We have developed a software module which performs 2-D and 3-D image compression based on discrete wavelet transform/subband coding techniques. The software allows the user to interactively determine the tradeoff between compression ratio and fidelity (by viewing the results) and to interactively define specific regions of the image - of any size and shape - that are to be preserved with full fidelity while the rest of the image is compressed (again, viewing the results). The compression achieved is superior to the JPEG standard algorithm. We present sample results on a variety of medical images and direct comparisons with JPEG results. We also show examples of the improvements gained by true 3-D compression of a 3-D image (as opposed to 2-D compression of each slice), discuss human visual system response issues, and describe extensions of the current approach to still more efficient compression schemes.