We examine whether the rules of cyclopean visual direction, as expressed by Hering and others, correctly predict the percept of visual direction for structured visual stimuli. Theoretical inspection of the rules of cyclopean visual direction shows a paradox for the binocular visual directions of stimuli in which objects partly occlude each other. We investigate how the rules of cyclopean direction are violated during viewing of structured random-dot stereograms with different depth planes. The directions of monocular and binocular visual elements are determined in an alignment task. Subjects align a monocular/binocular slider with a monocular/binocular test line present in the random-dot stereograms. The results show that the available rules of cyclopean direction are not sufficient for human vision in this general situation. The available rules can only be used for alignment of two binocularly visible lines or two monocular lines presented to the same eye. Alignment in these cases is predicted by almost any set of rules that transforms visible lines to a cyclopean eye. Stimulus conditions, in which either one line is presented to one eye and the other line to the other eye or one line is presented to one eye and the other line to two eyes, provide a more critical test for validity of the cyclopean rules. Our results show that the rules of cyclopean direction fail to predict alignment precisely in these conditions. Inspection of the data shows that binocular alignment is achieved by alignment of two monocular lines presented to a single eye.