  We study radiative corrections to deeply virtual Compton scattering in the
kinematics of HERA collider experiments to next--to--leading and
next--to--next--to--leading order. In the latter case the radiative corrections
are evaluated in a special scheme that allows us to employ the predictive power
of conformal symmetry. As observed before, the size of next--to--leading order
corrections strongly depends on the gluonic input, as gluons start to
contribute at this order. Beyond next--to--leading order we find, in contrast,
that the corrections for an input scale of few GeV^2 are small enough to
justify the uses of perturbation theory. For $\xi > 5 10^{-3}$ the modification
of the scale dependence is also small. However, with decreasing $\xi$ it
becomes moderate or even large, in particular for the phase.
