The hypothesis was tested that the coupling of parallax shifts between objects depicted on a monitor screen around a fixation point with the head movements of an observer viewing this screen monocularly around a point coinciding with the fixation point is sufficient to create a convincing depth impression and to enable the observer to make reliable estimations of depth. The estimates were based on monocular vision and involved the aligning of wedges. The investigation consisted of two analogous experiments carried out simultaneously, one on depth estimations virtually in the screen and one on depth estimations virtually in front of the screen. In each experiment three conditions were compared: an active condition in which the coupling of parallax shifts and observer's head movements operated, a passive condition in which it did not, and a real-life set-up to measure the maximum reliability in depth estimation. The hypothesis is confirmed: in the active condition the variances in the alignments are significantly smaller than in the passive condition and approach those in the real-life set-up. This holds not only for estimates in the screen but also for estimates in front of the screen, that is, we can make a thing apparently leap out of the screen towards the observer. Results are interpreted against the background of the debate between the direct and the indirect theories of perception.