In this paper we present a pruning algorithm and experimental results for our recently proposed Sparse Non-negative Matrix (SNM) family of language models (LMs). We show that when trained with only n-gram features SNMLM pruning based on a mutual information criterion yields the best known pruned model on the One Billion Word Language Model Benchmark, reducing perplexity with 18% and 57% over Katz and Kneser-Ney LMs, respectively. We also present a method for converting an SNMLM to ARPA back-off format which can be readily used in a single-pass decoder for Automatic Speech Recognition.