  We study the reionisation of the Universe by stellar sources using a
numerical approach that combines fast 3D radiative transfer calculations with
high resolution hydrodynamical simulations. Ionising fluxes for the sources are
derived from intrinsic star formation rates computed in the underlying
hydrodynamical simulations. Our mass resolution limit for sources is M~ 4.0 x
10^7 h^-1 M_sol, which is roughly an order of magnitude smaller than in
previous studies of this kind. Our calculations reveal that the reionisation
process is sensitive to the inclusion of dim sources with masses below ~10^9
h^-1 M_sol. We present the results of our reionisation simulation assuming a
range of escape fractions for ionising photons and make statistical comparisons
with observational constraints on the neutral fraction of hydrogen at z~6
derived from the z=6.28 SDSS quasar of Becker and coworkers. Our best fitting
model has an escape fraction of ~20% and causes reionisation to occur by z~8,
although the IGM remains fairly opaque until z~6. In order to simultaneously
match the observations from the z=6.28 SDSS quasar and the optical depth
measurement from WMAP with the sources modeled here, we require an evolving
escape fraction that rises from f_esc=0.20 near z~6 to f_esc>~10 at z~18.
