An improvement to an A-V dialysis graft construction that includes an elongated length of polymer tubing having an inlet end and an outlet end adapted to be attached to access needles. The improvement comprises a normally reduced diameter intermediate portion, providing a pressure drop from the inlet end of the length of polymer tubing to the outlet end for the purpose of improving flow to the extremity, not utilizing excess cardiac output and minimizing venous stenosis. A first embodiment comprises a gradual converging portion of the lumen followed by a gradual diverging portion. A second embodiment comprises an inflatable, annular stenosis balloon, providing a variable stenosis.
