Several unique intra-cardiac pressure vents, placement catheters, methods of placement and methods of treating heart failure are presented. The intra-cardiac pressure vents presented remain partially open under normal intra-cardiac pressures to allow sufficient flow from the left atrium to the right atrium to enable the relief of elevated left atrial pressure and resulting patient symptoms, and also limit the amount of flow from the right atrium to the left atrium by closing when the pressure in the right atrium exceeds the pressure in the left atrium by a predetermined amount.