We propose a hypothesis which generalizes the notion of duality to off-mass-shell current matrix elements. The hypothesis, referred to as strong light-cone dominance, is formulated in terms of the light-cone sum rules, which reflect causality and the light-cone structure of current commutators: We postulate that these sum rules are saturated quasilocally by individual resonance peaks, in a similar manner as duality requires resonances to saturate the FESR for the hadronic on-shell amplitudes. This reconstitutes scaling in an average sense in regions where the leading light-cone singularity does not dominate. In coordinate space this hypothesis implies that the leading light-cone singularity regulates (tames) the entire light-cone expansion in a neighbourhood of the surface of the light-cone, whose extension is of the order of an inverse mass difference between consecutive resonances. We investigate the hypothesis of strong light-cone dominance in the framework of narrow resonance models for the vertex and show that the leading light-cone singularity indeed normalizes the single particle contributions by means of a relation of the Drell-Yan-West type. A simple Veneziano-like vertex model is exhibited, which is strongly light-cone dominated. Furthermore, we show how to exploitthe hypothesis in a rather model-independent way. We present some applications to the non-forward four-point function and show in particular that strong light-cone dominancerequires scaling for exclusive electroproduction processes like γ ∗ + N → π + N.