  We compute a compact OPE formula describing power corrections to the
perturbative expression for the asymmetric $\widetilde{MOM}$-renormalized
running coupling constant up to the leading logarithm. By the use of the
phenomelogical hypothesis leading to the factorization of the condensates
through a perturbative vacuum insertion, the only relevant condensate in the
game is $<A^2>$. The validity of the OPE formula is tested by searching for a
good-quality coherent description of previous lattice evaluations of
$\widetilde{MOM}$-renormalized gluon propagator and running coupling.
