Assembly of a rim and of a flexible adapter, intended to make up, with a tyre, a rolling assembly. The rim having a mounting well that is extended axially by a boss, a rim seat and a rim flange that extends the rim seat axially on the outside, with a bearing face of substantially radial orientation. The adapter having an axially inner end intended to rest on the rim seat, an axially outer end and a substantially cylindrical body that connects the axially inner end and the axially outer end and is intended to receive, in cooperation with the axially outer end, a tyre bead. The rim seat of the rim has an inclination relative to the axis of rotation of between −2 and +6 degrees, the angle being counted as positive when the virtual vertex of the substantially frustoconical seat is situated axially on the outside.