We describe techniques for assessing evolutionary trees constructed by the parsimony criteria, when sequences exhibit irregular base compositions. In particular, we extend a recently described frequency-dependent significance test to handle any number of taxa and describe a modification of the Kishino–Hasegawa sites test. These modifications are useful for detecting historical signals beyond those patterns which arise purely from irregular base compositions between the compared sequences. We apply the test to extend our earlier studies on chloroplast origins using 16S rDNA sequences, where a failure to compensate for irregular base compositions between the compared sequences provides statistically significant support for unjustified phylogenetic inferences. We also describe how the techniques can be modified to determine how "tree-like" data are, given independent variation in the base frequencies.