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We have presented in several papers the musical potentialities of a data structure called the Factor’s Oracle (FO) that we have experimented in many situations involving style modeling, musical memory and anticipation models, real-time improvized interaction and performance analysis. We recall briefly the construction and properties of this structure and how we use it in music pattern analysis and generation. Then we describe a new heuristic for navigating the FO in order to significantly ameliorate the musical quality of the output. This heuristic method leads us to a powerful formal structure, derived from the FO, called the Suffix Link Tree (SLT).