A new stimulated Brillouin scattering (SBS) compression mechanism, quasi-steady-state SBS compression, in which the compression limit is one-tenth of the phonon lifetime with a high energy efficiency, is proposed and practically realized in this study. The feasibility of this approach is demonstrated experimentally, in which a compression of 0.36 tau(B) with an energy efficiency of 65% is achieved in a 3M Fluorinert Electronic Liquid FC-3283 and a compression output of 0.12 tau(B) (near-compression-limited) with an energy efficiency above 40% is obtained in acetone when the phonon lifetime to leading-edge to ratio is greater than 10. This ratio is identified experimentally as the key parameter in quasi-steady-state SBS compression. This work provides a practical approach to reliably generating one-tenth-phonon-lifetime pulses by quasi-steady-state SBS compression. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement