A method for more effectively concentrating blood platelets for use in medical procedures includes providing preparation and concentrating tubes. Anticoagulated whole blood is added to the preparation tube, which is centrifuged to separate red blood cells from a platelet plasma suspension The platelet plasma suspension is aspirated and loaded into the concentrating tube, which is itself centrifuged to separate the platelet plasma suspension into platelet poor plasma and platelet rich plasma layers. The platelet poor plasma is aspirated through a port of the concentrating tube and the remaining concentrated PRP is aspirated through the same or a different port of the concentrating tube.