  In this paper I show that simulations of reionization performed under the
Cosmic Reionization On Computers (CROC) project do converge in space and mass,
albeit rather slowly. A fully converged solution (for a given star formation
and feedback model) can be determined at a level of precision of about 20%, but
such a solution is useless in practice, since achieving it in production-grade
simulations would require a large set of runs at various mass and spatial
resolutions, and computational resources for such an undertaking are not yet
readily available.
  In order to make progress in the interim, I introduce a weak convergence
correction factor in the star formation recipe, which allows one to approximate
the fully converged solution with finite resolution simulations. The accuracy
of weakly converged simulations approaches a comparable, ~20% level of
precision for star formation histories of individual galactic halos and other
galactic properties that are directly related to star formation rates, like
stellar masses and metallicities. Yet other properties of model galaxies, for
example, their HI masses, are recovered in the weakly converged runs only
within a factor of two.
