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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/m from the 10.5 mm/m of pure xenon. The longitudinal diffusion remains around 4 mm/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 ; The NEXT Collaboration acknowledges support from the following agencies and institutions: the European Research Council (ERC) under the Advanced Grant 339787-NEXT; the Ministerio de Economía y Competitividad of Spain under grants FIS2014-53371-C04, the Severo Ochoa Program SEV-2014-0398 and the María de Maetzu Program MDM-2016-0692; the GVA of Spain under grants PROMETEO/2016/120 and SEJI/2017/011; the Portuguese FCT and FEDER through the program COMPETE, projects PTDC/FIS-NUC/2525/2014 and UID/FIS/04559/2013; the U.S. Department of Energy under contracts number DE-AC02-07CH11359 (Fermi National Accelerator Laboratory), DE-FG02-13ER42020 (Texas A&M) and de-sc0017721 (University of Texas at Arlington); and the University of Texas at Arlington. We acknowledge partial support from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreements No. 690575 and 674896