A high-resolution Brillouin scattering study of the soft acoustic mode of KH2PO4 in the hydrostatic-pressure range 0-4 kbar is presented. All spectra could be fitted closely by the usual mean-field coupled-mode model. From those fits, the pressure dependence of the ferroelectric-mode relaxation rate is derived. At pressures near and above the tricritical point, the transition can be approached so closely that the Brillouin spectrum becomes strongly overdamped and very narrow ( 50 MHz). Under those conditions, the elastic central peak of even the best available crystal becomes a dominant spectral feature, while the maximum dielectric constant is close to 106. © 1983 The American Physical Society.