Surgical methods and related medical devices for treating glaucoma are shown. The method includes trabecular bypass surgery, which involves bypassing diseased trabecular meshwork with the use of a seton implant. The seton implant is used to prevent a healing process known as filling in, which has a tendency to close surgically created openings in the trabecular meshwork. The surgical method and novel implant are addressed to the trabecular meshwork, which is a major site of resistance to outflow in glaucoma. In addition to bypassing the diseased trabecular meshwork at the level of the trabecular meshwork, existing outflow pathways are also used or restored. The seton implant is positioned through the trabecular meshwork so that an inlet end of the seton implant is exposed to the anterior chamber of the eye and an outlet end is positioned into fluid collection channels at about an exterior surface of the trabecular meshwork or up to the level of aqueous veins.