Successive refinement with conditionally less noisy side information

We consider the successive refinement of information problem with decoder side information. The rate-distortion region is unknown in general; Steinberg & Merhav and Tian & Diggavi solved it in the special case of degraded side information. We extend this special case to a new setup, conditionally less noisy side information, and we give a single-letter solution when one distortion function is deterministic.