Patients with unilateral, parietal brain damage frequently show visual extinction, which manifests in a failure to identify contralesional stimuli when presented simultaneously with other, ipsilesional stimuli (but full awareness for single stimulus presentations). Extinction reflects an impairment of spatial selective attention, leaving basic preattentive processing unaffected. For instance, access to bilaterally grouped objects is usually spared in extinction, suggesting that grouping occurs at a stage preceding (in the patients: abnormally biased) spatial-attentional selection. Here, we reinvestigated this notion by comparing (largely between participants, but also within a single-case participant) conditions with objects that varied in their dominant direction of grouping: from the attended to the non-attended hemifield (data from Conci et al., 2009) versus from the non-attended to the attended hemifield (new data). We observe complete absence of extinction when shape completion extended from the attended hemifield. By contrast, extinction was not diminished when object groupings propagate from the unattended hemifield. Moreover, we found the individual severity of the attentional impairment (assessed by a standard “inattention” test) to be directly related to the degree of completion in the unattended hemifield. This pattern indicates that grouping can overcome visual extinction only when object integration departs from the attended visual field, implying, contrary to many previous accounts, that attention is crucial for grouping to be initiated.