Over the period of 1987-1991, a series of theoretical and experimental results have suggested that multilayer perceptrons (MLP) are an effective family of algorithms for the smooth estimate of highly-dimensioned probability density functions that are useful in continuous speech recognition. The early form of this work has focused on hidden Markov models (HMM) that are independent of phonetic context, and for these models the MLP approaches have consistently provided significant improvements (once we learned how to use them). More recently, we have extended the theory, to context-dependent models, and are beginning the corresponding experiments. In this paper, after having reviewed the basic principles of our hybrid HMM/MLP approach, we describe a series of improvements that are analogous to the system modifications instituted for the leading conventional HMM systems over the last few years. Some of these methods directly trade off computational complexity for reduced requirements of memory and memory bandwidth. Results are presented on the widely-used Resource Management speech database that has been distributed by the National Institute of Standards and Technology.