The innermost carcass ply of a runflat tire (50) having a radial carcass ply is a discontinuous ply (52) that includes two portions (52a, 52b) each disposed within one of the sidewalls (43, 45). In one embodiment, each of the two discontinuous ply portions is composed of two layers (64, 66) of cross-biased cords (65, 67) which are disposed between the two wedge inserts (58b, 59b) in each sidewall. In another embodiment, the two portions (72a, 72b) of the discontinuous ply (72) are composed of wavy metal cords. In a third embodiment, a runflat tire incorporating either embodiment of the discontinuous ply (92a, 92b) is built using the locked, tie-in construction for the carcass ply.