  Using information from the marginality conditions of vertex operators for the
AdS_5 x S^5 superstring, we determine the structure of the dependence of the
energy of quantum string states on their conserved charges and the string
tension proportional to lambda^(1/2). We consider states on the leading Regge
trajectory in the flat space limit which carry one or two (equal) spins in
AdS_5 or S^5 and an orbital momentum in S^5, with Konishi multiplet states
being particular cases. We argue that the coefficients in the energy may be
found by using a semiclassical expansion. By analyzing the examples of folded
spinning strings in AdS_5 and S^5 as well as three cases of circular two-spin
strings we demonstrate the universality of transcendental (zeta-function) parts
of few leading coefficients. We also show the consistency with target space
supersymmetry with different states belonging to the same multiplet having the
same non-trivial part of the energy. We suggest, in particular, that a rational
coefficient (found by Basso for the folded string using Bethe Ansatz
considerations and which, in general, is yet to be determined by a direct
two-loop string calculation) should, in fact, be universal.
