A method of resistance spot welding a steel workpiece and an aluminum or aluminum alloy workpiece together includes several steps. One step involves inserting a cover between the aluminum or aluminum alloy workpiece and an adjacent welding electrode. In another step, the adjacent welding electrode is pressed against cover, and another opposed welding electrode is pressed against the steel workpiece at a weld site. In yet another step, electrical current is passed between the welding electrodes, passed through the cover, and passed through the workpieces in order to initiate and grow a molten weld pool within the aluminum or aluminum alloy workpiece.