Method for precision turning of a heat-treatable steel workpiece with a turning tool, comprising the steps of (a) precision turning the workpiece with a cutter of the turning tool and causing temporary heating of a part situated close to a surface of the workpiece and locally delimited close to an immediate vicinity of a cutter of the turning tool, (b) heating the surface locally, in a region directly behind a point of action of the cutter by a laser beam, (c) moving the laser beam together with the turning tool, (d) supplying the laser beam to the point of action via a glass fiber through a passage integrated in the turning tool, (e) dimensioning a power density at the point of action of the laser beam, which is directed onto the workpiece surface such that, taking into account a relative speed between the laser beam and the surface, material close to the surface is temporarily heated to a transformation temperature of the material to be machined, (f) self-quenching the material by cold volumes of the material which are situated more deeply in the workpiece with consequent hardening of the workpiece close to the surface;
- and (g) selecting a rotational speed of the workpiece during the precision turning so that a rotation time of the workpiece is shorter than a time for the self-quenching of workpiece parts which are heated to the transformation temperature.