  We describe a new method to produce intensity stable, highly coherent,
narrow-band x-ray pulses in self-seeded free electron (FEL) lasers. The
approach uses an ultra-short electron beam to generate a single spike FEL pulse
with a wide coherent bandwidth. The self-seeding monochromator then notches out
a narrow spectral region of this pulse to be amplified by a long portion of
electron beam to full saturation. In contrast to typical self-seeding where
monochromatization of noisy SASE pulses leads to either large intensity
fluctuations or multiple frequencies, we show that this method produces a
stable, coherent FEL output pulse with statistical properties similar to a
fully coherent optical laser.
