Abstract: By limiting the extent to which the degree of quantization is lowered to increase the amount of compressed data, problems of data rate overshoots and image quality degradation in multi layer composites may be avoided. In particular, when a more complex image occurs after a simple image, the quantization used to compress the complex image will not cause as large of a change in the total amount of compressed data. Recovery from such a change also may occur more quickly. Where quantization tables are adjusted using a scaling factor, a limit on the scaling factor may be established such that the target data rate is not achieved for simple images. When rendering multi layer composites, this limit is such that recompression of previously compressed data does not result in additional loss of information. As a result, degradation of image quality in each layer of the composite is avoided.