Roughly described, the invention is employed within a z-buffer-system having a host processor and graphics hardware that performs hierarchical z-buffering. The z-buffer system renders three-dimensional scenes having geometric primitives that are organized in bounding boxes or rooms-with-portals. As an image is being generated, some but not all z-pyramid values are written from the graphics system into memory that can be quickly accessed by the host processor. This enables the host processor to perform visibility tests that cull occluded bounding boxes or portals, thereby accelerating rendering by reducing the number of primitives that need to be sent to graphics hardware and processed.