A condensate pump includes a condensate reservoir, a liquid level float sensor operable to sense a liquid level within the condensate reservoir, and a pressure/vent valve including a pressure source, a pressure vent, and a primary piston slidably supported in a primary cylinder and sliding in the primary cylinder responsive to the liquid level sensor. A secondary piston is slidably supported in a secondary cylinder and moves responsive to a movement of the primary piston between a first secondary-piston position wherein the pressure source is in communication with a gas space of the condensate reservoir and the pressure vent is isolated from the gas space, and a second secondary-piston position wherein the pressure source is isolated from the gas space and the pressure vent is in communication with the gas space.