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The use of stimulated Brillouin scattering (SBS) for laser pulse compression by backward wave amplification in a tapered waveguide offers an attractive alternative to systems based on SRS for use with narrowband laser pulses. Almost one hundred percent conversion efficiencies may be achieved since it is not seriously limited by second Stokes production and with the added advantage that the Stokes pulse is a phase conjugate of the input pulse, under appropriate conditions. Due to the characteristically long damping times of Brillouin-active media, the SBS process is transient. In this regime, the tail of the Stokes pulse may experience a gain and loss modulation with the laser field resulting in a breakup of the Stokes pulse. This effect can be controlled by the geometric taper on the waveguide. A practical consideration of the scaling of a Brillouin compressor to high-power laser systems, notably KrF, is presented. Specific compressor configurations for the extraction of laser pulses in the nanosecond time scale are presented, and a survey of some promising compressor media indicate the practical possibility of accomplishing compression by SBS.