  At the earliest epochs of structure formation in cold dark matter (CDM)
cosmologies, the smallest nonlinear objects are the numerous small halos that
condense with virial temperatures below 10,000 K. Such ``minihalos'' are not
yet resolved in large-scale three-dimensional cosmological simulations. Here we
employ a semi-analytic method, combined with three-dimensional simulations of
individual minihalos, to examine their importance during cosmological
reionization. We show that, depending on when reionization takes place, they
potentially play an important role as sinks of ionizing radiation. If
reionization occurs at sufficiently high redshifts (z_r > 20), the
intergalactic medium is heated to 10,000 K and most minihalos never form. On
the other hand, if z_r < 20, a significant fraction (>10 percent) of all
baryons have already collapsed into minihalos, and are subsequently removed
from the halos by photoevaporation as the ionizing background flux builds up.
We show that this process can require a significant budget of ionizing photons;
exceeding the production by a straightforward extrapolation back in time of
known quasar and galaxy populations by a factor of up to 10 and 3,
respectively.
