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This paper proposes a novel method for exploiting comparable documents to generate parallel data for machine translation. First, each source document is paired to each sentence of the corresponding target document; second, partial phrase alignments are computed within the paired texts; finally, fragment pairs across linked phrase-pairs are extracted. The algorithm has been tested on two recent challenging news translation tasks. Results show that mining for parallel fragments is more effective than mining for parallel sentences, and that comparable in-domain texts can be more valuable than parallel out-of-domain texts.