An intraocular implant for use in a surgical procedure such as a cataract operation, or in a refractive-lens exchange surgery procedure, has a main portion and a peripheral portion peripheral to the main portion. The main portion is plate-like in shape and may be a lens or a plug for closing an aperture in the capsule of the eye. The implant has two or more lugs extending from the peripheral portion in a direction substantially perpendicular to a plane of the main portion. The lugs extend either from haptics, which protrude from the main portion, or from a short extension of the edge of the main portion. A method for fixing the implant into the eye involves making two or more voids in the capsule wall, offering up the implant to the capsule, so that the lugs lie adjacent to the voids, and inserting the lugs into the voids.