  We describe statistical and coherence properties of the radiation from x-ray
free electron lasers (XFEL) operating in the post-saturation regime. We
consider practical case of the SASE3 FEL at the European XFEL. We perform
comparison of the main characteristics of the X-ray FEL operating in the
post-saturation regime with and without undulator tapering: efficiency,
coherence time and degree of transverse coherence.
