For languages like Greek, where `affixal’ reflexives share their verbal morphology with passives, unaccusatives, middles, and experiencer verbs, a long-standing intuition holds that these reflexives are unaccusative. I provide novel evidence supporting this generalization, showing that the single overt argument in Greek reflexives is a) a deep object and b) the only argument in the structure. I argue that the morphosyntax of reflexives, their interpretive properties, and restrictions on reflexivization all follow from the fact that reflexivity is tied to the agent-introducing head Voice in Greek.