Phylogenomics seeks to use next-generation data to robustly infer an organism's evolutionary history. Yet, the practical caveats of phylogenomics motivate investigation of improved efficiency, particularly when quality of phylogenies are questionable. To achieve improvements, one goal is to maintain or enhance the quality of phylogenetic inference while severely reducing dataset size. We approach this by assessing which kinds of loci in phylogenomic alignments provide the majority of support for a phylogenetic inference of cockroaches in Blaberoidea. We examine locus substitution rate, saturation, evolutionary divergence, rate heterogeneity, stabilizing selection, and a priori information content as traits that may determine optimality. Our controlled experimental design is based on 265 loci for 102 blaberoidean taxa and 22 outgroup species. Loci with high substitution rate, low saturation, low sequence distance, low rate heterogeneity, and strong stabilizing selection derive more support for phylogenetic relationships. We found that some phylogenetic information content estimators may not be meaningful for assessing information content a priori. We use these findings to design concatenated datasets with an optimized subsample of 100 loci. The tree inferred from the optimized subsample alignment was largely identical to that inferred from all 265 loci but with less evidence of long branch attraction, improved statistical support, and potential 4-6x improvements to computation time. Supported by phylogenetic and morphological evidence, we erect three newly named clades (Anallactinae Evangelista & Wipfler subfam. nov., Orkrasomeria tax. nov. Evangelista, Wipfler, & Béthoux and Hemithyrsocerini Evangelista tribe nov.) and propose other taxonomic modifications. The diagnosis of Pseudophyllodromiidae Grandcolas, 1996 is modified to accommodate Anallactinae and Pseudophyllodromiinae Vickery & Kevan, 1983. The diagnosis of Ectobiidae Brunner von Wattenwyl, 1865 is modified to add novel morphological characters.