The invention of the present application provides data compression and archival features for data that has previously been transformed and compressed. In a first aspect of the present invention, compressed data that has previously been transformed and compressed is received, and coefficients in the compressed data are selected and discarded to reduce the amount of storage space required by the compressed data. In another aspect, the compressed data has previously been sub-sampled by a wavelet transform, and wavelet coefficients in the compressed data are selected and discarded. In another aspect, wavelet coefficients in the compressed data are dequantized, wavelet coefficients in the compressed data having less value for the data are selected, and the wavelet coefficients are requantized so as to cause more loss of data for the selected coefficients to reduce the amount of storage space required by the compressed data. In another aspect, groups of wavelet coefficients in unused color components of compressed image data are selected and discarded to reduce the amount of storage space required by the compressed image data.