  We quantify the detectability of stellar Milky Way satellites in the Sloan
Digital Sky Survey (SDSS) Data Release 5. We show that the effective search
volumes for the recently discovered SDSS--satellites depend strongly on their
luminosity, with their maximum distance, $D_{max}$, substantially smaller than
the Milky Way halo's virial radius. Calculating the maximum accessible volume,
$V_{max}$, for all faint detected satellites, allows the calculation of the
luminosity function for Milky Way satellite galaxies, accounting quantitatively
for their detectability. We find that the number density of satellite galaxies
continues to rise towards low luminosities, but may flatten at $M_V \sim -5$;
within the uncertainties, the luminosity function can be described by a single
power law $dN/dM_{V}= 10 \times 10^{0.1 (M_V+5)}$, spanning luminosities from
$M_V=-2$ all the way to the luminosity of the Large Magellanic Cloud. Comparing
these results to several semi-analytic galaxy formation models, we find that
their predictions differ significantly from the data: either the shape of the
luminosity function, or the surface brightness distributions of the models, do
not match.
