  We investigate the second order asymptotics (source dispersion) of the
successive refinement problem. Similarly to the classical definition of a
successively refinable source, we say that a source is strongly successively
refinable if successive refinement coding can achieve the second order optimum
rate (including the dispersion terms) at both decoders. We establish a
sufficient condition for strong successive refinability. We show that any
discrete source under Hamming distortion and the Gaussian source under
quadratic distortion are strongly successively refinable.
  We also demonstrate how successive refinement ideas can be used in
point-to-point lossy compression problems in order to reduce complexity. We
give two examples, the binary-Hamming and Gaussian-quadratic 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 $O(n^{\log(n)})$ algorithm that
asymptotically achieves the rate-distortion bound.
