due to changes in the criterion computed by the subject, rather than in the sensory noise. This model is also successfully used to predict the extent of the shifts in detection rate that occur as the inter‐stimulus interval alters, on the assumption that subjects attempt to keep their false positive rates constant. Finally it is suggested that in computing the appropriate criterion for each inter‐stimulus interval the subject uses a simple approximate method rather than the more complex