We perform a likelihood analysis of the recently released BOOMERanG and MAXIMA data, allowing for the possibility of a time-varying fine-structure constant. We find that in general these data prefer a value of \ensuremath{\alpha} that was smaller in the past (which is in agreement with measurements of \ensuremath{\alpha} from quasar observations). However, there are some interesting degeneracies in the problem which imply that strong statements about \ensuremath{\alpha} cannot be made using this method until independent accurate determinations of ${\ensuremath{\Omega}}_{b}{h}^{2}$ and ${H}_{0}$ are available. We also show that a preferred lower value of $\ensuremath{\alpha}$ comes mainly from the data points around the first Doppler peak, whereas the main effect of the high-$l$ data points is to increase the preferred value for ${\ensuremath{\Omega}}_{b}{h}^{2}$ (while also tightening the constraints on ${\ensuremath{\Omega}}_{0}$ and ${H}_{0}).$ We comment on some implications of our results.
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