We demonstrate the use of a deformable-mirror pulse shaper, combined with an evolutionary optimization algorithm, to correct high-order residual phase aberrations in a 1-mJ, 1-kHz, 15-fs laser amplif ier. Frequencyresolved optical gating measurements reveal that the output pulse duration of 15.2 fs is within our measurement error of the theoretical transform limit. This technique signif icantly reduces the pulse duration and the temporal prepulse energy of the pulse while increasing the peak intensity by 26%. It is demonstrated, for what is believed to be the f irst time, that the problem of pedestals in laser amplif iers can be addressed by spectral-domain correction. 2000 Optical Society of America OCIS codes: 140.7090, 140.3590, 320.5540, 320.5520.The past five years have seen considerable improvements in the capabilities of high-power ultrafast lasers. Ti : sapphire-based oscillator-amplifier systems can generate peak powers of ϳ100 TW at 10 Hz, or 0.3-1 TW at kilohertz repetition rates.