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 _ { b } h ^ { 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 _ { b } h ^ { 2 } = 0.024 , \Omega _ { m } h ^ { 2 } = 0.14 , H _ { 0 } = 49 and n = 1.02 . Compatible with 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 .