A pump head for a dosing device for dosed dispensing of a fluid, comprising a pump housing having a pressure chamber, an inlet valve delimiting the pressure chamber, a cone movably arranged in the pressure chamber of the pump housing and comprising a passageway, the cone being dimensioned in a region facing the inlet valve so that said cone can be guided in a form-fitting manner in the pressure chamber and being dimensioned smaller on average in the other regions, an outlet valve, via which the fluid is dispensed, the outlet valve being in fluid communication with the passageway of the cone, and a component which tapers the diameter of the pressure chamber in a region opposite the inlet valve and is designed to guide the cone, the pump head having at least one air inlet for guiding air, the air inlet comprising a passage for air between the cone and component and at least one passage opening for air in the pump housing, which are released when the cone is transferred into an outlet position in which the pump head dispenses fluid, characterized in that an insert is arranged between a fluidic outlet and the outlet valve, which insert has a sleeve comprising an inner cavity comprising the outlet valve, a passage opening (pin hole) leading through a wall of the sleeve, which passage opening opens into at least one fluid guide channel (E, F) arranged on the outer surface of the sleeve, wherein the at least one fluid guide channel is guided around the sleeve in an upper region thereof and is fed to an outlet end of the sleeve, and the at least one fluid guide channel is limited by a pump head upper part receiving the insert in a form-fitting manner. a pump housing having a pressure chamber, an inlet valve delimiting the pressure chamber, a cone movably arranged in the pressure chamber of the pump housing and comprising a passageway, the cone being dimensioned in a region facing the inlet valve so that said cone can be guided in a form-fitting manner in the pressure chamber and being dimensioned smaller on average in the other regions, an outlet valve, via which the fluid is dispensed, the outlet valve being in fluid communication with the passageway of the cone, and a component which tapers the diameter of the pressure chamber in a region opposite the inlet valve and is designed to guide the cone, the pump head having at least one air inlet for guiding air, the air inlet comprising a passage for air between the cone and component and at least one passage opening for air in the pump housing, which are released when the cone is transferred into an outlet position in which the pump head dispenses fluid, characterized in that an insert is arranged between a fluidic outlet and the outlet valve, which insert has a sleeve comprising an inner cavity comprising the outlet valve, a passage opening (pin hole) leading through a wall of the sleeve, which passage opening opens into at least one fluid guide channel (E, F) arranged on the outer surface of the sleeve, wherein the at least one fluid guide channel is guided around the sleeve in an upper region thereof and is fed to an outlet end of the sleeve, and the at least one fluid guide channel is limited by a pump head upper part receiving the insert in a form-fitting manner.