The introns-early view has been challenged for several genes; prominent instances are triose phosphate isomerase (TPI), aldolase, pyruvate kinase (PK), alcohol dehydrogenase (ADH), glyceraldehyde-3-phosphate dehydrogenase (GAPDH) and myosin heavy chain. While some of their introns appear to be phylogenetically ancient and/or to delineate exons corresponding to protein modules, a considerable number seemingly do not. But it is argued here that many of these anomalous introns are periodic, that is, relics of internal sequence repetitions within the ancestral gene. Some of these periodic-intron patterns are shared between related genes, as in the -barrels of TPI, aldolase and PK, or the Rossmann nucleotide-binding domain common to PK, ADH and GAPDH. This is further evidence for the ancestral status of these introns. The myosin heavy chain C-terminal rod region is paradoxical in that its sequence is clearly periodic but its intron placements are not; however, they exhibit a remarkable coherence of intron translational phases, suggesting that these introns may also have originally had a periodic arrangement now obscured by intron slipping.