This paper investigates the use of Gaussian Selection (GS) to reduce the state likelihood computation in HMM-based systems. These likelihood calculations contribute significantly (30 to 70%) to the computational load. Previously, it has been reported that when GS is used on large systems the recognition accuracy tends to degrade above a x3 reduction in likelihood computation. To explain this degradation, this paper investigates the trade-offs necessary between achieving good state likelihoods and low computation. In addition, the problem of unseen states in a cluster is examined. It is shown that further improvements are possible. For example, using a different assignment measure, with a constraint on the number of components per state per cluster, enabled the recognition accuracy on a 5k speaker-independent task to be maintained up to a x5 reduction in likelihood computation.