The demands on laser cutting machine tools are increasing constantly. In this paper, we focus on increasing productivity while minimizing the deterioration of part quality. Without specific countermeasures, increasing the dynamic settings leads to larger dynamic-induced contour errors of the workpiece. Software-based methods offer potential to improve the contour tracking under varying dynamic settings without the need for a mechanical redesign of the machine tool. Four such methods, which rely on different combinations of model- and/or sensor-based setpoint compensation, are implemented and tested on a laser cutting machine tool. A comparison with respect to productivity and contour accuracy of cut parts is presented, and the complexity of development as well as deployment for production are discussed.