  We study the spectrum of the reggeized gluon compound states in high-energy
QCD. The energy of the states depends on the total set of quantum numbers whose
values are constrained by the quantization conditions. To establish their
explicit form we apply the methods of nonlinear WKB analysis to the
Schr\"odinger equation for the $N$ reggeon state in the separated coordinates.
We solve the quantization conditions for the N=3 reggeon states in the leading
order of the WKB expansion and observe a good agreement of the obtained
spectrum of quantum numbers with available exact solutions.
