The laser cutting system for cutting a workpiece with a laser beam along a cutting line at a variable cutting speed includes a movable machining head for placing the laser beam on the respective workpiece, a user interface for specifying the respective cutting line and for specifying a minimum path accuracy of the laser beam, and a control device for controlling a movement of the machining head along the cutting line relative to the respective workpiece and for controlling a plurality of process variables of a cutting process. A second subset of the process variables comprises exclusively one or more process variables which have no influence on the power of the laser beam available for cutting. At least one process variable of the second subset can be controlled by way of the control device as a function of at least one variable control parameter.