The search space of Phrase-Based Statistical Machine Translation (PBSMT) systems can be represented under the form of a directed acyclic graph (lattice). The quality of this search space can thus be evaluated by computing the best achievable hypothesis in the lattice, the so-called oracle hypothesis. For common SMT metrics, this problem is however NP-hard and can only be solved using heuristics. In this work, we present two new methods for efficiently computing BLEU oracles on lattices: the first one is based on a linear approximation of the corpus BLEU score and is solved using the FST formalism; the second one relies on integer linear programming formulation and is solved directly and using the Lagrangian relaxation framework. These new decoders are positively evaluated and compared with several alternatives from the literature for three language pairs, using lattices produced by two PBSMT systems. 1