Much evidence suggests that we first perceive the overall layout of a scene or object followed later by the details. This coarse-to-fine temporal dynamic in visual processing is also found in Navon's classical paradigm where information at the global level of compound stimuli is processed faster than information at the local level (global precedence effect), and where information at the global level has larger effects on local level responses than local level information has on global level responses (asymmetric interference effects). Traditionally, global shape primacy in Navon's paradigm has been linked with a right hemisphere preference (left visual field advantage) for global shape processing, and a left hemisphere preference (right visual field advantage) for local shape processing. This link, however, has been based on measures which confound global precedence and interference effects. Indeed, when these measures are de-confounded, we find no evidence for larger global precedence effects in the left compared with the right visual field in a large sample of participants (N = 337). In comparison, global-to-local interference effects are found to be stronger in the left than in the right visual field. We argue that these findings can be accounted for by assuming that the right hemisphere plays a special role in integrating shape information across spatial scales, that is, without assuming the existence of a right hemisphere preference for global shape processing per se.