New high-resolution Brillouin scattering experiments are performed under hydrostatic pressures ranging from 0 to 10 GPa in vitreous silica. The hypersound-attenuation coefficient exhibits a sharp maximum located at 2 GPa, which appears to coincide with the well-known minimum in sound velocity. Two main processes contribute to sound damping: the thermal relaxation of local defects and the anharmonic interactions with thermal vibrations. By analyzing the temperature dependence of the velocity and subtracting the changes produced by the above mechanisms, the unrelaxed velocity is found. It is constant at low temperatures and increases anomalously above a temperature onset. We show that the onset strongly depends on pressure, which is in agreement with a dynamical origin of the structural changes that produce the hardening. Reference: S. Ayrinhac, B. Rufflé, M. Foret, H. Tran, S. Clément, R. Vialla, R. Vacher, J.-C. Chervin, P. Munsch, A. Polian, Phys. Rev. B 84, 024201 (2011)