Adapter for a rolling assembly having an axis of rotation comprising a tire having two beads, a rim with rim well (13) between two rim seats (12) each with an axially outer end, and width W between axially outer ends of these rim seats. The adapter, coupled between each bead and each rim seat, has two axially outer ends (2) each comprising seat (3) and bearing face (4) in a plane perpendicular to the axis of rotation. Body (5) connects outer axial ends (2) and comprises a main reinforcement, face (16) in contact with each seat (12) and with well (13) and positioned radially on the inside. The adapter has a total axial width L between each seat (3), and 60%≥W/L≥20%. Body (5) comprises immobilizing element (8) to wedge the adapter in the rim well (13).