A tire for the wheel of a cycle, such as a bicycle, as well as a wheel equipped with such a tire, the tire having a substantially toroidal geometry and including a mounting base adapted to be fixed to a rim that is wider than the tire, when inflated, a tread adapted to be in contact with the ground, and two sidewalls connecting the mounting base to the tread. The tire is provided, between each sidewall and the tread, with a spoiler for retaining a closed loop air circulation, whereby aerodynamic resistance is reduced.