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.
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