There has been considerable interest in what components of decision-making change when speed or accuracy is stressed. In many early studies, quite strict assumptions were made about parameter invariance across experimental conditions (sometimes called selective influence). Here we fit the standard diffusion model to the data from four large experiments with speed--accuracy instructions (with over a million total responses), allowing all model parameters to vary freely between the speed and accuracy conditions. Results show that most of the observed differences between speed and accuracy conditions appear in the boundary separation parameter, followed by nondecision time, with small effects on drift rates. However, changes in drift rates are accompanied by changes in across-trial variability in drift rate, which cancels out the effect of drift rate on accuracy and response time. Another analysis in which across-trial variance in drift rate was kept the same in fits to speed and accuracy conditions produced no difference in drift rates. Generally, if speed is stressed moderately, then both boundary separation and nondecision time are reduced and any changes in drift rate are compensated for by changes in the across-trial variance in drift rates. If speed is stressed to a high degree (Starns et al., 2012), boundary separation, nondecision time, and drift rates are reduced. This is because (we hypothesize) encoding is restricted leading to a lower degree of perceptual information or match with memory.