Best edge quality for thick metal plates is one of the current main challenges to create a unique selling proposition for laser cutting machines. Various approaches have been used to optimize the cutting performance of different materials. The reported results show in general that when a new material batch is loaded to the laser cutting machine, even of the same material type, diverse results are obtained. These differences have been attributed to fluctuations in the chemical composition of the used alloys. This letter analyses the influence of five different material compositions of Cr/Ni-steel (X5CrNi18-10/1.4301/SUS304/stainless steel) and compares achievable qualities and process windows using a solid state fusion cutting system. A larger process window is observed by increasing sulfur content of the material in this study.