Most inference methods in molecular phylogenetics assume that all lineages evolve at the same rate. This becomes unrealistic as dataset size and lineage rate heterogeneity increases, incurring in an assumption violation that can result in high statistical supports to incorrect relationships. I propose a method to minimize this violation on multi-gene phylogenies by (1) choosing on each gene outgroups that reinforce data artifacts the least, and (2) trimming on each gene taxa with highly different evolutionary rates until reaching lineage rate homogeneity. This was done on 10 genes (10516 bp) from 46 Siluriformes (Teleostei) taxa and 6 outgroups to assess disputed relationships among 3 supergroups within this order. Lineage rate homogeneity was reached on 7 of the 10 genes, and a concatenated analysis of these genes eliminated statistical support for a potential artifactual node that the untrimmed data supported fully. The resulting polytomy did not resolve the relationships among the taxa of my interest in Siluriformes. However, I confirm that high lineage rate heterogeneity can result in support to incorrect relationships, and propose a method to compensate for it.