Spatial resolution and contrast sensitivity requirements for some types of medical image techniques, including mammography, delay the implementation of new digital technologies, namely, computer-aided diagnosis, picture archiving and communications systems, or teleradiology. In order to reduce transmission time and storage cost, an efficient data-compression scheme to reduce digital data without significant degradation of medical image quality is needed. In this study, we have applied two region-based compression methods to digital mammograms. In both methods, after segmenting the breast region, a region-based discrete wavelet transform is applied, followed by an object-based extension of the set partitioning in hierarchical trees (OB-SPIHT) coding algorithm in one method, and an object-based extension of the set partitioned embedded block (OB-SPECK) coding algorithm in the other. We have compared these specific implementations against the original SPIHT and the new standard JPEG 2000, both using reversible and irreversible filters, on five digital mammograms compressed at rates ranging from 0.1 to 1.0 bit per pixel (bbp). Distortion was evaluated for all images and compression rates by the peak signal-to-noise ratio. For all images, OB-SPIHT and OB-SPECK performed substantially better than the traditional SPIHT and JPEG 2000, and a slight difference in performance was found between them. A comparison applying SPIHT and the standard JPEG 2000 to the same set of images with the background pixels fixed to zero was also carried out, obtaining similar implementation as region-based methods. For digital mammography, region-based compression methods represent an improvement in compression efficiency from full-image methods, also providing the possibility of encoding multiple regions of interest independently.