Until recently, molecular phylogenies based on a single or few orthologous genes often yielded contradictory results. Using multiple genes in a large concatenation was proposed to end these incongruences. Here we show that single-gene phylogenies often produce incongruences, albeit ones lacking statistically significant support. By contrast, the use of different tree reconstruction methods on different partitions of the concatenated supergene leads to well-resolved, but real (i.e. statistically significant) incongruences. Gathering a large amount of data is not sufficient to produce reliable trees, given the current limitation of tree reconstruction methods, especially when the quality of data is poor. We propose that selecting only data that contain minimal nonphylogenetic signals takes full advantage of phylogenomics and markedly reduces incongruence.