A subband image codec is presented that approximately attains a user-prescribed fidelity by allowing the encoder's compression rate to vary. The fixed distortion subband coding (FDSBC) system is suitable for use with future of packet-switched networks. The codec's design is based on an algorithm that allocates distortion among the subbands to minimize channel entropy. By coupling this allocation procedure with judiciously selected subband quantizers, an elementary four-band codec was obtained. Additional four-band structures may be nested in a hierarchical configuration for improved performance. Each of the configurations tested attains mean square distortions within 2.0 dB of the user-specific value over a wide range of distortion for several standard test images. Rate versus mean-square distortion performance rivals that of fixed-rate systems having similar complexity. The encoder's output is formatted to take advantage of prioritized packet networks. Simulations show that FDSBC is robust with respect to packet loss and may be used effectively for progressive transmission applications.>