Abstract: A process and apparatus for allocating bits between the stages of a multi-stage digital image compression scheme with quantizer feedback is disclosed. The process selects a quantization schedule (from a finite number of possibilities) for all stages that minimizes an estimate of total distortion while keeping total bit demand below a constraint; uses said schedule to actually quantize one stage of the compression scheme; selects a new quantization schedule for the remaining stages using estimates for distortion and bit demand that are updated to reflect the quantization of the previous stage; actually quantizes the next stage according to the new quantization schedule; and continues recursively until it has chosen an actual quantization scale for every stage of the compression scheme.