We present an algorithm for re-estimating parameters of backoff n-gram language models so as to preserve given marginal distributions, along the lines of well-known Kneser-Ney smoothing. Unlike Kneser-Ney, our approach is designed to be applied to any given smoothed backoff model, including models that have already been heavily pruned. As a result, the algorithm avoids issues observed when pruning Kneser-Ney models (Siivola et al., 2007; Chelba et al., 2010), while retaining the benefits of such marginal distribution constraints. We present experimental results for heavily pruned backoff n-gram models, and demonstrate perplexity and word error rate reductions when used with various baseline smoothing methods. An open-source version of the algorithm has been released as part of the OpenGrm ngram library.