The algorithms for adaptive quantization and adaptive prediction in existing adaptive differential pulse code modulation (ADPCM) are distinct and decoupled. The designs of the two algorithms are based on the assumption that they act independently whereas, due to the feedback configuration, they must interact in some way. The authors present a preliminary investigation of a new design approach where they perform joint adaptation based on a common cost function, considering the overall system. A “backward” adaptive algorithm is presented and applied to a simple example to demonstrate the feasibility of the general approach.