An approach to stereo image compression based on disparity compensation is proposed and evaluated. The scheme is motivated by the suppression theory in human vision. A methodology for evaluating compressed stereo images is proposed. It is based on time measurements of depth perception tasks performed by human subjects. Subjects taking part in the experiment were exposed to displays of stereo images, some of which had been compressed, and were asked to judge the relative depth within each display as fast as possible. Decision times were measured and used as the major dependent variable. It was shown that very deep compression of one of the images of a stereo pair does not interfere with the perception of depth in the stereo image.