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We demonstrate how successive refinement ideas can be used in point-to-point lossy compression problems in order to reduce complexity. We show two examples, the binary-Hamming and quadratic-Gaussian cases, in which a layered code construction results in a low complexity scheme that attains optimal performance. For example, when the number of layers grows with the block length n, we show how to design an O(nlog(n)) algorithm that asymptotically achieves the rate distortion bound. We then show that with the same scheme, used with a fixed number of layers, successive refinement is achieved in the classical sense, and at the same time the second order performance (i.e. dispersion) is also tight.