Suturing of corneal incisions requires significant skill. We demonstrate a noncontact method that will simplify the bonding process. 5-mm-long penetrating vertical and slanted incisions were made in corneas of eyes, extracted from dead piglets. A fiber-optic laser system was used for laser soldering of the incisions, under close temperature control, using albumin solder. The burst-pressure P_B immediately after the soldering was found to be P_B  ≈  92 and 875 mmHg, for vertical and slanted incisions, respectively. P_B  =  875  mmHg is an exceptionally high figure, ≈10 times the clinically acceptable value for sutured incisions. Laser soldering was then performed on penetrating incisions made in the corneas of live healthy piglets, of weight ≈10  Kg. After a healing period, the eyes were extracted, and the corneas were examined by histopathology and by optical coherence tomography. Our method immediately generated watertight and strong bonding without noticeable corneal shape distortion. These results would be beneficial for cataract surgery and for corneal transplantations. The fiber-optic system makes it much easier to bond corneal incisions. In the future, laser soldering could be automated and efficiently used by less experienced surgeons, thereby reducing the workload on the experienced ones.