A trellis quantizer that produces an output sequence adapted for successively refinable decoded approximation employs a multi-level trellis graph. At any given level a next refinement level is obtained by replacing each transition of the trellis graph at the given level with a trellis graph. The codevectors of the refined trellis quantizer can be optimized for all levels of refinements by an iterative process that assesses the distortions resulting from modifying the codevectors. The optimizing is carried out concurrently for all levels of refinement, achieving thereby a quantizer that is optimized for whatever level of refinement the quantizer is asked to carry out. This optimization takes into account the probability distribution of incoming signal levels.