An approach for supporting large vocabulary in speech recognition is to use broad phonetic classes to reduce the search to a subset of the dictionary. In this paper, we investigate the problem of defining an optimal classification for a given speech decoder, so that these broad phonetic classes are recognized as accurately as possible from the speech si gnal . More precisely, given Hidden Markov Models of phonemes, we define a similarity measure of the phonetic machines, and use a standard classification algorithm to find the optimal classification. Three measures are proposed, and compared with manual classifications.