A flexible vocabulary speech recognition system is provided for recognizing speech transmitted via the public switched telephone network. The flexible vocabulary recognition (FVR) system is a phoneme based system. The phonemes are modelled as hidden Markov models. The vocabulary is represented as concatenated phoneme models. The phoneme models are trained using Viterbi training enhanced by: substituting the covariance matrix of given phonemes by others, applying energy level thresholds and voiced, unvoiced, silence labelling constraints during Viterbi training. Specific vocabulary members, such as digits, are represented by allophone models. A* searching of the lexical network is facilitated by providing a reduced network which provides estimate scores used to evaluate the recognition path through the lexical network. Joint recognition and rejection of out-of-vocabulary words are provided by using both cepstrum and LSP parameter vectors.