  We study the first sub-leading correction $O((\ln s)^0)$ to the cusp
anomalous dimension in the high spin expansion of finite twist operators in
${\cal N}=4$ SYM theory. Since this approximation is still governed by a linear
integral equation (derived already from the Bethe Ansatz equations in a
previous paper), we finalise it better in order to study the weak and strong
coupling regimes. In fact, we emphasise how easily the weak coupling expansion
can be obtained, confirms the known four loop result and predicts the higher
orders. Eventually, we pay particular attention to the strong coupling regime
showing agreement and predictions in comparison with string expansion;
speculations on the 'universal' part (upon subtracting the collinear anomalous
dimension) are brought forward.
