A method for compressing blocks of electronic image data, each block comprising a plurality of elements of the electronic image data, the method comprising the steps of: generating a modulation value for each of said plurality of elements of image data; generating at least two sets of reduced size image data from the electronic image data, each element of each set of reduced size image data being representative of a plurality of elements of the electronic image data, wherein the sets of reduced size image data can be combined using the modulation values to provide a representation of the electronic image data; for each of the blocks: for each of a plurality of groups of modulation values generated for elements of the image data in the block, assigning a respective set of bits of modulation data, wherein each of said sets of bits of modulation data assigned to encode a respective group of modulation values comprises: (i) a plurality of modulation value choice bits indicating a set of one or more candidate modulation values for the group; and (ii) a plurality of modulation indicators for a respective plurality of modulation values in the group, wherein the modulation indicator for a respective modulation value in the group indicates which of the set of candidate modulation values is to be used to represent that modulation value in the group; and storing the sets of reduced size image data, and the sets of bits of modulation data for the groups of modulation values for each of the blocks of elements of the electronic image data, wherein a single element of each set of reduced size image data is stored for each of the blocks of electronic image data. generating a modulation value for each of said plurality of elements of image data; generating at least two sets of reduced size image data from the electronic image data, each element of each set of reduced size image data being representative of a plurality of elements of the electronic image data, wherein the sets of reduced size image data can be combined using the modulation values to provide a representation of the electronic image data; for each of the blocks: for each of a plurality of groups of modulation values generated for elements of the image data in the block, assigning a respective set of bits of modulation data, wherein each of said sets of bits of modulation data assigned to encode a respective group of modulation values comprises: (i) a plurality of modulation value choice bits indicating a set of one or more candidate modulation values for the group; and (ii) a plurality of modulation indicators for a respective plurality of modulation values in the group, wherein the modulation indicator for a respective modulation value in the group indicates which of the set of candidate modulation values is to be used to represent that modulation value in the group; and for each of a plurality of groups of modulation values generated for elements of the image data in the block, assigning a respective set of bits of modulation data, wherein each of said sets of bits of modulation data assigned to encode a respective group of modulation values comprises: (i) a plurality of modulation value choice bits indicating a set of one or more candidate modulation values for the group; and (ii) a plurality of modulation indicators for a respective plurality of modulation values in the group, wherein the modulation indicator for a respective modulation value in the group indicates which of the set of candidate modulation values is to be used to represent that modulation value in the group; and (i) a plurality of modulation value choice bits indicating a set of one or more candidate modulation values for the group; and (ii) a plurality of modulation indicators for a respective plurality of modulation values in the group, wherein the modulation indicator for a respective modulation value in the group indicates which of the set of candidate modulation values is to be used to represent that modulation value in the group; and storing the sets of reduced size image data, and the sets of bits of modulation data for the groups of modulation values for each of the blocks of elements of the electronic image data, wherein a single element of each set of reduced size image data is stored for each of the blocks of electronic image data.