A device (10; 100) for laser cutting a workpiece and producing workpiece parts, having a cutting head, the cutting head having an interface for a laser source for generating a machining laser beam with a power of at least 200 W, preferably at least 1 kW, an exit aperture for the machining laser beam, and laser beam optics between the interface and the exit aperture, the laser beam optics having at least one dynamic laser beam movement unit for producing a high frequency beam-shaping movement of the machining laser beam at least perpendicular to its direction of propagation; having a cutting head movement unit for performing a movement of the machining laser beam over the workpiece via the cutting head; and a control unit for controlling the cutting head movement unit and the laser beam movement unit, the control unit comprising - a determination module for determining at least one movement trajectory (X, Y) of the machining laser beam in at least one workpiece plane according to at least one predetermined contour (X, Y) of the workpiece parts to be produced; and - a memory unit from which at least one predetermined parameter selected from a movement parameter of the cutting head movement unit, a movement parameter of the laser beam movement unit and a parameter of a deviation of a cut contour from the predetermined contour is retrievable; characterised in that the control unit comprises - an optimisation module for adjusting the movement trajectory (X, Y) by overlaying the movement of the machining laser beam via the cutting head with the high frequency beam-shaping movement of the machining laser beam via the laser beam movement unit based on the at least one predetermined parameter retrievable from the memory unit; wherein the optimisation module is configured for optimising the movement trajectory (X; Y) by redundantly partitioning the movement trajectory of the machining laser beam between the cutting head movement unit and the laser beam movement unit. the cutting head having an interface for a laser source for generating a machining laser beam with a power of at least 200 W, preferably at least 1 kW, an exit aperture for the machining laser beam, and laser beam optics between the interface and the exit aperture, the laser beam optics having at least one dynamic laser beam movement unit for producing a high frequency beam-shaping movement of the machining laser beam at least perpendicular to its direction of propagation; having a cutting head movement unit for performing a movement of the machining laser beam over the workpiece via the cutting head; and a control unit for controlling the cutting head movement unit and the laser beam movement unit, the control unit comprising - a determination module for determining at least one movement trajectory (X, Y) of the machining laser beam in at least one workpiece plane according to at least one predetermined contour (X, Y) of the workpiece parts to be produced; and - a memory unit from which at least one predetermined parameter selected from a movement parameter of the cutting head movement unit, a movement parameter of the laser beam movement unit and a parameter of a deviation of a cut contour from the predetermined contour is retrievable; - a determination module for determining at least one movement trajectory (X, Y) of the machining laser beam in at least one workpiece plane according to at least one predetermined contour (X, Y) of the workpiece parts to be produced; and - a memory unit from which at least one predetermined parameter selected from a movement parameter of the cutting head movement unit, a movement parameter of the laser beam movement unit and a parameter of a deviation of a cut contour from the predetermined contour is retrievable; characterised in that the control unit comprises - an optimisation module for adjusting the movement trajectory (X, Y) by overlaying the movement of the machining laser beam via the cutting head with the high frequency beam-shaping movement of the machining laser beam via the laser beam movement unit based on the at least one predetermined parameter retrievable from the memory unit; - an optimisation module for adjusting the movement trajectory (X, Y) by overlaying the movement of the machining laser beam via the cutting head with the high frequency beam-shaping movement of the machining laser beam via the laser beam movement unit based on the at least one predetermined parameter retrievable from the memory unit; wherein the optimisation module is configured for optimising the movement trajectory (X; Y) by redundantly partitioning the movement trajectory of the machining laser beam between the cutting head movement unit and the laser beam movement unit.