Welding had traditionally faced two major challenges - obtaining a flawless bond (high internal weld quality) and obtaining a smooth surface transition (high external weld quality). While the former has been, and is being, well researched, the latter has received much less attention, despite the fact that post-weld surface finishing treatments such as machining and grinding can be costly or sometimes impossible. This paper presents an investigation of the production of welds with extremely high external weld quality - Net Shape Welds. A fibre laser was used to perform bead-on-plate welding of mild steel plates at a range of parameters. The quality of the welds was studied and the combinations of parameters that led to the transition to net shape welding were identified. The results show the significant factors controlling external weld quality and help identify a process window for producing net shape welds. The work can open the door to the use of fibre laser welding in many novel applications, such as precision welding technology, and complex welding, with potential benefit to a range of industries.