In laser welding, the weld bead is normally extended above or below the parent material surfaces due to melt flow and rapid solidification. This paper presents a study of achieving net shape (i.e. weld bead is flat to the parent material surfaces) butt welding of 1.5 mm mild steel sheets using a continuous wave single mode fibre laser (maximum 1 kW) at a range of laser powers, welding speeds and laser focal point positions. A series of experiments were performed using statistical design of experiment (DoE) techniques and analysis of variance (ANOVA) to identify significant variables and their interactions affecting the weld characteristics. The work shows that it is possible to obtain net shape welds on either the upper and lower surfaces of the material studied. There is an approximately linear relationship between upper surface weld bead offset from the surface and the welding speed. A welding speed of above 100 mm/sec is required for achieving net-shape butt welding at 500-550 W laser power.