A method for assembling a wheel rim and a wheel disc together to produce a vehicle wheel includes the steps of: (a) providing a rim defining an axis and including an inboard tire bead seat retaining flange, an inboard tire bead seat, a well portion, an outboard tire bead seat, and an outboard tire bead seat retaining flange, the inboard tire bead seat retaining flange including a radially extending first inner surface, the well portion including a radially extending second inner surface, the outboard tire bead seat retaining flange including a radially extending third inner surface; (b) providing a disc having a centrally located inner wheel mounting portion and an outer annular portion which terminates in an axially extending outer annular flange, the inner wheel mounting portion including an inboard mounting surface and an outboard mounting surface, the outer annular portion including an inner surface; (c) supporting the rim at the first inner and at least one of the second inner surface and the third inner surface; (d) supporting the disc at the inboard mounting surface and the outboard mounting surface; (e) selectively moving at least one of the rim and the disc toward one another to cause the outer annular flange of the disc to engage an inner surface of the rim in a press fit engagement therewith while supporting the rim and the disc as recited in steps (c) and (d), the rim and disc being selectively moved to produce a desired lateral runout dimension defined between the inboard mounting surface of the disc and the first inner surface of the inboard tire bead seat retaining flange of the rim; and (f) subsequent to step (e), welding the disc to the rim to thereby permanently join the rim and the disc together and produce the vehicle wheel.