  We consider the standard site percolation model on the three dimensional
cubic lattice. Starting solely with the hypothesis that $\theta(p)>0$, we prove
that, for any $\alpha>0$, there exists $\kappa>0$ such that, with probability
larger than $1-1/n^\alpha$, every pair of vertices inside the box $\Lambda(n)$
are joined by a path having at most $\kappa(\ln n)^2$ closed sites.
