  A weighted difference of the $g$-factors of the H- and Li-like ions of the
same element is theoretically studied and optimized in order to maximize the
cancelation of nuclear effects between the two charge states. We show that this
weighted difference and its combination for two different elements can be used
to extract a value for the fine-structure constant from near-future
bound-electron $g$-factor experiments with an accuracy competitive with or
better than the present literature value.
