Image data is subject to compression and decompression when it is respectively written to and read from a frame buffer. If a portion of the image data is identified as static (subject to less than a threshold amount of change for greater than a threshold time), then compression control parameters used for compression of that portion of the image are adjusted so as to increase the compression ratio achieved, hold the degree of lossiness substantially constant and increase the energy consumed while compressing that portion. The increased energy consumption during this high compression ratio compression is likely compensated for by a reduction in energy subsequently consumed when writing that frame-buffer image data to the frame buffer and reading that frame-buffer image data multiple times from the frame buffer. The compression characteristics varied may be to increase the block size used in the compression. Other variations in compression applied may be to change from single-pass compression to multi-pass compression, switch compression on and off altogether, or reorder the data when it has been compressed so as to match the order it will be read and so achieve support for longer read burst.