Perceiving objects as complete and coherent in 3D space is a fundamental achievement of the developing visual system, and previous work demonstrated that 4-month-old infants responded with significantly longer looking and increased oculomotor activity toward pictures of impossible cubes relative to possible ones (Shuwairi & Johnson, 2013). 4-month-olds also fixated to a greater extent specifically within the critical region of impossible displays, which was not observed reliably in younger infants. The findings suggested that they are able to selectively respond to vertex information that are diagnostic of structural coherence, and this ability strengthens considerably during the first several postnatal months. However, it left open the question of whether 4-month-olds would systematically respond with increased visual interest to other geometrically impossible figures. In the current investigation we tested 4-month-old infants in an eye-tracking paradigm with novel pairs of possible and impossible objects. We hypothesized that infants would engage in active comparison of the objects, and that impossible figures would generally evoke increased visual attention in order to ascertain global structural integrity. We replicated that infants showed a preference to fixate reliably longer on the impossible cube relative to possible one (p < .04) and produced a greater number of transitional saccades between the interior critical region and neighboring regions of the impossible cube (p < .01). In contrast, infants responded with non-significantly different dwell times for possible and impossible items across the other object pairs. However, there were reliable differences in transitional shifts of gaze between the upper and lower halves of the ovals (p < .01) and peg-squares (p < .05) as a function of possibility. The high degree of variability in infants' fixation behaviors toward these shapes may be due to individual differences in selective looking or emerging sensitivity to pictorial depth information. This may also be a stimulus-dependent response that manifests exclusively with certain shapes. By 4 months, infants are beginning to hone their selective looking mechanisms to adequately register shape defining contours and line junctions cues in static images, which enables them to detect conflicting local depth relations and distinguish between pictures of possible and impossible objects.