A new approach to the transient pulse compression by stimulated Brillouin scattering (SBS) is presented. The theoretical analysis involving the time-dependent SBS gain in explicit form leads to a nonlinear system of partial differential equations, solved numerically by a generalization of the split-step method. It is shown theoretically and confirmed experimentally that the phonon lifetime is not always an appropriate parameter that determines the lower limit to the pulse duration in SBS compressors. A half-cycle gain regime is found for pulses shorter than the phonon lifetime. Hence, under proper conditions, pulses as short as half the acoustic period can be produced.