This study concerns the computation of a Beam-Search, large vocabulary, continuous speech recognizer based on subword Continuous Observation Density Hidden Markov Models. To find the computational bottle necks, we perform recognition experiments on the standard Darpa Resource Management (RM) speech data base, and we measure the computational requirements of the variuous algorithm components, as functions of the Beam-Search beamwidth. It appears that the computation of the Beam-Search recognizer is dominated by the state likelihoods, not only when the word lexicon is defined in terms of context-dependent phone models, but also, more surprisingly, in the case of context-independent phones. The reason of this finding is that the number of likelihood computations is rather insensitive to the beamwidth reduction. Then, we improve the system efficiency by a factor of 6 (without significantly affecting its accuracy) with a combination of techniques aimed at reducing both the likelihood computation and the search.