A self adjusting venous equalizing graft (SAVE graft) which provides a self regulating stenosis is provided herein. The SAVE graft responds to increases or decreases in blood pressure which allows a higher pressure at the graft's arterial end and a lower pressure at the graft's venous end. This is ideal in that it mimics the natural pressure of a patient's circulatory system. A dialysis machine may draw blood at the arterial end, dialyze the blood, and return the blood to the patient at the graft's venous end. The lower pressure at the venous end prevents damage to the patient's vein. The SAVE graft may comprise a deformable stenosis control diaphragm or a venous controlled pressure nozzle which may expand or contract in response to blood pressure to self regulate the stenosis provided by the SAVE graft.