Within the expanding paradigm of medical imaging in Teleradio- logy-Telemedicine, there is increasing demand for transmitting diagnostic medical imagery. These are usually rich in radiological contents, especially in slicing modalities, and the associated file sizes are large which must be compressed with minimal file size to minimize transmission time and robustly coded to withstand required network medium. It has been reinforced through extensive research that the diagnostically important regions of medical images, Regions of Interest, must be compressed by lossless or near lossless algorithm, while on the other hand, the background region be compressed with some loss of information but still recognizable using JPEG2000 standard. Applying on MRI and CT scan images achieved different high compression ratios with varying quantization levels analogously reduced transmission time depending on sources of energy, the MAXSHIFT method proved very effective both objectively and subjectively.