For most people, human tool use is inextricably entwined with manual dexterity. This folk belief is widespread among scientists too. In this line, human tool use is based on motor programs about how the hand interacts with tools, implying that the use of end-effectors other than the hand should generate motor control difficulties (e.g., inability to reproduce a specific tool-use action over time), because these so-called programs characterize the spatiotemporal parameters of hand movements, but not of other end-effectors. To test this, we asked participants to perform three tool-use actions (e.g., pounding a nail) with four end-effectors (i.e., right foot, right elbow, left hand, right hand). We show that participants not only spontaneously performed the tool-use actions effectively, but also crucially kept tools' spatiotemporal parameters constant among the end-effectors. This phenomenon, which we call poly-dexterity, is at odds with the view that the human brain stores hand-centered motor programs for tool use. Poly-dexterity is instead consistent with the idea that, once the tool-use action is formed mentally, general motor programs can be applied to a variety of end-effectors. Reversing the usual evolutionary perspective, our findings support that, in the course of evolution, manual dexterity has come after tool-use skills.