This paper evaluates the performance of a system which compresses digital mammograms, In digital mammograms, important diagnostic features such as the microcalcifications appear in small clusters of few pixels with relatively high intensity compared with their neighboring pixels, These image features can be preserved in a compression system that employs a suitable image transform which can localize the signal characteristics in the original and the transform domain. Image compression is achieved by first decomposing the mammograms into different subimages carrying different frequencies, and then employing vector quantization to encode these subimages. Multiresolution codebooks are designed by the Linde-Buzo-Gray (LBG) algorithm and a family of fuzzy algorithms for learning vector quantization (FALVQ). The main advantage of the proposed approach is the design of separate multiresolution codebooks for different subbands of the decomposed image that carry different orientation and frequency information, The experimental results confirm the viability of the proposed compression scheme on digital mammograms.