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Fractal image compression turns out to be a powerful and competitive technology, which can be successively applied to a still image coding, especially at high compression rates. Unfortunately, a large amount of computation needed for the compression stage remains to be a serious obstacle in exploring this new perspective approach. Diversified attempts are made to improve the situation. In particular, theoretical investigations and experiments show that the problem-oriented use of invariant image parameters (image smoothness estimates) can serve the purpose.