A fluid dispenser pump (10) including a pump body (11) and a piston (20) that slides in leaktight manner in the pump body (11) between a rest position and an actuated position. The piston (20) is secured to an actuator rod (30) that extends axially out from the pump body (11). A ferrule (40) is mounted on the top edge (12) of the pump body (11), the ferrule (40) defining the rest position of the piston (20). The ferrule (40) co-operates in leaktight manner with the actuator rod (30) while the actuator rod (30) moves between the rest position and an intermediate position, and the ferrule (40) co-operates in non-leaktight manner with the actuator rod (30) while the actuator rod (30) moving between the intermediate position and the actuated position, so as to make it possible to vent the pump (10).