All sources are nearly successively refinable

Given an achievable quadruple (R₁, R₂, D₁, D₂) for progressive transmission, the rate loss at step i is defined as L_i=R_i-R(D_i). Let D₁ and D ₂ be any two desired distortion levels (D₂<D ₁). It is shown that for an i.i.d. source and for squared error, an achievable quadruple can be found for which L_i⩽1/2 bit/sample (a similar statement is proved for situations in which more than two steps are required). Moreover, an achievable quadruple can be found with L₂ arbitrarily small and L₁⩽1/2 bit/sample if D₂ is small enough. If an information-efficient description at D₁ is required (i.e., L₁=0), then there exists an achievable quadruple with L₂⩽1 bit/sample. The results are independent of both the source and the particular D₁, D₂ requirements and extend to any difference distortion measure. The techniques employed parallel Zamir´s bounding of the rate loss in the Wyner-Ziv problem. Bounds for the rate loss in other multiterminal source coding problems also are given