An ophthalmological laser system and operating method wherein laser-supported operative interventions can be achieved with higher accuracy. The cornea is irradiated with an ophthalmological laser and a detection light confocally recorded, the cornea being scanned in three-dimensions by irradiation with an illuminating laser power using a scanner unit along several directions at several points. Using the simultaneously recorded detection light the position and/or shape of a posterior boundary surface of the cornea is determined. A lamella parallel to the posterior boundary surface can then be cut.