Qualitative depth and shape information is obtained from stereo disparities with almost no computations, and with no prior knowledge (or computation) of the camera's parameters. First, two expressions are derived that order matched points in the images in two distinct depth-consistent ways from image coordinates only. Their use demonstrates some anomalies that have been observed in psychophysical experiments, most notably the induced-size effect. Second, the same approach is applied to estimate some qualitative behavior of the normal to the surface of any object in the field of view. In a similar way an algorithm is developed to compute axes of zero curvature from disparities alone. The algorithm is shown to be quite robust against violations of the basic assumptions of the computation on synthetic images, with relatively large controlled deviations. It performs almost as well on real images, as demonstrated on an image of four cans at different orientations. In this example, the true zero-curvature axes have been found for three cans, and an estimate with some small error has been found for the fourth.