Ultrasonic velocity and attenuation data are presented at T < 1 K for pure KTaO3 and for KTaO3:X where X = Na and Li. Evidence is obtained for coherent tunnelling of Na ions within a correlation volume containing many impurities through barriers with distributed height and asymmetry parameters. Tunnelling is correlated with dipole-glass formation. No evidence of tunnelling is found in KTaO3 and KTaO3:Li. © 1989 IOP Publication Ltd.