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The problem of encoding a discrete memoryless source with respect to a single-letter fidelity criterion, using a block code of length and rate , is considered. The probability of error, , is defined to be the minimum probability, over all such codes, that the source will generate a sequence which cannot be encoded with distortion or less. For sufficiently large , that decreases doubly exponentially with blocklength, is shown. It is known that for some finite , denoted by . An upper bound to is also presented and numerically evaluated. The results derived hold independently of the source statistics. It is shown that a theorem of Omura and Shohara for symmetric sources is a special case of the results herein. Additionally, a useful characterization of for row-balanced distortion matrices is obtained.