In this paper, we present a wavelet-based medical image compression scheme so that images displayed on different devices are perceptually lossless. Since visual sensitivity of human varies with different subbands, we apply the perceptual lossless criteria to quantize the wavelet transform coefficients of each subband such that visual distortions are reduced to unnoticeable. Following this, we use a high compression ratio hierarchical tree to code these coefficients. Experimental results indicate that our perceptually lossless coder achieves a compression ratio 2-5 times higher than typical lossless compression schemes while producing perceptually identical image content on the target display device.