A run-flat insert 200 for enabling a vehicle to run for limited duration on a deflated tire 20, is mounted in an assembly comprising a pneumatic tire 20 and a wheel rim 10, and said insert is mounted inside the tire and secured to the wheel rim. The insert 200 has improved characteristics in load carrying, vehicle handling, mass, and shock transmission. Such a run-flat insert 200 comprises an outer, reinforced annular band 220 that is coupled with a sidewall portion 230 having little resistance to compressive loads, and the sidewall portion 230 tell mates in a base member 240 fitted around the wheel rim 10 for securing the insert 200 to the rim 10.