A criterion for pruning parameters from N-gram backoff language models is developed, based on the relative entropy between the original and the pruned model. It is shown that the relative entropy resulting from pruning a single N-gram can be computed exactly and efficiently for backoff models. The relative entropy measure can be expressed as a relative change in training set perplexity. This leads to a simple pruning criterion whereby all N-grams that change perplexity by less than a threshold are removed from the model. Experiments show that a production-quality Hub4 LM can be reduced to 26 % its original size without increasing recognition error. We also compare the approach to a heuristic pruning criterion by Seymore and Rosenfeld [9], and show that their approach can be interpreted as an approximation to the relative entropy criterion. Experimentally, both approaches select similar sets of N-grams (about 85% overlap), with the exact relative entropy criterion giving marginally better performance. 1.