A shaft-mounted overhead door operator is disclosed having a motor, a torque transfer component such as a gear train, and a clutch that is axially movable to engage or disengage the clutch. While the door operator has power, the clutch is engaged to ensure door operator can raise, lower, and stop the overhead door as directed from a remote control. The clutch can be released in the event of a loss of power or by direction from the remote control in which case the clutch releases the shaft of the overhead door. The shaft-mounted overhead door is small, having a width no greater than three times the diameter of the shaft to which it is mounted.