[en] We quantify perturbative and non-perturbative QCD effects in the exclusive J/ψ-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. (author)