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Minimum phone error (MPE) acoustic parameter estimation involves calculation of edit distances (errors) between correct and incorrect hypotheses. In the context of large-vocabulary continuous-speech recognition, this error calculation becomes prohibitively expensive and so errors are approximated. This paper introduces a novel error approximation technique. Analysis shows that this approximation yields a higher correlation to the Levenshtein error metric than a previously used approximation. Experimental evaluations on a large-vocabulary recognition task demonstrate that the novel approximation also delivers significant performance improvements over the previously used approximation when applied to MPE acoustic model estimation.