Three remarkable anomalies related to the acoustic branches of quantum paraelectric (QPE) oxides are presented. In SrTiO 3, an additional shear-like sheet is observed for modes propagating in the tetragonal plane, and shear branches polarized parallel to the tetragonal axis show an anomalous softening on cooling in the QPE-regime. Both in SrTiO 3 and KTaO 3, a new doublet is observed in Brillouin scattering which is due to second sound, the wave-like propagation of heat. These effects are discussed in terms of large anharmonic polarization clusters.