A multi-piece punctal plug has one a superficial plug removably connected to an anchor plug deeper in the naso-lacrimal canaliculus. The anchor is fixed to the wall of the lacrimal duct while the superficial plug is axially and detachably secured to the anchor plug so that the multi-plug complex may be inserted or removed together as one, or the superficial plug may be detached separately and replaced securely without disturbing the anchor. Removal and insertion is accomplished by a specific tool having an end for reversibly engaging the plugs.