Backward stimulated Brillouin scattering was used to control the growth of amplified spontaneous emission (ASE), reducing the unwanted emission in a pulse-amplified cw Ti:sapphire laser system from 22% to less than 1 x 10(-4) in the final output. Suppression of ASE substantially improved the spectral quality of the laser and broadened the range over which the laser is useful. The output duration was compressed, but the pulse remained nearly transform limited.