When a spiky object is occluded, we expect its spiky features tocontinue behind the occluder. Although many real-world objects contain complex features, it is unclear how more complex features are amodally completed and whether this process is automatic. To investigate this issue, we created pairs of displays with identical contour edges up to the point of occlusion, but with occluded portions exchanged. We then asked participants to search for oddball targets among distractors and asked whether relations between searches involving occluded displays would match better with relations between searches involving completions that are either globally consistent or inconsistent with the visible portions of these displays. Across two experiments involving simple and complex shapes, search times involving occluded displays matched better with those involving globally consistent compared with inconsistent displays. Analogous analyses on deep networks pretrained for object categorization revealed a similar pattern of results for simple but not complex shapes. Thus, deep networks seem to extrapolate simple occluded contours but not more complex contours. Taken together, our results show that amodal completion in humans is sophisticated and can be based on extrapolating global statistical properties.