The dc conductivity and the conductivity relaxation of ZrF4-BaF2-YF3-LiF glasses with varying BaF2 and LiF contents have been studied in the temperature range from 300 K to just below the glass transition temperature and in the frequency range 10 Hz-2 MHz. It has been observed that the conductivity shows a minimum and the activation energy a maximum at similar to 20 mol% LF content. The glass decoupling index also shows a minimum at the same composition and has been associated with the minimum of the conductivity. The small variation of the relaxation parameter beta for the low LiF content is consistent with the weak coupling model. The relaxation parameter beta exhibits a minimum at a composition different from that of the conductivity, resulting from the competitive influence of Ba2+ and Li+ cations on the ionic mobility.