A recent trend in automatic speech recognition systems is the use of continuous mixture-density hidden Markov models (HMMs). Despite the good recognition performance that these systems achieve on average in large vocabulary applications, there is a large variability in performance across speakers. Performance degrades dramatically when the user is radically different from the training population. A popular technique that can improve the performance and robustness of a speech recognition system is adapting speech models to the speaker, and more generally to the channel and the task. In continuous mixture-density HMMs the number of component densities is typically very large, and it may not be feasible to acquire a sufficient amount of adaptation data for robust maximum-likelihood estimates. To solve this problem, we propose a constrained estimation technique for Gaussian mixture densities. The algorithm is evaluated on the large-vocabulary Wall Street Journal corpus for both ...