The performance of wavelet compression algorithms is generally judged solely as a function of the compression ratio and the vidual artifacts which are perceivable in the reconstructed image. The problem then becomes one of obtaining the best compression with fewest visible artifacts--a very subjective measure. Our wavelet compression algorithm uses an information theoretic analysis for the design of the compression maps. We have previously shown that maximizing the information for a given visual communication channel also maximizes the visual quality of the restored image. We utilize this to design quantization maps which maximize information for a given compression ratio. Hence we are able to design quantization maps which maximize the restorability of an image--i.e. the information content, the image quality, and the mean-square difference fidelity--for a given compression ratio.