A method for welding two metal parts from aluminum alloys with the steps: melting of the metal parts to be joined in a weld region through an energy input by means of a laser beam with the formation of a weld seam, smoothing the surface of the weld seam through a further energy input with partial melting of the weld seam in the region of the surface, wherein the further energy input is a defocused laser beam, of which the focal point is positioned in the beam direction in front of or behind the surface of the weld seam, wherein the defocused laser beam and the surface normal of a surface of the two metal parts to which the laser beam is applied, incorporate an angle of greater than or equal to 5 degrees, and a connecting arrangement welded with this method.