The earliest Eocene odonate genus Furagrion Petrulevičius et al. from the Danish Fur Formation is revised based on eighteen specimens, two of which apparently have been lost since their publication. The holotype of Phenacolestes jutlandicus Henriksen, type species of Furagrion, is incomplete and lacks the characters currently used to differentiate species, genera and higher taxa in Odonata. We, therefore, propose that the holotype is set aside and a recently discovered nearly complete Fur Formation fossil is designated as neotype. Furagrion possesses all of the nine wing character states currently used along with head shape for diagnosing the Dysagrionidae; however, Furagrion has a characteristically zygopteran head, not the distinctive head shape of the suborder Cephalozygoptera. We, therefore, treat it as a zygopteran unassigned to family. These nine wing character states appear in different combinations not only in various Zygoptera and Cephalozygoptera, but also in the Frenguelliidae, an Eocene family of Argentina that may represent an unnamed suborder. We recognise these taxa as constituting a dysagrionoid grade, in which these character states appear either convergently or as symplesiomorphies. Furagrion morsi Zessin is synonymized with Phenacolestes jutlandicus Henriksen, syn. nov. and Morsagrion Zessin with Furagrion Petrulevičius, Wappler, Wedmann, Rust, and Nel, syn. nov.