This invention relates to a premix burner for operating a heat generator. The burner at least has a swirl generator, a mixing section downstream of the swirl generator and a transition piece for transferring the swirl flow from the swirl generator into the mixing section. The invention further refers to a transition piece for such a premix burner. The transition piece (2) comprises an inlet, connected to the swirl generator (1), an outlet, connected to the mixing tube, and a continuing flow limiting interior contour (12) between said inlet and said outlet, wherein at least in an inlet section, said interior contour (12) is curved radially inwards towards the inner diameter of the mixing tube, and wherein at the outlet, the interior contour (12) is flush with an interior flow limiting contour of the mixing tube.