Abstract: A venerable view holds that the border between perception and cognition is built into our cognitive architecture, and that this imposes limits on the way information can flow between them (see Fodor 1983; Pylyshyn 1999). While the deliverances of perception are freely available for use in reasoning and inference, there are strict constraints on the flow of information in the opposite direction. Despite its plausibility, this approach to the perception-cognition border has faced heavy criticism in recent years. Consequently, many authors have either abandoned the perception-cognition border altogether, or they have defended alternative conceptions of it. In contrast, this talk 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 delimitable 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. I argue that DRH enjoys both theoretical and empirical support. Moreover, unlike previous versions of the architectural approach, DRH allows us to take seriously the wealth of evidence that expectations and endogenous attention exert top-down influences on perceptual processing. Finally, I'll defend the view against some objections.