Speech recognition in which the log probabilities of the null and alternative hypothesis are computed for an input speech sample by comparison with specific stored speech vocabularies/grammars and with general speech characteristics. The difference in probabilities is normalized by the magnitude of the null hypothesis to derive a likelihood factor which is compared with a rejection threshold that is utterance-length dependent. Advantageously, a high-order polynomial representation of the rejection threshold length dependency may be simplified by a series of piece-wise constants which are stored as rejection thresholds to be selected in accordance with the length of the input speech sample.