A mounted assembly of the tubeless type for a bicycle, includes a rim and a tire having beads. The rim includes two wings attached to two seats which receive the tire beads. A tire reception zone is formed between the wings. The rim and/or the tire includes a stabilizing structure for stabilizing the air pressure at the level of the tire's outer surface, in zones which are neither in contact with the ground nor in contact with the rim, to a value of less than 2 bar. The stabilizing structure enables air to be conducted from the tire to atmosphere if a bead loses contact with its seat. The stabilizing structure can be in the form of holes in the wings and/or the seats, or in the form of channels or projections disposed on the wings. Alternatively, the stabilizing structure can be in the form of projections formed on the tire sidewall and arranged to contact the wings.