All sources are nearly successively refinable

Given an achievable quadruple (R₁, R₂, D₁, D₂) for successive refinement with D₂ <D₁, the rate loss at step i is defined as L_i =R_i-R(D_i). It is shown that for a memoryless source and for MSE, an achievable quadruple can be found such that L_i⩽1/2 bit. Moreover, an achievable quadruple can be found with L₂ arbitrarily small and L₁⩽1/2 bit 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. 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