In this talk I show results of cosmological simulations suggesting a
possible identification of at least some dwarf spheroidal galaxies in
the Local Group as the fossils of the first galaxies (``pre-reionization
fossils'').  I also revisit the problem of gas accretion onto
minihalos after reionization. I show that primordial minihalos with
$v_{cir}<20$~km~s$^{-1}$ stop accreting gas after reionization, as it is
usually assumed, but in virtue of their increasing concentration and
the decreasing temperature of the intergalactic medium as redshift
decreases, they may have a late phase (at redshift $z<2$) of gas
accretion and possibly star formation. As a result we expect that
pre-reionization fossils have a more complex star formation history
than previously envisioned. The dwarf spheroidal galaxy Leo~T fits
with this scenario. Another prediction of the model is the existence
of a population of gas rich minihalos that never formed stars. A
subset of compact high-velocity clouds may be identified as such
objects but the bulk of them may still be undiscovered.