Previous studies have shown that Joint Photographic Experts Group (JPEG) 2000 compression is better than JPEG at higher compression ratio levels. However, some findings revealed that this is not valid at lower levels. In this study, the qualities of compressed medical images in these ratio areas ( approximately 20), including computed radiography, computed tomography head and body, mammographic, and magnetic resonance T1 and T2 images, were estimated using both a pixel-based (peak signal to noise ratio) and two 8 x 8 window-based [Q index and Moran peak ratio (MPR)] metrics. To diminish the effects of blocking artifacts from JPEG, jump windows were used in both window-based metrics. Comparing the image quality indices between jump and sliding windows, the results showed that blocking artifacts were produced from JPEG compression, even at low compression ratios. However, even after the blocking artifacts were omitted in JPEG compressed images, JPEG2000 outperformed JPEG at low compression levels. We found in this study that the image contrast and the average gray level play important roles in image compression and quality evaluation. There were drawbacks in all metrics that we used. In the future, the image gray level and contrast effect should be considered in developing new objective metrics.