A method of transplanting a cornea from a donor to a recipient is disclosed. An undercut is incised within stromal tissue of the donor cornea. Following formation of the undercut, the donor cornea is grafted onto a recipient. The undercut may be formed before or after the cornea is removed from the donor, and is preferably formed by photoaltering the stromal tissue using a laser. A sidecut may also be incised in the donor cornea, thereby forming a corneal flap, prior to grafting. In addition, a corneal section may be excised from the donor cornea using a trephine, a laser, or other appropriate surgical equipment.