We compute a compact OPE formula describing power corrections to the perturbative expression for the asymmetric 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 . The validity of the OPE formula is tested by searching for a good-quality coherent description of previous lattice evaluations of MOM-renormalized gluon propagator and running coupling.