  We extend the earlier suggested QCD-motivated model for the $Q^2$-dependence
of the generalized Gerasimov-Drell-Hearn (GDH) sum rule which assumes the
smooth dependence of the structure function $g_T$, while the sharp dependence
is due to the $g_2$ contribution and is described by the elastic part of the
Burkhardt-Cottingham sum rule. The model successfully predicts the low crossing
point for the proton GDH integral, but is at variance with the recent very
accurate JLAB data. We show that, at this level of accuracy, one should include
the previously neglected radiative and power QCD corrections, as boundary
values for the model. We stress that the GDH integral, when measured with such
a high accuracy achieved by the recent JLAB data, is very sensitive to QCD
power corrections. We estimate the value of these power corrections from the
JLAB data at $Q^2 \sim 1 {GeV}^2$. The inclusion of all QCD corrections leads
to a good description of proton, neutron and deuteron data at all $Q^2$.
