Methods and apparatus can fit coverings to treat eyes. The covering can be identified so as to provide improved flow of tear liquid under the covering. The covering can be identified based on an inner corneal curvature and an outer corneal curvature and one or more of a limbus sag height or a conjunctival sag height. The covering may form a chamber when placed on the eye to pump tear liquid under at least a portion of the covering. The covering may comprise an outer portion with rigidity to resist movement on the cornea and an inner portion to contact the cornea and provide an environment for epithelial regeneration. The covering may comprise a material having high oxygen permeability, for example silicone, with a wettable coating disposed on at least an upper surface of the coating.