A method of inserting and securing a corneal implant in engaging and fluid-flow limiting relation to the posterior cornea, such as to treat edema. The method includes securing a corneal implant in fluid flow limiting relation to the posterior cornea through an incision in the eye and securing it in place by a variety of steps such as corneal insertion or laser bonding, and preferably by inserting a removable corneal implant including a central region and a plurality of retention member(s) disposed on the periphery thereof into the eye so as to releaseably and removably engage a portion of the eye and thereby retain the corneal implant in abutting and engaging relation with the posterior cornea. The retention members of the corneal implant may also comprise haptic leg(s) extending from the central region and having a biasing configuration structured to be disposed in contacting relation with the iris and/or iridocorneal angle in biasing relation of the central region against the posterior cornea.