A fluid dispenser head for mounting on an actuator rod of a dispenser member that is displaceable down and up along an axis (X), the head including an axial connection sleeve for engaging on the actuator rod and defining an inlet duct, the head further including a dispenser endpiece defining an endpiece channel that is connected to the inlet duct via a connection channel, the endpiece including a free dispenser end defining a dispenser orifice that is situated at a downstream end of the endpiece channel, the head further including a bearing surface on which axial pressure can be exerted so as to drive in the actuator rod, where the endpiece extends substantially parallel to the axis (X), and is offset away from the axis.