We recently proposed a symmetry-based scalable lossless compression method for 3D medical images using the 2D integer wavelet transform and the embedded block coder with optimized truncation (EBCOT). In this paper, we present two major contributions that enhance our early work: 1) a new block-based intra-band prediction method that exploits the global and local symmetries of the wavelet-transform sub-bands based on the main axis of symmetry as detected using the analytical Fourier-Mellin transform; and 2) a new inter-slice DPCM prediction method that exploits the correlation between slices. Performance evaluations on real 3D medical images show an average improvement of up to 17% in lossless compression ratios when compared to the state-ofthe-art compression methods including 3D-JPEG2000, JPEG2000 and H.264 intra-coding.