Phylogenetic inference artifacts can occur when sequence evolution deviates from assumptions made by the models used to analyze them. The combination of strong model assumption violations and highly heterogeneous lineage evolutionary rates can become problematic in phylogenetic inference, and lead to the well-described long branch attraction (LBA) artifact. Here, we define an objective criterion for assessing lineage evolutionary rate heterogeneity among predefined lineages: the result of a likelihood ratio test between a model in which the lineages evolve at the same rate (homogeneous model) and a model in which different lineage rates are allowed (heterogeneous model). We implement this criterion in the algorithm Lineage Specific Sequence Subsampling (LS(3)), aimed at reducing the effects of LBA in multi-gene datasets. For each gene, LS(3) sequentially removes the fastest-evolving taxon of the ingroup and tests for lineage rate homogeneity until all lineages have uniform evolutionary rates. The sequences excluded from the homogeneously evolving taxon subset are flagged as potentially problematic. The software provides the user with the possibility to remove the flagged sequences for generating a new concatenated alignment. We tested LS(3) with simulations and two real datasets containing LBA artifacts: a nucleotide dataset regarding the position of Glires within mammals and an amino-acid dataset concerning the position of nematodes within bilaterians. The initially incorrect phylogenies were corrected in all cases upon removing data flagged by LS(3).