Brillouin scattering showing an unusual low temperature softening of some transverse modes in SrTiO3 had been reported previously. The earlier data, complemented by newer Brillouin results, and supplemented by high quality hyper Raman data on the soft mode, demonstrate that this anomalous softening is to a large extent caused by a bilinear coupling of the strain with the gradient of the electrical polarization fluctuations. This coupling had been identified long ago in KTaO3, but at the large momentum exchanges that are achieved in neutron spectroscopy. To our knowledge, it is the first time that the signature of this coupling is observed in any material at the small wave vectors of optical Brillouin scattering. (C) 1999 Elsevier Science B.V, All rights reserved.