A pneumatic radial ply tire (86, 104) having a tread (106), a carcass (96, 108) with two sidewalls (88a, 88b, 116a, 116b), a radial ply structure (98, 110), and a belt structure (103, 117) located radially between the tread and the radial ply structure. Each sidewall is reinforced with at least one wedge insert (89a, 89b, 118a, 118b, 120a, 120b) which comprises alternating regions (90a, 90b, 122a, 122b) of flexible material and layers (91a, 91b, 124a, 124b) of stiffer material. The layer (91a, 91b, 124a, 124b) of stiffer material constrain the lateral expansion of the wedge insert (89a, 89b, 118a, 118b, 120a, 120b) during runflat operation to provide good riding comfort during normal inflation operation and good sidewall reinforcement during runflat operation.