We are conducting a redshift survey of 177 flat-spectrum radio sources in 3 samples covering the 5 GHz flux ranges 50–100 , 100–200 and 200–250 mJy . So far , we have measured 124 redshifts with completenesses of 80 % , 68 % and 58 % for the bright , intermediate , and faint flux ranges . Using the newly determined redshift distribution we can derive cosmological limits from the statistics of the 6 gravitational lenses in the JVAS sample of 2500 flat-spectrum radio sources brighter than 200 mJy at 5 GHz . For flat cosmological models with a cosmological constant , the limit using only radio data is \Omega _ { 0 } > 0.27 at 2 - \sigma ( 0.47 < \Omega _ { 0 } < 1.38 at 1 - \sigma ) . The limits are statistically consistent with those for lensed quasars , and the combined radio + optical sample requires \Omega _ { 0 } > 0.38 at 2 - \sigma ( 0.64 < \Omega _ { 0 } < 1.66 at 1 - \sigma ) for our most conservative redshift completeness model and assuming that there are no quasar lenses produced by spiral galaxies . Our best fit model improves by approximately 1 - \sigma if extinction in the early-type galaxies makes the lensed quasars fainter by \Delta m = 0.58 \pm 0.45 mag , but we still find a limit of \Omega _ { 0 } > 0.26 at 2 - \sigma in flat cosmologies . The increasing fraction of radio galaxies as compared to quasars at fainter radio fluxes ( rising from \sim 10 % at 1 Jy to \sim 50 % at 0.1 Jy ) explains why lensed optical emission is common for radio lenses and partly explains the red color of radio-selected lenses .