A method of operating a dosing device. A dosing valve is provided with low-pressure and high-pressure chambers delimited by a piston whose travel is limited to a predefined maximum stroke. A pump operates to deliver the liquid at pre-delivery pressure. The dosing valve actuates under direction of a control unit by opening a 2/2 directional valve to direct the pumped liquid into the low-pressure chamber, and in response, the piston initiates a stroke. The liquid is injected from the high-pressure chamber into the exhaust-gas stream during the stroke of the piston, and the injection stops when the piston reaches maximum stroke. The control unit holds the directional valve open for longer than the piston requires to perform its maximum stroke so that the dosing valve delivers a predetermined volumetric dose of the liquid into the exhaust-gas stream, the predetermined volumetric dose corresponding directly to the maximum stroke of the piston.