A corneal cover for placement on a patient's eye during eye surgery. A generally concave central arcuate portion has a first radius of curvature. A generally concave peripheral arcuate portion has a second radius of curvature larger than the first radius of curvature. One of a stem projecting from the peripheral arcuate portion, and a lip projecting from an outer periphery is provided to grasp the corneal cover, with a tool or manually, to place it on the eye and to remove it from the eye. The corneal cover has substantially no corrective power. The corneal cover is made of a hydrophobic material so it does not need to be irrigated during surgery.