  We continue investigation of the spectrum of semiclassical quantum strings in
AdS5 x S5 on the examples of folded (S,J) string (with spin S in AdS5 and
orbital momentum J in S5) dual to an sl(2) sector state in gauge theory and its
(J',J) counterpart with spin J' in S5 dual to an su(2) sector state. We study
the limits of small spins and large J at weak and strong coupling, pointing out
that terms linear in spins provide a generalization of "protected" coefficients
in the energy that are given by finite polynomials in 't Hooft coupling
\lambda\ (or square of string tension) for any value of \lambda. We propose an
expression for the coefficient of the term linear in spin J' in the (J',J)
string energy which should be the su(2) sector counterpart of the "slope
function" in the sl(2) sector suggested by Basso in arXiv:1109.3154.
