The purposes of this paper are four-fold: (a) develop a variety of wavelet methods, including standard, hyperbolic, and adaptive wavelet bases, for the compression of high-resolution digital mammograms, (b) apply different levels of compression to the images and determine the dependence of the information loss on the compression ratio, (c) determine qualitatively the types of artifacts and errors introduced to the compressed reconstructed images by the various wavelets and make a relative comparison, and (d) discriminate among the various wavelet bases and select those worthy of further analysis and study.< >