  We study approximate decimations in SU(N) LGT that connect the short to long
distance regimes. Simple `bond-moving' decimations turn out to provide both
upper and lower bounds on the exact partition function. This leads to a
representation of the exact partition function in terms of successive
decimations whose effective couplings flows are related to those of the easily
computable bond-moving decimations. The implications for a derivation of
confinement from first principles are discussed.
