Previous research indicated that 4-month-old infants perceive the unity of a center-occluded object when its visible ends share a common lateral translation in space. The present work investigated the class of motion relationships that can specify object unity to infants, specifically, asking whether it includes all rigid translations. 3 experiments tested the informativeness of 2 axes of translation not previously studied: translation in depth and vertical translation. These motions also allowed assessment of certain interpretations of previous results that invoke specific sensory consequences of lateral movement, rather than perceived motion, as underlying perceived unity. Experiment 1 provided evidence that a small extent of translation in depth specified the unity of an object, but only to the subgroup of infants who detected the motion. Experiment 2 used a greater displacement in depth and found clear evidence for perception of object unity. Experiment 3 indicated that vertical translation, in which the 2 visible areas of the partly hidden object undergo dissimilar changes, also specifies object unity to infants. These results suggest that infants' perception of object unity depends on perceived coherence of motion, no matter how specified, and that the class of informative motions includes all rigid translations.