To tackle incongruence, the topological conflict between different gene trees, phylogenomic studies couple concatenation with practices such as rogue taxon removal or the use of slowly evolving genes. Phylogenomic analysis of 1,070 orthologues from 23 yeast genomes identified 1,070 distinct gene trees, which were all incongruent with the phylogeny inferred from concatenation. Incongruence severity increased for shorter internodes located deeper in the phylogeny. Notably, whereas most practices had little or negative impact on the yeast phylogeny, the use of genes or internodes with high average internode support significantly improved the robustness of inference. We obtained similar results in analyses of vertebrate and metazoan phylogenomic data sets. These results question the exclusive reliance on concatenation and associated practices, and argue that selecting genes with strong phylogenetic signals and demonstrating the absence of significant incongruence are essential for accurately reconstructing ancient divergences.