  We combine observational data on a dozen independent cosmic properties at
high-$z$ with the information on reionization drawn from the spectra of distant
luminous sources and the cosmic microwave background (CMB) to constrain the
interconnected evolution of galaxies and the intergalactic medium since the
dark ages. The only acceptable solutions are concentrated in two narrow sets.
In one of them reionization proceeds in two phases: a first one driven by
Population III stars, completed at $z\sim 10$, and after a short recombination
period a second one driven by normal galaxies, completed at $z\sim 6$. In the
other set both kinds of sources work in parallel until full reionization at
$z\sim 6$. The best solution with double reionization gives excellent fits to
all the observed cosmic histories, but the CMB optical depth is 3-$\sigma$
larger than the recent estimate from the Planck data. Alternatively, the best
solution with single reionization gives less good fits to the observed star
formation rate density and cold gas mass density histories, but the CMB optical
depth is consistent with that estimate. We make several predictions, testable
with future observations, that should discriminate between the two reionization
scenarios. As a byproduct our models provide a natural explanation to some
characteristic features of the cosmic properties at high-$z$, as well as to the
origin of globular clusters.
