An apparatus is provided for draining aqueous humor from an eye for reducing intraocular pressure. The draining apparatus comprises a tube defining a passage for fluid flow between an inlet end and an outlet end. An outlet assembly contacts the conjunctival layer externally of the eyeball. The outlet assembly comprises a housing in fluid communication with the outlet end of the tube and having an aperture for allowing egress of aqueous humor onto the external ocular surface. A resistive component is disposed in the housing for providing resistance to a flow of aqueous humor. A pair of tabs project outwardly and are adapted to be disposed subconjunctivally for securing the draining apparatus relative to the eyeball.