  The recent observations of cross temperature-polarization power spectra of
the Cosmic Microwave Background (CMB) made by the WMAP satellite are in better
agreement with a high value of the Thomson scattering optical depth \tau
\approx 0.17. This value is close to \tau = 0.3, which is taken as the upper
limit in the parameter extraction analysis made by the WMAP team. However,
models with \tau \sim 0.3 provide a good fit to current CMB data and are not
significantly excluded when combined with Large Scale Structure data. By making
use of a self-consistent reionization model, we verify the astrophysical
feasibility of models with \tau \sim 0.3. It turns out that current data on
various observations related to the thermal and ionization history of the
intergalactic medium are not able to rule out \tau \sim 0.3. The possibility of
a very extended reionization epoch can significantly undermine the WMAP
constraints on crucial cosmological parameters such as the Hubble constant, the
spectral index of primordial fluctuations and the amplitude of dark matter
clustering.
