We describe some new methods for constructing discrete acoustic phonetic hidden Markov models (HMMs) using tree quantizers having very large numbers (16–64 K) of leaf nodes and tree-structured smoothing techniques. We consider two criteria for constructing tree quantizers (minimum distortion and minimum entropy) and three types of smoothing (mixture smoothing, smoothing by adding 1 and Gaussian smoothing). We show that these methods are capable of achieving recognition accuracies which are generally comparable to those obtained with Gaussian mixture HMMs at a computational cost which is only marginally greater than that of conventional discrete HMMs. We present some evidence of superior performance in situations where the number of HMM distributions to be estimated is small compared with the amount of training data. We also show how our methods can accommodate feature vectors of much higher dimensionality than are traditionally used in speech recognition.