The invention includes a rim for a cycle wheel, having a U-shaped radial cross section, with two lateral sidewalls and a bridge connecting the sidewalls and located so as to be opposite an axis rotation of the wheel. The sidewalls each define a planar braking surface, adapted to cooperate with a brake pad. The height of at least one braking surface, measured radially, is not constant over the circumference of the rim and has at least one variation in height.