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The usual approach to improve the interface between automatic speech recognition (ASR) and machine translation (MT) is to use ASR word lattices for translation. In comparison with the previous research along this line, this paper presents an efficient algorithm for lattice-based search in MT. This algorithm utilizes confusion network information to enable phrase-level reordering, and is also able to process general lattices. The proposed search is not constrained to be monotonic; thus, it is able to perform the same type of reordering given lattice input as any statistical phrase-based search algorithm with a single sentence input. Using the concept described in this paper, we are able to significantly improve speech translation results on several small and large vocabulary tasks. The improvements of the MT quality as measured by BLEU are as high as 5% relative. We also show that the proposed lattice-based translation can outperform state-of-the-art translation of confusion networks and has advantages in terms of translation speed. Furthermore, we propose and evaluate a novel approach that shares the benefits of lattice-based translation with those translation systems which are not designed to process word lattices.