Gaussian Mixture Model (GMM) computation is known to be one of the most computation-intensive components of speech recognition. In our previous work, context-independent model based GMM selection (CIGMMS) was found to be an effective way to reduce the cost of GMM computation without significant loss in recognition accuracy. In this work, we propose three methods to further improve the performance of CIGMMS. Each method brings an additional 5-10 % relative speed improvement, with a cumulative improvement up to 37 % on some tasks. Detailed analysis and experimental results on three corpora are presented. 1.