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In this paper we propose a method of reducing the search space of a discourse parsing process, while keeping unaffected its capacity to generate cohesive and coherent tree structures. The parsing method uses Veins Theory (VT), by developing incrementally a forest of parallel discourse trees, evaluating them on cohesion and coherence criteria and keeping only the most promising structures to go on with at each step. The incremental development is constrained by two general principles, well known in discourse parsing: sequentiality of the terminal nodes and attachment restricted to the right frontier. A set of formulas rooted on VT helps to guess the most promising nodes of the right frontier where an attachment can be made, thus avoiding an exhaustive generation of the whole search space and in the same time maximizing the coherence of the discourse structures. We report good results of applying this approach, bringing in a significant improvement in the discourse parsing process