Methods and apparatus for decreasing cardiac pressure in a patient by implanting a shunt communicating with an area outside a first portion, whereby a volume of blood sufficient to reduce pressure in a first portion is released. Preferably, the end diastolic pressure in the left ventricle is reduced, which is accomplished by having the shunt communicate with the left ventricle so a small volume of blood is released from the left ventricle. Most preferably, the shunt selectively permits flow when a pressure differential between the left ventricle and another chamber of a heart above a threshold pressure, so that shunting is prevented during left ventricular systole, or, alternatively, selectively permits flow when a pressure differential between the left ventricle and another chamber of a heart is between a lower threshold and a higher threshold. In certain embodiments a semi-passive check-valve is controlled and actuated by an external signal.