An improvement to an A–V dialysis graft construction (10) that includes an elongated length of polymer tubing (12) having an inlet end (13) and an outlet end (14) for attachment to access needles (15) (15) wherein, the improvement includes a normally reduced diameter intermediate portion (16) that restricts the flow of blood from the inlet end (13) of the length of polymer tubing (12) to the outlet end (14) for the purpose of minimizing venous stenosis.