In an attempt to reconcile results of previous studies, several theorists have suggested that object recognition performance should range from viewpoint invariant to highly viewpoint dependent depending on how easy it is to differentiate the objects in a given recognition situation. The present study assessed recognition across depth rotations of a single general class of novel objects in three contexts that varied in difficulty. In an initial experiment, recognition in the context involving the most discriminable object differences was viewpoint invariant, but recognition in the least discriminable context and recognition in the intermediate context were equally viewpoint dependent. In a second experiment, utilizing gray-scale versions of the same stimuli, almost identical viewpoint-cost functions were obtained in all three contexts. These results suggest that differences in the geometry of stimulus objects, rather than task difficulty, lie at the heart of previously discrepant findings.