The theoretical fundamentals of laser weldability of metals are surveyed and relevant thermophysical parameters are identified – such as vapour pressure, keyhole pressure, beam irradiance, surface tension and viscosity. The derived approach for improving the laser weldability implies the use of a Yb fibre laser with an initial large beam diameter, a top-hat beam profile and a high laser power, which enables the formation of a large and stable keyhole during deep penetration welding. For validating the effectiveness of the developed approach, it is applied to various high-alloyed and hard-to-weld Al–Zn–Mg–Cu alloys. Defect-free welds are obtained even for AA7034 – the alloy with the highest (Zn+Mg+Cu) content commercially available. As reference, the same alloys are welded by using a conventional Nd:YAG laser with a small beam diameter, a Gaussian beam profile and medium laser power. The laser weldability deteriorates with increasing (Zn+Mg+Cu) content in terms of porosity and excess of penetration. The obtained results highlight the importance of the laser system used on the laser weldability of Al–Zn–Mg–Cu alloys.