A modified display list contains a series of n nested bounding volumes. The first bounding volume in the series contains the remaining n-1 bounding volumes the series. The second bounding volume contains the remaining n-2 bounding volumes in the series, and so on. Upon invocation, the graphics display system processes the modified list sequentially and tests the bounding volumes as they are encountered. As soon as a bounding volume is encountered whose coordinates define a region that should not be rendered, further sequential processing of rendering commands in the list may be halted. If any state commands remain in the list, those commands or an equivalent set of state commands may be executed, and then processing of the list is complete. Alternatively, if push/pop state commands exist on either side of the list, then processing of the list may be halted without more.