Medlin tested multiple outgroups with 18S rRNA dataset and found that haptophytes, ciliates, prasinophytes and chlorophytes recovered monophyletic Coscinodiscophyceae, Mediophyceae, Bacillariophyceae with strong BT support. Theriot et al. added six plastid genes to the diatom dataset but with only one outgroup, Bolidomonas and omitted most of the V4 region of that gene and bases beyond position 1200; they recovered a grade of clades from radial into polar centrics, into araphid pennates into the monophyletic raphid pennates. Their structural gradation hypothesis (SGH) contrasts to the CMB hypothesis of Medlin and Kaczmarska. We selected only those species with all seven genes from their dataset and added the entire 18S RNA gene to make a new dataset to which we sequentially added heterokont, haptophyte, and prasinophyte/chlorophyte outgroups. We analysed it using 1) evolutionary models with parameters relaxed across genes and codon positions for coding sequences (codon partition analysis scheme = CP) and 2) no partitions or evolutionary models as applied to each gene, using only optimised models of evolution for the entire dataset (NCP). CP recovered a monophyletic mediophycean and bacillariophycean clade and three coscinodiscophycean clades. Sequentially adding more outgroups did not change clade topology but dramatically increased BT support. NCP recovered a monophyletic Coscinodiscophyceae and Bacillariophyceae and three Mediophyceae clades, each with strong bootstrap support. Morphological data was added and analyzed similarly. NCP recovered three monophyletic classes and CP recovered the Bacillariophyceae arising from within the Mediophyceae, making the subphylum monophyletic but the class was paraphyletic. Each analysis was tested with SH tests in PAUP and IQTree. Plastid inheritance in the diatoms is not homogenous and thus their phylogenies may not be homologous. If so, then our application of gene models may be overparametrising the data. The application of no partitioning models with morphological data supported the CMB hypothesis.