Weld simulation methods have often employed mathematical functions to describe the size and shape of the molten pool of material transiently present in a weld. However, while these functions can sometimes accurately capture the fusion boundary for certain welding parameters in certain materials, they do not necessarily oﬀer a robust methodology for the more intricate weld pool shapes that can be produced in materials with a very low thermal conductivity, such as the titanium alloy Ti-6Al-4V. Cross-sections of steady-state welds can be observed which contain a dramatic narrowing of the pool width at roughly half way in to the depth of the plate of material, and a signiﬁcant widening again at the base. These eﬀects on the weld pool are likely to do with beam focusing height. However, the resultant intricacy of the pool means that standard formulaic methods to capture the shape may prove relatively unsuccessful. Given how critical the accuracy of pool shape is in determining the mechanical response to the heating, an alternative method is presented. By entering weld pool width measurements for a series of depths in a Cartesian co-ordinate system using FE weld simulation software Sysweld, a more representative weld pool size and shape can be predicted, compared to the standard double ellipsoid method. Results have demonstrated that signiﬁcant variations in the mid-depth thermal proﬁle are observed between the two, even though the same values for top and bottom pool-widths are entered. Finally, once the beneﬁts of the Cartesian co-ordinate method are demonstrated, the robustness of this approach to predict a variety of weld pool shapes has been demonstrated upon a series of nine weld simulations, where the two key process parameters (welding laser power and travel speed) are explored over a design space ranging from 1.5 to 3 kW and 50 to 200 mm/s. Results suggest that for the faster travel speeds, the more detailed Cartesian co-ordinate method is better, whereas for slower welds, the traditional double ellipsoid function captures the fusion boundary as successfully as the Cartesian method, and in faster computation times.