A new region of interest (ROI) coding called partial multiply bitplane alternating shift (PMBAShift) is presented in this paper. In PMBASluft, the partial most significant bitplanes of ROI are shifted up and no overlap with any bitplane of background (BG). The most significant bitplanes of BG and general significant bitplanes of ROI coefficients are shifted up by bitplane-by-bitplane alternating scaling. Finally, the least significant bitplanes of ROI and the general significant bitplanes of BG are obtained in the original position and the least significant bitplanes of BG coefficients are shifted down and no overlap with any bitplane. The new method not only retains advantages of maximum shift (Maxshift) method, but also efficiently compresses multiple ROIs according to different degrees of interest without any shape information. A new region of interest (ROI) coding called partial multiply bitplane alternating shift (PMBAShift) is presented in this paper. In PMBASluft, the partial most significant bitplanes of ROI are shifted up and no overlap with any bitplane of background (BG). The most significant bitplanes of BG and general significant bitplanes of BG and general significant bitplanes of ROI coefficients are shifted up by bitplane-by-bitplane alternating scaling. Finally, the least significant bitplanes of ROI and the general significant bitplanes of BG are obtained in the original position and the least significant bitsplanes of BG coefficients are shifted down and no overlap with any bitplane. The new method not only retains advantages of maximum shift (Maxshift) method, but also efficiently compresses multiple ROIs according to different degrees of interest without any shape information.