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The efficient measurement of the threshold and slope of the psychometric function (PF) is an important objective in psychoacoustics. This paper proposes a procedure that combines a Bayesian estimate of the PF with either a look one-ahead or a look two-ahead method of selecting the next stimulus presentation. The procedure differs from previously proposed algorithms in two respects: (i) it does not require the range of possible PF parameters to be specified in advance and (ii) the sequence of probe signal-to-noise ratios optimizes the threshold and slope estimates at a performance level, ɸ, that can be chosen by the experimenter. Simulation results show that the proposed procedure is robust and that the estimates of both threshold and slope have a consistently low bias. Over a wide range of listener PF parameters, the root-mean-square errors after 50 trials were ~1.2 dB in threshold and 0.14 in log-slope. It was found that the performance differences between the look one-ahead and look two-ahead methods were negligible and that an entropy-based criterion for selecting the next stimulus was preferred to a variance-based criterion. [ABSTRACT FROM AUTHOR]