A motor vehicle tire is disclosed with a pair of post-cure run-flat inserts, each of the pair of post-cure run-flat inserts is disposed within a tire cavity between a shoulder region and a respective upper sidewall region of the tire. The tire further includes a cylindrical sidewall defining an interior cylindrical cavity, each of the cylindrical sidewall and the interior cylindrical cavity extending 360 degrees about a rotational axis of the tire, the cylindrical sidewall having an exterior surface contacting a radially inner surface of an inner liner between the shoulder region and the respective upper sidewall region during a normal inflation condition of the tire.