A pump for a fluid product having a pump body held in place by a valve holder fastened in the pump body; a piston sliding around a rod, provided with an inner axial channel axially closed on the lower side of the rod and communicating with the outside of the rod via a radial orifice, the piston having an outer sealing lip and an inner sealing lip; a gland having upwards an oblique or frustoconical surface of inclination appropriate to that of the inner sealing lip of the piston; an actuating spring between the rod and piston; and a return spring between the valve holder and the rod, urging the piston towards its rest position. The valve holder has an axial sleeve having an axial rib forming a mechanical stop in the actuating position between the lower axial end of the rod and the rib.