Observers performed several different detection tasks using both the PEST adaptive psychophysical procedure and a fixed‐level (method of constant stimuli) psychophysical procedure. In two experiments, PEST runs targeted atP(C)=0.80 were immediately followed by fixed‐level detection runs presented at the difficulty level resulting from the PEST run. The fixed‐level runs yieldedP(C) about 0.75. During the fixed‐level runs, the probability of a correct response was greater when the preceding response was correct than when it was wrong. Observers, even highly trained ones, perform in a nonstationary manner. The sequential dependency data can be used to determine a lower bound for the observer’s ‘‘true’’ capability when performing optimally; this lower bound is close to the PEST target, and well above the forced choiceP(C). The observer’s ‘‘true’’ capability is the measure used by most theories of detection performance. A further experiment compared psychometric functions obtained from a set of PEST runs using different targets with those obtained from blocks of fixed‐level trials at different levels. PEST results were more stable across observers, performance at all but the highest signal levels was better with PEST, and the PEST psychometric functions had shallower slopes. We hypothesize that PEST permits the observer to keep track of what he is trying to detect, whereas in the fixed‐level method performance is disrupted by memory failure. Some recently suggested ‘‘more virulent’’ versions of PEST may be subject to biases similar to those of the fixed‐level procedures. Experimenters are advised to use the original version of PEST rather than fixed‐level psychophysics or ‘‘improved’’ versions of PEST when accuracy as well as speed of psychophysical measurement is important.