Automatically detecting discourse segments is an important preliminary step towards full discourse parsing. Previous research on discourse segmentation have relied on the assumption that elementary discourse units (EDUs) in a document always form a linear sequence (i.e., they can never be nested). Unfortunately, this assumption turns out to be too strong, for some theories of discourse like SDRT allows for nested discourse units. In this paper, we present a simple approach to discourse segmentation that is able to produce nested EDUs. Our approach builds on standard multi-class classification techniques combined with a simple repairing heuristic that enforces global coherence. Our system was developed and evaluated on the first round of annotations provided by the French Annodis project (an ongoing effort to create a discourse bank for French). Cross-validated on only 47 documents (1,445 EDUs), our system achieves encouraging performance results with an F-score of 73% for finding EDUs.