  Within the framework of xenon-based double beta decay experiments, we propose
the possibility to improve the background rejection of an electroluminescent
Time Projection Chamber (EL TPC) by reducing the diffusion of the drifting
electrons while keeping nearly intact the energy resolution of a pure xenon EL
TPC. Based on state-of-the-art microscopic simulations, a substantial addition
of helium, around 10 or 15~\%, may reduce drastically the transverse diffusion
down to 2.5~mm/$\sqrt{\mathrm{m}}$ from the 10.5~mm/$\sqrt{\mathrm{m}}$ of pure
xenon. The longitudinal diffusion remains around 4~mm/$\sqrt{\mathrm{m}}$.
Light production studies have been performed as well. They show that the
relative variation in energy resolution introduced by such a change does not
exceed a few percent, which leaves the energy resolution practically unchanged.
The technical caveats of using photomultipliers close to an helium atmosphere
are also discussed in detail.
