  The two-tensor-pomeron model is applied to deeply virtual Compton scattering
(DVCS) on a proton. A good description of the DVCS HERA data at small
Bjorken-$x$ is achieved due to a sizeable interference of soft and hard pomeron
contributions. We present two fits which differ somewhat in the strength of the
hard pomeron contribution. We describe, in the same framework, both the low
$Q^{2}$ and high $Q^{2}$ regimes and the transition between them. We find that
the soft-pomeron contribution is considerable up to $Q^{2} \sim 20$ GeV$^{2}$.
The reggeon exchange term is particularly relevant for describing the
scattering of a real photon on a proton measured at lower $\gamma p$ energies
at FNAL. We find that the ratio of $\gamma^{*} p \to \gamma p$ cross-sections
for longitudinally and transversely polarized virtual photons strongly
increases with $t$. Our findings may be checked in future lepton-nucleon
scattering experiments in the low-$x$ regime, for instance, at a future
Electron-Ion Collider (EIC) at the BNL and LHeC at the LHC.
