  We consider power-behaved contributions to hard processes in QCD arising from
non-perturbative effects at low scales which can be described by introducing
the notion of an infrared-finite effective coupling. Our method is based on a
dispersive treatment which embodies running coupling effects in all orders. The
resulting power behaviour is consistent with expectations based on the operator
product expansion, but our approach is more widely applicable. The
dispersively-generated power contributions to different observables are given
by (log-)moment integrals of a universal low-scale effective coupling, with
process-dependent powers and coefficients. We analyse a wide variety of
quark-dominated processes and observables, and show how the power contributions
are specified in lowest order by the behaviour of one-loop Feynman diagrams
containing a gluon of small virtual mass. We discuss both collinear safe
observables (such as the e+e- total cross section and \tau hadronic width, DIS
sum rules, e+e- event shape variables and the Drell-Yan K-factor) and collinear
divergent quantities (such as DIS structure functions, e+e- fragmentation
functions and the Drell-Yan cross section).
