A recent taxonomic revision of Procellariiformes by Penhallurick and Wink (2004) based on cytochrome b sequence data contains analytical and conceptual flaws that compromise the validity of the taxonomic recommendations. We identify two major shortcomings in the work. First, we question the practice of basing taxonomic recommendations on tree clades that receive no statistical support, and also highlight inconsistences in the tree-searching methods used. Second, we question Penhallurick and Wink’s claim to be following the multidimensional biological species concept, because they have put forward taxonomic proposals that violate this species concept (as well as the phylogenetic species concept). We discuss these analytical and conceptual shortcomings and make recommendations against the taxonomic rearrangements proposed by Penhallurick and Wink.