Additive reliability-based models have been successfully used to describe multisensory integration. More recently, these models which disregard potential influences of cue consistency were also applied to predict intrasensory integration of visual depth cues. The current study aimed at investigating whether interactions among visual cues affect their integration. Observers judged the depth of hemicylinders that were defined by stereoscopic disparity, shading, and texture gradients that could be manipulated independently. By using a novel multiple-observation task, single-cue weights and observer sensitivity were estimated for conditions with reduced reliability of single cues as well as for pairwise cue consistencies. Less reliable cues were found to be downweighted in the combined percept which is in accordance with reliability-based cue integration schemes. Moreover, a specific influence of cue consistency was revealed. When shading and disparity indicated a consistent depth of the stimulus, the weight of the texture cue was reduced while d’ increased above the predictions of additive integration rules. Thus, shading and disparity seemed to be processed interactively. These results suggest that cue combination in visual depth perception is highly flexible and depends on single-cue properties as well as on interrelations among cues.