We measured the probability of detecting the target in a visual search task, as a function of the following parameters: the discriminability of the target from the distractors, the duration of the display, and the number of elements in the display. We examined the relation between these parameters at criterion performance (80% correct) to determine if the parameters traded off according to the predictions of a limited capacity model. For the three dimensions that we studied, orientation, color, and spatial frequency, the observed relationship between the parameters deviates significantly from a limited capacity model. The data relating discriminability to display duration are better than predicted over the entire range of orientation and color differences that we examined, and are consistent with the prediction for only a limited range of spatial frequency differences–from 12 to 23%. The relation between discriminability and number varies considerably across the three dimensions and is better than the limited capacity prediction for two of the three dimensions that we studied. Orientation discrimination shows a strong number effect, color discrimination shows almost no effect, and spatial frequency discrimination shows an intermediate effect. The different trading relationships in each dimension are more consistent with early filtering in that dimension, than with a common limited capacity stage. Our results indicate that higher-level processes that group elements together also play a strong role. Our experiments provide little support for limited capacity mechanisms over the range of stimulus differences that we examined in three different dimensions.