What is the degree to which knowledge influences visual perceptual processes? This question, which is central to the seeing-versus-thinking debate in cognitive science, is often discussed using examples claimed to be proof of one stance or another. It has, however, also been muddled by the usage of different and unclear definitions of perception. Here, for the well-defined process of perceptual organization, I argue that including speed (or efficiency) into the equation opens a new perspective on the limits of top-down influences of thinking on seeing. While the input of the perceptual organization process may be modifiable and its output enrichable, the process itself seems so fast (or efficient) that thinking hardly has time to intrude and is effective mostly after the fact.