The frequent exchange of genetic material among prokaryotes means that extracting a majority or plurality phylogenetic signal from many gene families, and the identification of gene families that are in significant conflict with the plurality signal is a frequent task in comparative genomics, and especially in phylogenomic analyses. Decomposition of gene trees into embedded quartets (unrooted trees each with four taxa) is a convenient and statistically powerful technique to address this challenging problem. This approach was shown to be useful in several studies of completely sequenced microbial genomes.