A cylinder-piston unit, with at least one cylinder accommodating an injection solution and having an outlet opening, and with at least one piston. The cylinder, or a component mounted upstream of the cylinder, has an end face from which, during correct emptying of the cylinder-piston unit, a short cannula protrudes, which has an outlet opening at its free end. The outlet opening has a surface with a border which has a point near the bottom or an edge near the bottom. The point near the bottom or the edge near the bottom lies 0.15-0.3 mm away from the end face or the front-most point or edge thereof. A cylinder-piston unit is developed which is intended for a disposable injector and which is suitable for virtually painless penetration of the human skin, among other reasons for the administration of highly viscous injection solutions.