A corneal only is configured to adhere to the cornea so as to inhibit epithelial growth under the onlay. Structures can be provided on the onlay to adhere the onlay to the eye. At least one of an epithelial layer or the water inhibiting layer can be provided on or over the onlay, for example a natural epithelial layer or water inhibiting layer that inhibits, for example minimizes, water penetration into the onlay, so as to adhere the onlay to the eye with pumping of the endothelium. The water inhibiting layer may comprise a therapeutic covering positioned over the onlay to inhibit swelling of the cornea. The posterior surface of the onlay may be shaped so as to fit the anterior exposed surface of the cornea.
