Stereoscopic displays must present separate images to the viewer's left and right eyes. Crosstalk is the unwanted contamination of one eye's image from the image of the other eye. It has been shown to cause distortions, reduce image quality and visual comfort and increase perceived workload when performing visual tasks. Crosstalk also affects one's ability to perceive stereoscopic depth although little consideration has been given to the perception of depth magnitude in the presence of crosstalk. In this paper we extend a previous study (Tsirlin, Allison & Wilcox, 2010, submitted) on the perception of depth magnitude in stereoscopic occluding and non-occluding surfaces to the special case of crosstalk in thin structures. Crosstalk in thin structures differs qualitatively from that in larger objects due to the separation of the ghost and real images and thus theoretically could have distinct perceptual consequences. To address this question we used a psychophysical paradigm, where observers estimated the perceived depth difference between two thin vertical bars using a measurement scale. Our data show that crosstalk degrades perceived depth. As crosstalk levels increased the magnitude of perceived depth decreased, especially for stimuli with larger relative disparities. In contrast to the effect of crosstalk on depth magnitude in larger objects, in thin structures, a significant detrimental effect was found at all disparities. Our findings, when considered with the other perceptual consequences of crosstalk, suggest that its presence in S3D media even in modest amounts will reduce observers' satisfaction.