Fabric treatment layers (130a, 130b, 132a, 132b) are deployed in the sidewall regions of a runflat tire (100) having a metal-reinforced first ply (120). In one embodiment, parallel cord, reinforced fabric treatment layers (130a, 130b, 132a 132b) sandwich the metal forced first ply (120) and inhibit buckling of the reinforcing cords (70) of the first ply during runflat operation when the ply cords or wires are bearing compression loads. In another embodiment, a single woven fabric treatment layer (170a, 170b) is disposed in each sidewall region (152,154) at a location immediately axially inward of the metal-reinforced first ply (160).