  Spectroscopic observations of a sample of 42 flat-spectrum radio sources from
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 sample
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 distribution has
been studied. The spectra, obtained with the Willam Herschel Telescope (WHT),
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 exhibits
little variation over more than two orders of magnitude in radio flux density,
there is evidence for a decreasing fraction of quasars at weaker flux levels.
In this paper we present the results of our spectroscopic observations, and
discuss the implications for constraining cosmological parameters with
statistical analyses of the CLASS survey.
