Where we look when we scan visual scenes is an old question that continues to inspire both fundamental and applied research. Recently, it has been reported that depth is an important variable in driving eye movements: the directions of spontaneous saccades tend to follow depth gradients, or, equivalently, surface tilts (L. Jansen, S. Onat, & P. König, 2009; M. Wexler & N. Ouarti, 2008). This has been found to hold for both simple and complex scenes and for a variety of depth cues. However, it is not known whether saccades are aligned with individual depth cues, or with a combination of depth cues. If saccades do follow a combination of depth cues, then it is interesting to ask whether this combination follows the same rules as the well-studied case of depth cue combination in conscious perception. We showed subjects surfaces inclined in depth, in which perspective and binocular disparity cues specified different plane orientations, with different degrees of both small and large conflict between the two sets of cues. We recorded subjects' spontaneous saccades while they scanned the scene, as well as their reports of perceived plane orientation. We found that distributions of spontaneous saccade directions followed the same pattern of depth cue combination as perceived surface orientation: a weighted linear combination of cues for small conflicts, and cue dominance for large conflicts. The weights assigned to the cues varied considerably from one subject to the next but were strongly correlated for saccades and perception; moreover, for both perception and saccades, cue weights could be modified by manipulating cue reliability in a way compatible with Bayesian theories of optimal cue combination. We also measured vergence, which allowed us to calculate the orientation of the plane fitted to points scanned in depth. Contrary to perception and saccades, vergence was dominated by a single cue, binocular disparity.