Compression ratio (CR) has been the de facto standard index of compression level for medical images. The aim of the study is to evaluate the CR, peak signal-to-noise ratio (PSNR), and a perceptual quality metric (high-dynamic range visual difference predictor HDR-VDP) as objective indices of image fidelity for Joint Photographic Experts Group (JPEG) 2000 compressed body computed tomography (CT) images, from the viewpoint of visually lossless compression approach. A total of 250 body CT images obtained with five different scan protocols (5-mm-thick abdomen, 0.67-mm-thick abdomen, 5-mm-thick lung, 0.67-mm-thick lung, and 5-mm-thick low-dose lung) were compressed to one of five CRs (reversible, 6:1, 8:1, 10:1, and 15:1). The PSNR and HDR-VDP values were calculated for the 250 pairs of the original and compressed images. By alternately displaying an original and its compressed image on the same monitor, five radiologists independently determined if the pair was distinguishable or indistinguishable. The kappa statistic for the interobserver agreement among the five radiologists' responses was 0.70. According to the radiologists' responses, the number of distinguishable image pairs tended to significantly differ among the five scan protocols at 6:1-10:1 compressions (Fisher-Freeman-Halton exact tests). Spearman's correlation coefficients between each of the CR, PSNR, and HDR-VDP and the number of radiologists who responded as distinguishable were 0.72, -0.77, and 0.85, respectively. Using the radiologists' pooled responses as the reference standards, the areas under the receiver-operating-characteristic curves for the CR, PSNR, and HDR-VDP were 0.87, 0.93, and 0.97, respectively, showing significant differences between the CR and PSNR (p = 0.04), or HDR-VDP (p < 0.001), and between the PSNR and HDR-VDP (p < 0.001). In conclusion, the CR is less suitable than the PSNR or HDR-VDP as an objective index of image fidelity for JPEG2000 compressed body CT images. The HDR-VDP is more promising than the PSNR as such an index.