  For a generic gauge-invariant correlator <{\cal Q}[A_{\mu}]>_{A}, we
reformulate the standard D=4 Yang-Mills theory as a renormalizable system of
two interacting fields a_{\mu} and B_{\mu} which faithfully represent high- and
low-energy degrees of freedom of the single gauge field A_{\mu} in the original
formulation. It opens a possibility to synthesize an infrared-nonsingular
weak-coupling series, employed to integrate over a_{\mu} for a given background
B_{\mu}, with qualitatively different methods. These methods are to be applied
to evaluate the resulting (after the a_{\mu}-integration) representation of
<{\cal Q}[A_{\mu}]>_{A} in terms of gauge-invariant generically non-local
low-energy observables, like Wilson loops. The latter observables are averaged
over B_{\mu} with respect to a gauge-invariant Wilsonean effective action
S_{eff}[B]. To avoid a destructive dissipation between the high- and low-energy
excitations, we implement a specific fine-tuning of the interaction between the
pair of the fields: prior to the integration over B_{\mu}, the expectation
value <a_{\mu}>_{a} vanishes, in the tree order of the loop-wise expansion, for
an arbitrary configuration of B_{\mu}.
