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The summary of a phylogenetic analysis (typically a consensus tree) can be substantially biased by so-called rogue taxa (or briefly: rogues). Rogues assume varying phylogenetic positions in the tree collection that is used to build the consensus tree and thereby decrease the resolution of the consensus. We present an accurate and straight-forward algorithm for identifying rogues that assesses the effect on the consensus tree support values by removing one taxon at a time. Our approach improves the resolution of the consensus tree and, at the same time, increases the support values of existing relationships. We compare our algorithm to three competing methods (leaf stability index, taxonomic instability index, and Pattengale's algorithm) on a large number of real biological data sets. We show that it outperforms stability-based methods since rogue taxa are not necessarily the most unstable taxa with respect to stability measures. Our algorithm is more memory-efficient than Pattengale's approach while instances, where Pattengale's algorithm outperforms our approach, appear to be rare on real data. Finally, we find that, it is advisable to conduct a de novo bootstrap analysis after rogues have been removed from the sequence alignment.