An ophthalmic implant for treating or alleviating the symptoms of glaucoma having a plate shaped to fit the surface of an eye. The plate has an inner ridge that defines a primary drainage region. Intraocular pressure is reduced by the transfer of aqueous fluid from the interior of the eyeball through a tube to the primary drainage region. To minimize post-operative hypotony, a secondary drainage region is provided on the plate outside the primary drainage region and defined either by the outer edge of the plate or an outer ridge having a lower profile than the inner ridge. When the pressure of fluid in the primary drainage region builds, fluid spills into the secondary drainage region. Fluid that is transferred to the plate is absorbed in surrounding tissues.
