A paradigm for the determination of time-accuracy functions (TAFs) for individual participants is introduced for two pairs of tasks differing in cognitive complexity, that is, word scanning vs cued recognition and figural scanning vs figural reasoning. TAFs can be used to test dissociations of cognitive processes beyond scale-related ambiguities of ordinal interactions. The approach is applied to examine the cognitive-aging hypothesis that a single slowing factor can account for interactions between adult age and cognitive task complexity. Twenty young and 20 old adults participated in 17 sessions. Presentation times required for 75, 87.5, and 100% accuracies were determined for each task with a variant of the psychophysical method of limits. Accuracy was fit by negatively accelerated functions of presentation time. State-trace analyses showed that different slowing factors are required for high- and low-complexity tasks. Relations to speed-accuracy and performance-resource functions are discussed. (C) 1994 Academic Press, Inc.