A recently published study analyzed the phylogenetic relationship between the genera Centrodinium and Alexandrium, confirming an earlier publication showing the genus Alexandrium as paraphyletic. This most recent manuscript retained the genus Alexandrium, introduced a new genus Episemicolon, resurrected two genera, Gessnerium and Protogonyaulax, and stated that: “The polyphyly [sic] of Alexandrium is solved with the split into four genera”. However, these reintroduced taxa were not based on monophyletic groups. Therefore this work, if accepted, would result in replacing a single paraphyletic taxon with several non-monophyletic ones. The morphological data presented for genus characterization also do not convincingly support taxa delimitations. The combination of weak molecular phylogenetics and the lack of diagnostic traits (i.e., autapomorphies) render the applicability of the concept of limited use. The proposal to split the genus Alexandrium on the basis of our current knowledge is rejected herein. The aim here is not to present an alternative analysis and revision, but to maintain Alexandrium. A better constructed and more phylogenetically accurate revision can and should wait until more complete evidence becomes available and there is a strong reason to revise the genus Alexandrium. The reasons are explained in detail by a review of the available molecular and morphological data for species of the genera Alexandrium and Centrodinium. In addition, cyst morphology and chemotaxonomy are discussed, and the need for integrative taxonomy is highlighted.