Improved acoustic modeling can significantly decrease the error rate in large-vocabulary speech recognition. Our approach to the problem is twofold. We first propose a scheme that optimizes the degree of mixture tying for a given amount of training data and computational resources. Experimental results on the Wall Street Journal (WSJ) Corpus show that this new form of output distribution achieves a 25% reduction in error rate over typical tiedmixture systems. We then show that an additional improvement can be achieved by modeling local time correlation with linear discriminant features.