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We present the rate-distortion function and bound the rate loss for a system with some side information (s.i.) known at both the encoder and decoder, and some known only at the decoder. We extend the corresponding Wyner-Ziv rate-distortion results to give a lower bound for jointly Gaussian sources and upper and lower bounds for binary symmetric sources. Applying the construction from our binary upper bound to the Heegard and Berger (HB) problem of decoding when s.i. may be present improves the best upper bound for that problem. Applying it to the two-receiver system with different s.i. at each decoder provides a new upper bound.