In a computer system with a screen display on which is formed a plurality of at least partially overlapping windows associated with different applications, a depth buffer is added to the display adapter for providing with different applications, a depth buffer is added to the display adapter for providing clipping assistance to the software-based window manager. A refresh buffer stores pixel data for each pixel of the display. The window manager monitors the current depth position of each of the pixels within the display and generates a depth value for each pixel. In response to an input request for window rearrangement, the window manager assigns a new depth value to each pixel in a window affected by the request, requests that each application affected by the rearrangement to retransmit pixel values for the pixels associated with at least the portion of a affected window which will become visible as a result of the rearrangement, and transmits new depth values for at least the pixels within the affected portions of such windows. The depth buffer receives and compares the new depth values with the current depth value for each pixel. If the comparator determines that the new pixel value has a depth value associated with the same window or a window closer to the viewer, the depth buffer notifies the refresh buffer to store the new pixel values for each of the applications affected by the rearrangement.