  We present a parameterization of the non-collinear (virtual) Compton
scattering tensor in terms of form factors, in which the Lorentz tensor
associated with each form factor possesses manifest electromagnetic gauge
invariance. The main finding is that in a well-defined form factor expansion of
the scattering tensor, the form factors are either symmetric or antisymmetric
under the exchange of two Mandelstam variables, $s$ and $u$. Our decomposition
can be used to organize complicated higher-order and higher-twist contributions
in the study of the virtual Compton scattering off the proton. Such procedures
are illustrated by use of the virtual Compton scattering off the lepton. In
passing, we note the general symmetry constraints on Ji's off-forward parton
distributions and Radyushkin's double distributions.
