The invention improves tire flat spotting by providing a bead assembly that has bead filler elements disposed outside the body cords so that the turn up portion of the ply of body cords is disposed immediately back against the main portion of the ply of body cords above the bead core. This carcass structure increases the stiffness of the lower sidewall and decreases the flat spotting experience by the tire. In one embodiment of the invention, a reinforcing ply is wrapped around the bead filler elements to further increases the stiffness of the lower sidewall. In another embodiment, a bead filler element is disposed inside the body cords so that an air pocket is not formed in the carcass during the manufacturing process.