Recent papers have focused attention on a 62-million-year cycle in marine animal diversity over the Phanerozoic (the most recent 542 million years), leading some to propose extragalactic causes. These studies were based on the same or similar queries of Phanerozoic biodiversity from J. John Sepkoski's Compendium. Here we show, using two collections extracted from the larger and more extensively annotated Paleobiology Database, that the 62 Myr cycle in marine biodiversity is present but only weakly significant in each collection and is almost entirely the result of oscillations in the diversity of gastropods, bivalves, and articulate brachiopods (GBA). A 62 Myr cycle also appears in the diversity of genera from nearshore marine environments but not from genera from offshore environments. Another previously recognized 140 Myr cyclicity is persistent in most phylogenetic classes. We also find that the growth in marine diversity during the most recent 100 million years in the Paleobiology Database is no more than one-half that of the Sepkoski Compendium.