  We compute primordial light-element abundances for cases with fine structure
constant alpha different from the present value, including many sources of
alpha dependence neglected in previous calculations. Specifically, we consider
contributions arising from Coulomb barrier penetration, photon coupling to
nuclear currents, and the electromagnetic components of nuclear masses. We find
the primordial abundances to depend more weakly on alpha than previously
estimated, by up to a factor of 2 in the case of ^7Li. We discuss the
constraints on variations in alpha from the individual abundance measurements
and the uncertainties affecting these constraints. While the present best
measurements of primordial D/H, ^4He/H, and ^7Li/H may be reconciled pairwise
by adjusting alpha and the universal baryon density, no value of alpha allows
all three to be accommodated simultaneously without consideration of systematic
error. The combination of measured abundances with observations of acoustic
peaks in the cosmic microwave background favors no change in alpha within the
uncertainties.
