  Positron initiated deeply virtual Compton scattering (DVCS) off $^4$He and
$^3$He nuclei is described. The way the so-called $d-$term could be obtained
from the real part of the relevant Compton form factor is summarized, and the
importance and novelty of this measurement is discussed. The measurements
addressed for $^3$He targets could be very useful even in a standard
unpolarized target setup, measuring beam spin and beam charge asymmetries only.
The unpolarized beam charge asymmetries for DVCS off $^3$He and $^4$He are also
estimated, at JLab kinematics and, for $^4$He, also at a configuration typical
at the future Electron-Ion Collider. Incoherent DVCS processes, in particular
the ones with tagging the internal target by measuring slow recoiling nuclei,
and the unique possibility offered by positron beams for the investigation of
Compton form factors of higher twist, are also briefly addressed.
