A tire carcass is disclosed herein which includes a first radial ply with shoulder portions and lateral edge portions, each of the lateral edge portions being wrapped around a bead core, a carcass crown portion, the carcass crown portion having a first edge and a second edge, a non-continuous second radial ply, the second radial ply having a right side extending from approximately the first edge of the carcass crown portion, and extending approximately around the first bead core and a left side extending from approximately the second edge of the carcass crown portion, and extending approximately around the second bead core.