The present invention relates to a tire construction and method of correcting one or more tire uniformity characteristics. A tire has two beads and a carcass reinforcement ply having reinforcement cords. The method is characterized by the steps of A) forming a portion of the tire with a material (typically a thermoplastic), that can be rendered plastic (such as by heating) and rendered non-plastic (such as by cooling), which, in turn, respectively, permits and restricts reorientation of the reinforcement cords; B) rendering the material plastic, after the tire has been vulcanized, to permit one or more of the reinforcement cords to be reoriented; C) reorienting one or more reinforcement cords with respect to other rein-forcement cords or tire components; and D) rendering the material non-plastic, to restrict further reorientation of adjacent reinforcement cords. Reorientation of the cords can be achieved without stretching them beyond their elastic limit.