A cycle wheel having a U-shaped radial cross section, with two lateral sidewalls located on opposite sides of a median plane of the rim and each demarcated by an outer surface facing away from the median plane, on the one hand, and a bridge connecting the sidewalls and including an outer surface facing toward the axis of rotation of the wheel, on the other hand. At least one median zone of the outer surface of the bridge, which has a transverse width measured perpendicular to the median plane and greater than 4 mm, is machined over the entire circumference of the rim.