The invention describes a wavelet compression method for color converted image planes (Y, Cb and Cr), wherein a relatively low (e.g. zero) degree of compression is performed in areas of an original color image having relatively higher importance, a relatively higher degree of compression in those areas indicated to be of lower importance. It performs a hierarchical encoding of a reduced wavelet image by discarding wavelet coefficients which satisfy the two criteria of firstly corresponding to image areas of relatively lower importance and secondly being below a certain wavelet coefficient threshold. The wavelet coefficient threshold is determined from a calculation histogram to remove a percentage of the image and can be specified as an input parameter by a user.