To use the small horizontal disparities between images projected to the eyes for the recovery of three-dimensional information, our visual system must first identify which feature in one eye's image corresponds with which in the other. The earliest level of disparity processing in primates (V1) contains cells that are spatial-frequency tuned. If such cells have a disparity range that covers only a single period of their mean tuning frequency, there will always be exactly one potential match within this range. Here, this 'size-disparity' hypothesis was tested by measuring the contrast sensitivity of stereopsis as a function of disparity for single bandpass-filtered items. It was found that thresholds were low and relatively constant up to disparities an order of magnitude larger than is predicted by this constraint. Furthermore, peak sensitivity was relatively independent of spatial frequency. A control experiment showed that binocular correlation of the carrier is necessary for this task. In a third experiment, the maximum disparity that supports threshold performance was compared for an isolated bandpass item and bandpass-filtered noise. This limit was found to be five times larger for the isolated stimuli. In summary, these findings show that the initial stage of disparity detection is not limited by the size-disparity constraint. For stimuli with multiple false targets, however, processes subsequent to this stage reduce the disparity range over which the correspondence problem can be solved.