A pneumatic radial ply tire (50) having a tread (52), a carcass (60) with two sidewalls (77, 78), one or more radial plies (70, 72), two annular beads (36a′, 36b′), a belt structure (56) located radially between the tread and the radial ply structure (58), a fabric underlay (54), deployed radially inward of the belt structure, and a tread insert (66) deployed between the belt structure and the fabric underlay. Said underlay (66) contains circumferentially aligned high-modulus fibers or cords (88) which, in combination with metal belt structure (56) and the tread insert (66), contribute to circumferential tread rigidity. Insert (66), in conjunction with the belt structure (56) and the radial ply structure (58), contributes to lateral tread rigidity. The circumferential and lateral stiffening of the tread (52) enhances high-speed runflat handling and contributes to improved runflat operational life.