Methods and apparatus are disclosed for causing the optical center of the eye to align "HIGH point" of the anterior surface of the cornea. In accordance with one aspect of the invention relating to corneal ablation procedures, the HIGH point of the eye is used as the pole of a spherical surface which is fitted approximately to a portion of the anterior surface of the cornea within a "bounded region." For corneal ablation procedures, the "bounded region" comprises a generally inverted-cup shaped region of the anterior surface of the eye bounded at its periphery by a plane which is substantially perpendicular to a local z-axis. During the operation local high points which project above the spherical surface are ablated. According to another aspect of the invention relating to radial keratotomy procedures, a pair of incisions in the plane of a "great circle" are formed in the cornea to weaken and flatten it. As used herein, a "great circle" is formed by a plane containing the HIGH point and parallel to the local z-axis. The "bounded region" for radial keratotomy procedures is defined absolutely in terms of a circle projected onto the corneal surface which is centered about an axis passing through the HIGH point and parallel to the z-axis.