Classical statistical language models, called n-gram models, describe natural language using the probabilistic relationship between a word to predict and the n-1 contiguous words preceding it. Obviously, the linguistic relationships present in a sentence are more complex. A first remark is that there exist distant relationships. We present here some recent work on an alternative model to n-gram models, based on the split of the history, dealing with the interpolation between distant bigram models. More precisely, our model is a cheaper alternative to high order n-grams. In conventional n-grams, when n is greater than 3, events are less frequent and statistics are not reliable. To deal with this problem, and to accurately estimate parameters, we combine a smoothed bigram with distant 3-bigram, distant 4-bigram and a cache composed of 100 words. We present new progresses obtained by using a simulated annealing algorithm in order to calculate the best parameters of this linear combination. With a 20K vocabulary and 40 million words for training, our algorithm improved the perplexity by 5.4% in comparison with the Baum-Welch algorithm. Moreover, this new model outperforms a smoothed bigram by 6.1% in terms of perplexity.