We show that the observed luminosity function, radial distribution and velocity dispersion distribution of the very faint Milky Way satellites can be quantitatively well matched by predictions from cosmological simulations that are based on a canonical population of dark matter sub-halos, if the stellar content of these sub-halos is regulated by the suppression of gas cooling through photo-heating after re-ionization. While this approach to resolving the 'missing satellite' discrepancy has been well established qualitatively, recent developments have permitted a considerably more quantitative and rigorous treatment: the census of Milky Way satellite galaxies has recently been greatly expanded with discoveries of many new satellites, some nearly 100-times fainter than the previously known ones. They have all been characterized photometrically and stellar velocity dispersions exist for most. A recent quantification of SDSS's efficiency and limitations in finding these new objects has shown that for most of them the maximal volume in which they could have been found is much smaller than the 'virial volume' of the MW halo. Starting with a semi-analytic model for the population of dark matter sub-halos, we model their possible stellar content by applying previously published prescriptions about star-formation efficiencies before and after re-ionization and by presuming that star-formation seizes once the small halos become satellites. We then apply the known observational detection function to this set of mock Milky Way satellites and compare them to the observations. Within these detection limitations the observed luminosity distribution can also be well matched over $Delta$M_{V approx 10} for plausible choices of the star-formation suppression. The distribution of stellar velocity dispersions can be well matched too. This present approach appears to be the first successful attempt at modeling the apparent number discrepancy between expected sub-halos and satellite galaxies, with such quantitative detail and with a rigorous accounting of the observational selection effects.