The search space of Phrase-Based Statistical Machine Translation (PBSMT) systems can be represented as a directed acyclic graph (lattice). By exploring this search space, it is possible to analyze and understand the failures of PBSMT systems. Indeed, useful diagnoses can be obtained by computing the so-called oracle hypotheses, which are hypotheses in the search space that have the highest quality score. For standard SMT metrics, this problem is, however, NP-hard and can only be solved approximately. In this work, we present two new methods for efficiently computing oracles on lattices: the first one is based on a linear approximation of the corpus bleu score and is solved using generic shortest distance algorithms; the second one relies on an Integer Linear Programming (ILP) formulation of the oracle decoding that incorporates count clipping constraints. It can either be solved directly using a standard ILP solver or using Lagrangian relaxation techniques. These new decoders are evaluated and compared with several alternatives from the literature for three language pairs, using lattices produced by two PBSMT systems.