A description is given of a psychophysical method that incorporates the beneficial features of the method of limits (ML) and the method of constant stimuli (MCS). Successive stimuli in a series are presented in random order. The data are treated either as data of a ML experiment or as data of a MCS experiment. The mean threshold is the same as that obtained in the ML or in the MCS. For a given number of judgments, the accuracy of the mean threshold is about the same as the accuracy obtained with the ML. The method eliminates knowledge of the order of the stimuli, and allows evaluation of time-correlated fluctuations in sensitivity.