Composition vector trees (CVTrees) are inferred from whole-genome data by an alignment-free and parameter-free method. The agreement of these trees with the corresponding taxonomy provides an objective justification of the inferred phylogeny. In this work, we show the stability and self-consistency of CVTrees by performing bootstrap and jackknife re-sampling tests adapted to this alignment-free approach. Our ultimate goal is to advocate the viewpoint that time-consuming statistical re-sampling tests can be avoided at all in using this alignment-free approach. Agreement with taxonomy should be taken as a major criterion to estimate prokaryotic phylogenetic trees.