The invention relates to the extrusion of tire components with a large change of gauge across their cross-sectional area. It is provided a method and an assembly for extruding such a tire component with an extruder feeding a flow channel with a downstream die opening, whereby a deflector is provided in the flow channel upstream the die opening such that a flow of rubber is slowed down in front of broad portions of the cross-sectional area of the downstream die, avoiding distortion or bending of the extruded tire component.