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Finite mixture models are being increasingly used in statistical inference and to provide a model-based approach to cluster analysis. Mixture models can be fitted to independent data in a straightforward manner via the expectation-maximization (EM) algorithm. In this paper, we look at ways of speeding up the fitting of normal mixture models by using variants of the EM, including the so-called sparse and incremental versions. We also consider an incremental version based on imposing a multiresolution kd-tree structure on the data. Examples are given in which the EM algorithm can be speeded up by a factor of more than fifty for large data sets of small dimension.