This study concerned the perception of bodily orientation. We varied the orientation of the body relative to the visible surroundings and, independently, relative to the direction of balance. This created 3 tilt conditions that are commonly believed to create conflict between the visual, vestibular, and somatosensory systems. First, we replicated earlier effects, confirming the existence of the visual frame effect and the Müller effect, when participants made passive judgments about orientation. In later experiments using the same tilt conditions, participants executed a pointing task. In the pointing task errors were greatly reduced and in some cases were entirely absent. Based on these data (and similar findings in other studies), we argue that illusions of body orientation are highly task-specific and may not be general properties of the perception of orientation. The use of tilt relative to different referents made it possible for us to contrast the sensory conflict interpretation of orientation perception (which predicts frequent errors arising from indirect perception) with an alternative based on the pickup of intermodal relations extending across perceptual systems (which predicts generally accurate performance arising from direct perception). By conducting comparisons across pairs of tilt conditions, we were able to hold constant the stimulation to individual perceptual systems while varying the higher order relation across systems. The results of these pairwise comparisons were compatible with the hypothesis that in perceiving orientation people rely on information in these higher order patterns.