The influence of a monocular depth cue, blur, on the apparent depth of stereoscopic scenes will be studied in this paper. When 3D images are shown on a planar stereoscopic display, binocular disparity becomes a pre-eminent depth cue. But it induces simultaneously the conflict between accommodation and vergence, which is often considered as a main reason for visual discomfort. If we limit this visual discomfort by decreasing the disparity, the apparent depth also decreases. We propose to decrease the (binocular) disparity of 3D presentations, and to reinforce (monocular) cues to compensate the loss of perceived depth and keep an unaltered apparent depth. We conducted a subjective experiment using a two- alternative forced choice task. Observers were required to identify the larger perceived depth in a pair of 3D images with/without blur. By fitting the result to a psychometric function, we obtained points of subjective equality in terms of disparity. We found that when blur is added to the background of the image, the viewer can perceive larger depth comparing to the images without any blur in the background. The increase of perceived depth can be considered as a function of the relative distance between the foreground and background, while it is insensitive to the distance between the viewer and the depth plane at which the blur is added.