1. A method of data compression for colour images wherein it incorporates the following steps: a) establishing a value for a number of scales into which a wavelet transformation is to be made; b) distinguishing areas in an original colour image of relatively higher importance from those of relatively lower importance; c) transforming the colour image into a second image in a different colour system having relatively more image information in a first component and relatively less in other components; d) sub-sampling the other components to reduce their respective numbers of pixels; e) transforming the first component and the sub-sampled components into wavelet coefficients with the said number of scales; f) transforming the importance-distinguished areas to correspond to location and number of scales of the wavelet transformation; and g) establishing a wavelet coefficient threshold and forming a reduced wavelet image by discarding wavelet coefficients which both correspond to image areas of relatively lower importance and are below the said threshold.