  We show that numerical simulations of reionization that resolve the Lyman
Limit systems (and, thus, correctly count absorptions of ionizing photons) have
converged to about 10% level for 5<z<6.2 and are in reasonable agreement
(within 10%) with the SDSS data in this redshift interval. The SDSS data thus
constraint the redshift of overlap of cosmic HII regions to z_{OVL} =
6.1+-0.15. At higher redshifts, the simulations are far from convergence on the
mean Gunn-Peterson optical depth, but achieve good convergence for the mean
neutral hydrogen fraction. The simulations that fit the SDSS data, however, do
not have nearly enough resolution to resolve the earliest episodes of star
formation, and are very far from converging on the precise value of the optical
depth to Thompson scattering - any value between 6 and 10% is possible,
depending on the convergence rate of the simulations and the fractional
contribution of PopIII stars. This is generally consistent with the third-year
WMAP results, but much higher resolution simulation are required to come up
with the sufficiently precise value for the Thompson optical depth that can be
statistically compared with the WMAP data.
