Spectroscopic observations of a sample of 42 flat-spectrum radio sources fr
om the Cosmic Lens All-Sky Survey (CLASS) have yielded a mean redshift of (
z) = 1.27 with an rms spread of 0.95, at a completeness level of 64%. The s
ample consists of sources with a 5 GHz flux density of 25-50 mJy, making it
the faintest flat-spectrum radio sample for which the redshift distributio
n has been studied. The spectra, obtained with the William Herschel Telesco
pe, consist mainly of broad-line quasars at z > 1 and narrow-line galaxies
at z < 0.5. Though the mean redshift of flat-spectrum radio sources exhibit
s little variation over more than 2 orders of magnitude in radio flux densi
ty, there is evidence of a decreasing fraction of quasars at weaker flux le
vels. We present the results of our spectroscopic observations and discuss
the implications for constraining cosmological parameters with statistical
analyses of CLASS.