  We quantify perturbative and non-perturbative QCD effects in the exclusive
$J/\psi$-photoproduction cross section, and in the shrinkage of the
differential cross section with respect to momentum transfer, $t$. We predict
that in the high energy THERA region there will always be a significant
contribution to this process that rises quickly with energy. This implies that
the taming of the rise of the cross section with energy, due to both the
expansion of spatially-small fluctuations in the photon and to higher twist
effects, is rather gradual.
