Recent published experimental results obtained on deep penetration laser welding realized under reduced ambient pressure have shown very interesting results: resulting weld seams have geometrical characteristics that are similar to those obtained with electron beams. They show an increased penetration depth that can reach a factor two compared to atmospheric experiments, a larger aspect ratio with narrow and parallel sides of the weld seam. Also some humps around the rim of the keyhole appear. Of course, these modifications depend on the ambient pressure, but one also observes that these interesting improvements become independent of the ambient pressure below some critical pressure and also disappear at high welding speeds. Moreover, it is also observed that this critical pressure, below which these improvements do not vary, increases with the welding speed. In these previous publications, all these different characteristic results have not been explained. It is therefore the purpose of this paper to explain these different results. This has been obtained by using 3D numerical simulations of deep penetration laser welding and by studying the corresponding variation of physical parameters inside the keyhole (temperature, recoil pressure, and hydrodynamics of the vapor plume). An explanation for the evolution of these resulting weld seam geometries, as a function of the main operating parameters is proposed: ambient pressure, welding speed, and laser beam parameters (power and beam spot diameter). It is then possible to estimate this characteristic critical pressure, which is compared favorably with the corresponding previous experimental results. As a consequence, this analysis allows to define the optimum conditions for the improvement of the weld seam characteristics realized under reduced ambient pressure for an industrial environment.