We fit the BOOMERANG, MAXIMA and COBE-DMR measurements of the cosmic microw
ave background anisotropy in spatially hat cosmological models where depart
ures from standard recombination of the primeval plasma are parametrized th
rough 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 pea
k in the measured spectrum can be accommodated either by a relatively large
baryon density, by a tilt towards the red in the spectrum of density fluct
uations, or by a delay in the time at which neutral hydrogen formed. The ra
tio between the second and first peak decreases by around 25% either if the
baryon density Omega (b)h(2) is increased or the spectral index n decrease
d 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 ar
e 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(*) =90
0, Omega (b)h(2)=0.024, Omega (m)h(2)=0.14, H-0=49 and n=1.02. Compatible w
ith present data at 95% confidence level 780<z(*)<1150, 0.018<Omega (b)h(2)
<0.036, 0.07<Omega (m)h(2)<0.3 and 0.9<n<1.2.