A method of making a flush syringe assembly comprises providing a plurality of syringe barrels having a chamber with a conically-shaped distal wall and providing a plurality of stoppers having a conically-shaped distal surface. The method further includes selecting a stopper from the plurality of stoppers and a barrel from the plurality of barrels so that the total included angle of the distal wall of the selected barrel is greater than the total included angle of the selected stopper distal surface, and inserting the selected stopper into the chamber of the selected barrel.