A series of experiments examined the characteristics of train-duration response functions and two statistics derived from these functions: train-duration thresholds and maximum rates. Train-duration response functions exhibited a steplike appearance. The slope of the train-duration curves was not influenced by either reward or performance manipulations, which suggests that the animals were not matching their response rates to changes in these factors along the steep part of the function. Substantial shifts in train-duration thresholds were observed following changes in the reward value of the brain stimulation, whereas maximum rates were affected by changes in factors such as response effort. The results of Experiments 1 through 6 demonstrate several similarities and differences between train-duration response functions and the reward summation functions generated with manipulations of stimulation frequency. The experiments described in this report provide convergent evidence for the validity of both of these approaches.