  We present a summary of recent constraints on the value of the fine-structure
constant at the epoch of decoupling from the recent observations made by the
Wilkinson Microwave Anisotropy Probe (WMAP) satellite. Within the set of models
considered, a variation of the value of $\alpha$ at decoupling with respect to
the present-day value is now bounded to be smaller than 2% (6%) at 95%
confidence level. We point out that the existence of an early reionization
epoch as suggested by the above measurements will, when more accurate cosmic
microwave background polarization data is available, lead to considerably
tighter constraints. We find that the tightest possible constraint on $\alpha$
is about $0.1 %$ using CMB data alone--tighter constraints will require further
(non-CMB) priors.
