An apparatus for processing graphics primitives for display includes rasterization, depth testing, and rendering circuitry. The depth testing circuitry determines if a selected graphics fragment would be obscured when displayed by comparing a depth comparison function and a depth value associated with the selected graphics fragment with a stored depth value. The depth testing circuitry suppresses rendering operations for the fragment if the selected fragment would be obscured. An update indication shows a possible change direction due to the updating for a stored depth value which depends on a received depth comparison function. The depth testing for the selected fragment is performed using the possible change direction shown by the update indication to modify the depth comparison function to allow for updating of the stored depth value by the rendering operations.