The ATLAS detector data on di-lepton production is used in order to impose constraints on Z boson masses associated with a variety of 3-3-1 and E 6 motivated Z models. Lower mass bounds for the different models are established at 95% confidence level. Our numerical analysis is extrapolated up to 14 TeV, and further to 30 TeV and 100 TeV, for a broad range of luminosities. Some of our results can be compared with the ATLAS published bounds, being, for those cases, in fairly good agreement. We also report the vector and axial charges for all the 3-3-1-motivated Z models without exotic electric charges for leptons, known in the literature. To the best of our knowledge most of this charges were not reported before.