According to some accounts, an individual participates in joint intentional cooperative action by virtue of conceiving of him- or herself and other participants as if they were parts of a single agent or body that performs the action. I argue that this notional singularization move fails if they act as if they were parts of a single agent. It can succeed, however, if the participants act as if to bring about the goal of a properly functioning single body in action of which they would be parts. This latter version of the move manages to capture the cooperative character of joint intentional cooperative action. It does this without requiring of participants that they act on higher-order interlocking intentions.