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This paper describes two effective algorithms that reduce the computational complexity of state likelihood computation in mixture-based Gaussian speech recognition systems. We consider a baseline recognition system that uses nearest-neighbor search and partial distance elimination (PDE) to compute state likelihoods. The first algorithm exploits the high dependence exhibited among subsequent feature vectors to predict the best scoring mixture for each state. The method, termed best mixture prediction (BMP), leads to further speed improvement in the PDE technique. The second technique, termed feature component reordering (FCR), takes advantage of the variable contribution levels made to the final distortion score for each dimension of the feature and mean space vectors. The combination of two techniques with PDE reduces the computational time for likelihood computation by 29.8% over baseline likelihood computation. The algorithms are shown to yield the same accuracy level without further memory requirements for the November 1992 ARPA Wall Street Journal (WSJ) task.