  We compute a formula including OPE power corrections to describe the running
of a QCD coupling non-perturbatively defined through the ghost and gluon
dressing functions. This turns out to be rather accurate. We propose the ``{\it
plateau}''-procedure to compute $\Lambda_{\bar{\rm MS}}$ from the lattice
computation of the running coupling constant. We show a good agreement between
the different methods which have been used to estimate $\Lambda_{\bar{\rm
MS}}^{N_f=0}$. We argue that $\Lambda_{\bar{\rm MS}}$ or the strong coupling
constant computed with different lattice spacings may be used to estimate the
lattice spacing ratio.
