  We consider extensions of the soft-gluon effective coupling that generalize
the Catani--Marchesini--Webber (CMW) coupling in the context of soft-gluon
resummation beyond the next-to-leading logarithmic accuracy. Starting from the
probability density of correlated soft emission in d dimensions we introduce a
class of soft couplings relevant for resummed QCD calculations of
hard-scattering observables. We show that at the conformal point, where the
d-dimensional QCD $\beta$ function vanishes, all these effective couplings are
equal and they are also equal to the cusp anomalous dimension. We present
explicit results in d dimensions for the soft-emission probability density and
the soft couplings at the second-order in the QCD coupling $\alpha_s$. In d=4
dimensions we obtain the explicit relation between the soft couplings at ${\cal
O}(\alpha_s^3).$ Finally, we study the structure of the soft coupling in the
large-$n_F$ limit and we present explicit expressions to all orders in
perturbation theory. We also check that, at the conformal point, our
large-$n_F$ results agree with the known result of the cusp anomalous
dimension.
