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The rate loss of a multi-resolution source code (MRSC) describes the difference between the rate needed to achieve distortion Di in resolution i and the rate-distortion function R(Di). We generalize the rate loss definition and bound the rate losses of multiple description source codes (MDSCs) and additive MRSCs (AMRSCs). For a 2-description MDSC (2DSC), the rate loss of description i with distortion Di is defined as Li=Ri-R(Di), i=1, 2, where Ri is the rate of the ith description; the rate loss associated with decoding the two descriptions together to achieve central distortion D0 is measured as L0=R1+R2-R(D0) or as L12=L1+L2. We show that given an arbitrary source with variance σ2, there exists a 2DSC with L1≤0.5 and (a) L0≤1 if D0≤D1+D2-σ2, (b) L12≤1 if 1/D0≤1/D1+1/D2-1/σ2, (c) L0≤LG0+1.5 and L12≤LG12+1 otherwise, where LG0 and LG12 are the joint rate losses of a normal (0, σ2) source. An AMRSC is an MRSC with the kth-resolution reconstruction equal to the sum of the first k side reproductions of an MDSC. We obtain one bound on the rate loss of an AMRSC.