An integral rim intended for mounting a tire having at least two beads and including, when viewed in meridian section, at least a first rim seat, a second rim seat, and a rim base which is without a groove. The first rim seat slopes downwardly towards the outside. The second rim seat has a generatrix, the axially inner end of which is on a circle of diameter at least as great as the diameter of the circle on which the axially inner end of the first rim seat is located. The assembly formed by such a rim and a supporting ring for the thread.