Fusion joining of stainless steel to copper without a filler material for pipe processing proves itself to be challenging due to the very different material properties of the joining partners and very heterogeneous characteristics in the weld metal due to different mixing ratios. One of the most common weld defects in this material combination is solidification cracking in the weld metal due to liquid copper accumulation between the stainless steel grain boundaries, which cannot withstand the tensile tensions while cooling down. Consequently, these cracks can reduce the mechanical properties, lead to leakages or cause faster corrosion. To prevent cracking, a precise control of the melting and mixing ratio of stainless steel and copper is needed. Laser beam welding offers many capabilities to influence the resulting weld metal shape and size as well as the mixing ratios with different approaches such as parameter optimization, inline process control, or the use of different beam shapes. This work shows different weld configurations and applications using sheets with thicknesses in the area of 1 mm and pipe samples. The main focus is on different solutions to influence the copper dilution and the weld metal geometry for solidification crack prevention. Therefore, a design of experiment approach and inline weld depth control using optical coherence tomography (OCT) data is used for the lap weld configuration to limit the copper dilution below 10 wt. \% in steel dominated weld metals. Moreover, the benefits of adjustable intensity profiles for the butt weld configuration to control the shape and dimensions of the weld metal and mixing behavior with different power distributions in the laser beam welding spot are shown. The overall results indicate that solidification cracking in steel-copper joints can be influenced by different process approaches.