We consider the lossy image compression problem and propose a model-residual approach. Polynomial basis images encode the model image and powerful new trellis codes quantize the residual part. A simple bit allocation scheme determines the residual bit rates and a variety of rates are attainable without entropy coding. The trellis structure is also used to form a joint source and channel coding scheme for the residual components. Results are shown for the 0.4-1.6 bits per pixel region. Comparisons are made to several state-of-theart techniques and show that the proposed scheme is very competitive.