  Improved measurement of the Cosmic Microwave Background polarization from
Planck allows a detailed study of reionization beyond the average optical
depth. The lower value of the optical depth disfavours an early onset and an
early completion of reionization in favour of a redsfhit range where different
astrophysical probes provide sensible information on the sources of
reionization and the status of the intergalactic medium. In this work we extend
our previous study in which we constrained reionization by combining three
different probes - CMB, UV luminosity density and neutral hydrogen fraction
data - in both treatment and data: we first allow variation in the UV source
term varying the product of the efficiency of conversion of UV luminosity into
ionizing photons and the escape fraction together with the reionization and
cosmological parameters, and then we investigate the impact of a less
conservative cut for the UV luminosity function. We find that the estimate for
the efficiency is consistent within 95% C.L. with the fixed value we considered
in our previous results and is mostly constrained by the QHII data. We find
that allowing the efficiency to vary does not affect significantly our results
for the average optical depth for monotonic reionization histories, recovering
$\tau=0.0519_{-0.0008}^{+0.0010}$ at 68% CL , consistent with our previous
studies. Using a less conservative cut for the UV luminosity function, we find
$\tau=0.0541_{-0.0016}^{+0.0013}$ at 68% CL, due to the faint end of the
luminosity function in the data we use, that also prefers a larger contribution
from higher redshifts.
