Disclosed are high stability ink delivery system systems and methods for their use, in which a secondary reservoir is placed upstream of a printhead. The secondary reservoir can be opened to the atmosphere through a valve, such as based on the reading of a pressure sensor placed at a point before the printhead. The purpose of this valve is to open the secondary reservoir to the atmosphere when the pressure sensor indicates that the secondary reservoir can be open while avoiding air aspiration, and closing it when this condition is not satisfied.