The EM algorithm is the most important tool to obtain the maximum likelihood estimator in finite mixture models due to its stability and simplicity. However, its convergence rate is often slow because the conventional EM algorithm is based on a large missing data space. Several techniques have been proposed in the literature to reduce the missing data space. In this paper, we review existing methods and propose a new EM algorithm for Gaussian mixtures, which reduces the missing data space while preserving the stability of the conventional EM algorithm. The performance of the proposed method is evaluated with other existing methods via simulation studies.