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This paper describes a study of translation hypotheses that can be obtained by iterative, greedy oracle improvement from the best hypothesis of a state-of-the-art phrase-based Statistical Machine Translation system. The factors that we consider include the influence of the rewriting operations, target languages, and training data sizes. Analysis of our results provide new insights into some previously unanswered questions, which include the reachability of previously unreachable hypotheses via indirect translation (thanks to the introduction of a rewrite operation on the source text), and the potential translation performance of systems relying on pruned phrase tables.