  The redshift distribution of flat-spectrum radio sources with 5 GHz flux
densities S>5 mJy is a key component in using current radio lens surveys to
probe the cosmological model. We have constructed the first flat-spectrum radio
sample in the flux density range 3-20 mJy. Our new sample has 33 sources; we
have determined the redshifts of 14 of these (42% complete). The low mean
redshift, <z>~0.75, of our faintest sample needs to be confirmed by further
observations to improve the sample completeness. We also increased the redshift
completeness of several surveys of brighter flat-spectrum sources. While the
mean redshift, <z>~1.1 of flat-spectrum samples fainter than 1 Jy is nearly
constant, the fraction of the sources identifiable as quasars steadily drops
from ~80% to ~10% as the flux density of the sources decreases.
