  In this paper we generalize the results of arXiv:0806.4758 to non-zero value
J of angular momentum in S^5. We compute the 1-loop correction to the energy of
the folded spinning string in AdS_5 x S^5 in the particular limit of slow short
string approximation. In this limit the string is moving in a near-flat central
region of AdS_5 slowly rotating in both AdS_5 and S^5. The one-loop correction
should represent the first subleading correction to strong coupling expansion
of the anomalous dimension of short gauge theory operators of the form Tr D^S
Z^J in the SL(2) sector.
