Some new stereoscopic effects are reported that arise from dichoptic stimuli containing no binocular disparity. In one effect, identical arrays of small black discs are presented to the two eyes and slightly smaller white discs are superimposed on one of each pair of black discs. This creates the impression of a surface with holes in it, through which is seen a surface with fluctuating black and white areas. This is referred to as the ‘sieve effect’. The white discs must subtend less than about 1 deg of visual angle. With larger discs the black and white areas no longer exhibit alternating rivalry but combine to produce binocular lustre. This destroys the sieve effect. The sieve effect is weak or nonexistent when the black and white discs are the same size, showing that well-defined binocular rims are required for the effect. When the monocular white discs are reduced to dots, the impression of a surface seen through holes gives way to the impression of an array of dots behind or standing out from the background. In this case the monocular dots permanently dominate the homogeneous backgrounds in the other eye and the impression of depth can be explained in terms of apparent parallax or of disparity due to the instability of vergence.