A pneumatic radial ply tire (50) has a tread (52), a carcass (61) with two sidewalls (77, 78), a single radial ply (70) reinforced with inextensible metal cords, two annular beads (36a′, 36b′), and a belt structure (58) located radially between the tread and the radial ply structure (56). Each sidewall (77, 78) is reinforced with wedge inserts (59a, 59b) containing stiffener layers (72a, 72b, 73a, 73b) that carry the compressive loading to which the tire is subjected during runflat operation. The incorporation of wedge-insert stiffeners (72a, 72b, 73a, 73b) provides a light-weight runflat tire having a simplified construction.