A planning system for generating control data for a treatment device for eye surgery that creates at least two incision surfaces in the cornea using a laser apparatus is provided. The planning system includes a processor configured to specify the cornea incision surfaces based on data of a refractive correction, the cornea incision surfaces including an lenticule incision and a cap incision, at least one of the cap incision or the lenticule incision being irregularly shaped and having extensions to the surrounding tissue, and generate a control data record for the cornea incision surfaces for purposes of controlling the laser apparatus.