Abstract. We present a new implication of Wu's (1997) Inversion Transduction Grammar (ITG) Hypothesis, on the problem of retrieving truly parallel sentence translations from large collections of highly non-parallel documents. Our approach leverages a strong language universal constraint posited by the ITG Hypothesis, that can serve as a strong inductive bias for various language learning problems, resulting in both efficiency and accuracy gains. The task we attack is highly practical since non-parallel multilingual data exists in far greater quantities than parallel corpora, but parallel sentences are a much more useful resource. Our aim here is to mine truly parallel sentences, as opposed to comparable sentence pairs or loose translations as in most previous work. The method we introduce exploits Bracketing ITGs to produce the first known results for this problem. Experiments show that it obtains large accuracy gains on this task compared to the expected performance of state-of-the-art models that were developed for the less stringent task of mining comparable sentence pairs.