Species tree reconstruction from genome-wide data is increasingly being attempted, in most cases using a two-step approach of first estimating individual gene trees and then summarizing them to obtain a species tree. The accuracy of this approach, which promises to account for gene tree discordance, depends on the quality of the inferred gene trees. At the same time, phylogenomic and phylotranscriptomic analyses typically use involved bioinformatics pipelines for data preparation. Errors and shortcomings resulting from these preprocessing steps may impact the species tree analyses at the other end of the pipeline. In this article, we first show that the presence of fragmentary data for some species in a gene alignment, as often seen on real data, can result in substantial deterioration of gene trees, and as a result, the species tree. We then investigate a simple filtering strategy where individual fragmentary sequences are removed from individual genes but the rest of the gene is retained. Both in simulations and by reanalyzing a large insect phylotranscriptomic data set, we show the effectiveness of this simple filtering strategy.