A lighting or signaling device for emitting a lighting or signaling beam according to a main direction, of the type comprising a light source, a flux-recovering mirror comprising a set of reflecting tiles, the reflective surface of each reflecting tile being constituted by a first conical segment with two focal points, a first focal point of which is situated on the light source and a second focal point of which is situated, in relation to reflecting tile in a specific direction in relation to the main direction, each reflecting tile forming an image of the light source. A surface of at least one reflecting tile has at least one second conical segment with two focal points a first focal point of which is situated on the light source and a second focal point of which is situated at a distance from the second focal point of the first conical segment with two focal points.