  We fit the BOOMERANG, MAXIMA and COBE/DMR measurements of the cosmic
microwave background anisotropy in spatially flat cosmological models where
departures from standard recombination of the primeval plasma are parametrized
through a change in the fine structure constant $\alpha$ compared to its
present value. In addition to $\alpha$ we vary the baryon and dark matter
densities, the spectral index of scalar fluctuations, and the Hubble constant.
Within the class of models considered, the lack of a prominent second acoustic
peak in the measured spectrum can be accomodated either by a relatively large
baryon density, by a tilt towards the red in the spectrum of density
fluctuations, or by a delay in the time at which neutral hydrogen formed. The
ratio between the second and first peak decreases by around 25% either if the
baryon density $\Omega_bh^2$ is increased or the spectral index $n$ decreased
by a comparable amount, or if neutral hydrogen formed at a redshift $z_*$ about
15% smaller than its standard value. We find that the present data is best
fitted by a delay in recombination, with a lower baryon density than the best
fit if recombination is standard. Our best fit model has $z_*= 900$,
$\Omega_bh^2=0.024$, $\Omega_mh^2=0.14$, $H_0=49$ and $n=1.02$. Compatible with
present data at 95% confidence level $780< z_*<1150$,
$0.018<\Omega_bh^2<0.036$, $0.07< \Omega_m h^2 < 0.3$ and $0.9<n<1.2$.
