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 visual comfort, and increase perceived workload during the performance of 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. We extend a previous study (Tsirlin, Allison, and Wilcox, 2011) on the perception of depth magnitude in stereoscopic occluding and non-occluding surfaces to the special case of crosstalk in thin structures. We use a paradigm in which observers estimated the perceived depth difference between two thin vertical bars using a measurement scale. Our data show that as crosstalk levels increase, the magnitude of perceived depth decreases, 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 has been 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.