  The problem of an efficiency increase of an FEL amplifier is now of great
practical importance. Technique of undulator tapering in the post-saturation
regime is used at the existing x-ray FELs LCLS and SACLA, and is planned for
use at the European XFEL, Swiss FEL, and PAL XFEL. There are also discussions
on the future of high peak and average power FELs for scientific and industrial
applications. In this paper we perform detailed analysis of the tapering
strategies for high power seeded FEL amplifiers. Application of similarity
techniques allows us to derive universal law of the undulator tapering.
