A regular, grouped Kanizsa triangle has been shown to break through interocular suppression faster than an ungrouped, random Kanizsa triangle [Wang et al., 2012, PLoS ONE, 7(6): e40106]. In an earlier neuropsychological study Conci et al. [2009, Neuropsychologia, 47, 726-732] showed that low-level collinear contour facilitation and high-level surface filling-in both contribute separately to a reduction in extinction in patients with visual neglect when viewing Kanizsa stimuli. Since Wang et al. (2012) did not include control conditions similar to Conci et al. (2009), it is not clear whether the Kanizsa triangle broke through suppression due to collinear contour facilitation or higher-level surface completion mechanisms [Kogo et al., 2010, Psychological Review, 117(2), 406-439]. In this study, we compared suppression times of regular and random versions of a Kanizsa square, a cross stimulus (allowing collinear contour facilitation but no surface completion) and a surface stimulus (allowing surface completion but no collinear contour facilitation). Our results suggest that neither collinear contour facilitation nor surface completion mechanisms play a primary role in determining suppression times. Rather, the regularity of the stimulus seems to play a crucial role. This hypothesis was tested further by breaking down the regularity of the different classes of stimuli.