In Colless' (1995,Syst. Biol. 44, 102-108) results, cladograms for randomly generated matrices were strongly asymmetrical, and he used this to maintain that real cladograms provide little evidence on asymmetry of phylogeny. His position, however, depended on retaining poorly supported groups as if they were well-supported. If poorly supported groups are removed, as with parsimony jackknifing, well-structured real data can still give strong asymmetry, while random matrices simply yield unresolved trees, obviating Colless' argument.