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For symmetric sources we examine the rate of convergence to the rate-distortion function using block codes and tree codes. With block codes the average distortion decreases toward distortion at a doubly exponential rate in block length for any fixed rate greater than , the rate-distortion function. For tree codes a difference equation for the probability distribution of the distortion is derived with tree depth as an independent variable. Its numerical solution suggests that the same doubly exponential convergence behavior applies to tree codes.