Liquid supply system, comprising a soda machine adapted to carbonize water from a water supply to a predetermined CO2 concentration, the soda machine comprising: - a CO2 container containing CO2 at a CO2 container pressure, - a soda tank connected to the water supply and to the CO2 container, - a relief pipe with a controllable air relief valve adapted to release the pressure from the soda tank during the filling of the soda tank with water, - a CO2 release mechanism for releasing and injecting CO2 gas from the CO2 container directly into the soda tank through a nozzle located in the soda tank, and - a check valve installed in the line connecting the CO2 container and the soda tank and preventing CO2 gas from flowing back from the soda tank to the CO2 container, wherein the CO2 release mechanism furthermore comprises - a lever mechanism (264, 332) for opening the CO 2 container against the closing force of a container closing valve, and - an actuator with a movable actuator part adapted to move between an activated position and a non-activated position, - a spring coupled between the lever mechanism (264, 332) and the movable actuator part and biasing the movable actuator part toward the non-activated position, characterized in that the CO2 release mechanism furthermore comprises a gap reducing mechanism adapted to reduce a backlash between components of the CO2 release mechanism and the CO2 container due to accumulated engineering tolerances of these components and/or due to changes in the mounting position of the CO2 container when the CO2 container is exchanged, wherein the gap reducing mechanism furthermore comprising - at least one clamping element pivotably connected to the movable actuator part and being displaceable between a clamping position, in which said at least one clamping element is in clamping engagement with the lever mechanism (264, 332), and a release position, in which the lever mechanism (264, 332) may freely move relative to the movable actuator part, a movement of the movable actuator part from its activated position to its non-activated position displacing the at least one clamping element towards its release position. - a CO2 container containing CO2 at a CO2 container pressure, - a soda tank connected to the water supply and to the CO2 container, - a relief pipe with a controllable air relief valve adapted to release the pressure from the soda tank during the filling of the soda tank with water, - a CO2 release mechanism for releasing and injecting CO2 gas from the CO2 container directly into the soda tank through a nozzle located in the soda tank, and - a check valve installed in the line connecting the CO2 container and the soda tank and preventing CO2 gas from flowing back from the soda tank to the CO2 container, - a lever mechanism (264, 332) for opening the CO 2 container against the closing force of a container closing valve, and - an actuator with a movable actuator part adapted to move between an activated position and a non-activated position, - a spring coupled between the lever mechanism (264, 332) and the movable actuator part and biasing the movable actuator part toward the non-activated position, the CO2 release mechanism furthermore comprises a gap reducing mechanism adapted to reduce a backlash between components of the CO2 release mechanism and the CO2 container due to accumulated engineering tolerances of these components and/or due to changes in the mounting position of the CO2 container when the CO2 container is exchanged, wherein the gap reducing mechanism furthermore comprising - at least one clamping element pivotably connected to the movable actuator part and being displaceable between a clamping position, in which said at least one clamping element is in clamping engagement with the lever mechanism (264, 332), and a release position, in which the lever mechanism (264, 332) may freely move relative to the movable actuator part, a movement of the movable actuator part from its activated position to its non-activated position displacing the at least one clamping element towards its release position. - at least one clamping element pivotably connected to the movable actuator part and being displaceable between a clamping position, in which said at least one clamping element is in clamping engagement with the lever mechanism (264, 332), and a release position, in which the lever mechanism (264, 332) may freely move relative to the movable actuator part, a movement of the movable actuator part from its activated position to its non-activated position displacing the at least one clamping element towards its release position.