Abstract: The NEXT experiment aims at searching for the hypothetical neutrinoless double-beta decay from the Xe-136 isotope using a high-purity xenon TPC. Efficient discrimination of the events through pattern recognition of the topology of primary ionisation tracks is a major requirement for the experiment. However, it is limited by the diffusion of electrons. It is known that the addition of a small fraction of a molecular gas to xenon reduces electron diffusion. On the other hand, the electroluminescence (EL) yield drops and the achievable energy resolution may be compromised. We have studied the effect of adding several molecular gases to xenon (CO2, CH4 and CF4) on the EL yield and energy resolution obtained in a small prototype of driftless gas proportional scintillation counter. We have compared our results on the scintillation characteristics (EL yield and energy resolution) with a microscopic simulation, obtaining the diffusion coefficients in those conditions as well. Accordingly, electron diffusion may be reduced from about 10 for pure xenon down to 2.5 using additive concentrations of about 0.05%, 0.2% and 0.02% for CO2, CH4 and CF4, respectively. Our results show that CF4 admixtures present the highest EL yield in those conditions, but very poor energy resolution as a result of huge fluctuations observed in the EL formation. CH4 presents the best energy resolution despite the EL yield being the lowest. The results obtained with xenon admixtures are extrapolated to the operational conditions of the NEXT-100 TPC. CO2 and CH4 show potential as molecular additives in a large xenon TPC. While CO2 has some operational constraints, making it difficult to be used in a large TPC, CH4 shows the best performance and stability as molecular additive to be used in the NEXT-100 TPC, with an extrapolated energy resolution of 0.4% at 2.45 MeV for concentrations below 0.4%, which is only slightly worse than the one obtained for pure xenon. We demonstrate the possibility to have an electroluminescence TPC operating very close to the thermal diffusion limit without jeopardizing the TPC performance, if CO2 or CH4 are chosen as additives.