Abstract: The relatively harsh "ride" of a non-pneumatic tire ("NPT") is greatly improved by a ring of elastomeric material referred to as a "ride-enhancing insert" ("RI"). The RI is pre-positioned on the outer surface of a wheel rim on which the NPT is to be molded of elastomeric material, most preferably a polyurethane, which is peculiarly well-suited to survive normal use on various vehicles, particularly as a replacement for a conventional spare tire, or "minispare" in an automobile. The RI is surprisingly tolerant of stress and heat loads generated by operation of the NPT/RI. The RI has a large effect on the spring rate of the NPT when deflected over a cleat, and a reduction in spring rate when deflected over a smooth laminar surface. This is of particular importance since the deflection over a cleat is where the improvement in ride is most noticeable.