We present a new phrase-based conditional exponential family translation model for statistical machine translation. The model operates on a feature representation in which sentence level translations are represented by enumerating all the known phrase level translations that occur inside them. This makes the model a good match with the commonly used phrase extraction heuristics. The model's predictions are properly normalized probabilities. In addition, the model automatically takes into account information provided by phrase overlaps, and does not suffer from reference translation reachability problems. We have implemented an open source translation system Sinuhe based on the proposed translation model. Our experiments on Europarl and GigaFrEn corpora demonstrate that finding the unique MAP parameters for the model on large scale data is feasible with simple stochastic gradient methods. Sinuhe is fast and memory efficient, and the BLEU scores obtained by it are only slightly inf...