A method of matching a tire to a wheel rim of a wheel to compensate for wheel rim run-out and tire force variations includes the steps of mounting a bare wheel on a spindle of a balancer and measuring the rim run-out, said wheel rim having a bead seat, mounting a tire on the wheel to form a wheel/tire assembly, mounting the wheel/tire assembly on the spindle and measuring tire force variation, determining a desired change in wheel rim run-out to reduce the tire force variation, removing the tire from the wheel, adding a shim to the bead seat of the wheel rim, the shim being selected to correspond to the desired change in wheel rim run-out, and remounting the tire on the wheel. The wheel shim is preferably elongate and has a width sized to fit in the bead seat of the wheel rim, the thickness of the wheel shim being substantially less than the width of the wheel shim, and the length of the wheel shim being substantially greater than the width of the wheel shim. The wheel shim has a bottom surface adapted to be disposed in the bead seat and has a top surface adapted to be in contact with the bead of a tire to be mounted on the wheel.