For butt joint welding of 8 mm and of 16 mm thick stainless steel a 15 kW fibre laser was applied, achieving full penetration for a welding speed of 7 m/min and 3 m/min, respectively. Optics with a focal length ranging from 500 mm to 150 mm focus the laser beam to a spot diameter of 0.65 to 0.2 mm with a focal depth of 18 to 4 mm and a cw-power density of 4 to 48 MW/cm2. Although narrow sound welds can be achieved, heavy spatter ejection along with underfill can take place at the top and root side, particularly for high power density and for low line energy. Various advanced analysis methods were developed. Spatter was observed by high speed imaging of the weld pool surface and of the keyhole. Quantitative evaluation of the drop size and flight trajectories enabled categorisation into four spatter modes, revealing favoured conditions for spatter suppression. Modelling subsequent to the drop evaluation provided additional analysis. An illustrative theoretical description and the formulation of a standard documentation methodology were developed. This aims to generalise and transfer knowledge as a guideline for spatter suppression in other laser welding situations.