1. A method for training a speech recognizer in a speech recognition system, said method comprising the steps of: providing a data base containing a plurality of acoustic speech units; generating a homoscedastic hidden Markov model (HMM) from said plurality of acoustic speech units in said data base; said generating step comprises forming a set of pooled training data from said plurality of acoustic speech units and estimating a single global covariance matrix using said pooled training data set, said single global covariance matrix representing a tied covariance matrix for every Gaussian probability density function (PDF) for every state of every hidden Markov model structure in said homoscedastic hidden Markov model; and loading said homoscedastic hidden Markov model into the speech recognizer.