A system that compresses a digital image. During operation, the system obtains a digital image in which the image components are de-correlated into separate channels containing luminance information and chrominance information. Next, the system receives a quality number for the luminance channel and a quality number for the chrominance channels, and uses the quality numbers to determine a target bitrate for the luminance channel and for the chrominance channels, respectively. Given the target bitrate for the luminance channel and the target bit rate for the chrominance channels, the system performs rate distortion optimizations separately on the luminance and chrominance channels to determine which portions of the luminance bitstream and which portions of the chrominance bitstream are to be included in the final bitstream. The system then uses the stored rate-distortion information to generate a preview of the digital image without performing entropy coding each time the quality settings are changed.