A graphics processing subsystem defines a bounding area as the portion of the display buffer and other memory buffers occupied by one or more rendered objects. When clearing the memory buffers, only the portions of the buffers corresponding to the bounding area need to be cleared. A graphics pipeline includes a bounding area memory to store bounding area values. The bounding area values are modified during rendering so that each rendered primitive falls within the bounding area values. The graphics processing subsystem clears a portion of the memory buffer in response to a clear command specifying a bounding area. The clear command may include a set of bounding area values defining the bounding area, or alternatively a reference to the bounding area memory. For applications that draw objects in isolation, the bounding area will be smaller than the window, resulting in a decreased time requirement for clearing the memory buffer.