The increasing interest in the statistical approach to Machine Translation is due to the development of effective algorithms for training the probabilistic models proposed so far. However, one of the open problems with Statistical Machine Translation is the design of efficient algorithms for translating a given input string. For some interesting models, only (good) approximate solutions can be found. Recently a Dynamic Programming-like algorithm has been introduced which computes approximate solutions for some models. These solutions can be improved by using an iterative algorithm that refines the succesive solutions and uses a smoothing technique for some probabilistic distribution of the models based on an interpolation of different distributions. The technique resulting from this combination has been tested on the “Tourist Task ” corpus, which was generated in a semi-automated way. The best results achieved were a word-error rate of 9.3% and a sentence-error rate of 44.4%. 1.