When a graphics processor is processing data for an application on a host processor, the graphics processor generates in advance of their being required for display by the application a plurality of frame sequences corresponding to a plurality of different possible “future states” for the application. The graphics processing system, when producing a frame in a sequence of frames corresponding to a given future state for the application, determines one or more region(s) of the frame that are to be produced at a first, higher quality, and producing the determined region(s) of the frame at a first, higher quality, whereas other regions of the frame are produced at a second, lower quality.