A new approach to sub-phonon lifetime pulse compression by stimulated Brillouin scattering (SBS) is presented. Triangular and step pulse pumps are both used as a pump source in a single-cell SBS compression setup. Compared with a Gaussian pump (shortest compressed pulse is the phonon lifetime with the highest energy conversion, approximately 60% under the same conditions), the compression ratio is significantly improved in the case of triangular and step pulse pumps, and there is some improvement in the energy conversion when a step pulse pump is used. A pulse as short as a quarter of a phonon lifetime is produced by a triangular pulse pump, with an energy conversion above 30%. The pump pulse shape is identified as the key parameter in achieving sub-phonon lifetime pulse compression. By using a step pulse shape, a 4.5 ns pump pulses with a 60mJ at 1064-nm are compressed down to 292 ps (below semi-phonon-lifetime) in 3M Fluorinert Electronic Liquid FC-770 with an energy conversion above 65%. This work presents a route to reliable generation of sub-semi-phonon-lifetime pulses by SBS compression.