  A new strategy is presented for systematically treating super-leading
logarithmic contributions including higher-order Glauber exchanges for
non-global LHC observables in renormalization-group (RG) improved perturbation
theory. This represents an important improvement over previous approaches, as
it allows for the consistent inclusion of the scale dependence of the strong
coupling, thereby providing more reliable estimates of the scale uncertainties
in theoretical predictions. The key idea is to rearrange the relevant RG
evolution operator in such a way that all double-logarithmic corrections are
exponentiated from the outset. This forms the starting point for the first
resummation of super-leading logarithms at leading order in RG-improved
perturbation theory for arbitrary $2\to M$ scattering processes. Moreover, the
asymptotic scaling of subleading logarithmic corrections from higher-order
Glauber exchanges is determined, demonstrating their parametric suppression.
