A venerable view holds that a border between perception and cognition is built into our cognitive architecture and that this imposes limits on the way information can flow between them. While the deliverances of perception are freely available for use in reasoning and inference, there are strict constraints on information flow in the opposite direction. Despite its plausibility, this approach to the perception-cognition border has faced criticism in recent years. This article develops an updated version of the architectural approach, which (...) I call the dimension restriction hypothesis (DRH). According to DRH, perceptual processes are constrained to compute over a bounded range of dimensions, while cognitive processes are not. This view allows that perception is cognitively penetrable, but places strict limits on the varieties of penetration that can occur. The article argues that DRH enjoys both theoretical and empirical support, and also defends the view against several objections. (shrink)