Non-stoichiometric or fluorine-substituted LixMn2O4 are known to present a reversible redox step at 4.5 V as well as a reduction step at 3.3 V appearing to the expense of the usual 4.0-4.15 V. We present results of very slow stepwise potentiodynamic studies which allowed to localise the oxidation step associated to the 3.3 V reduction level close to 3.95 V. We propose the cubic spinel lattice parameter value as the key parameter for knowing a priori if these redox states will be present or not, with 8.215 Angstrom as threshold value. In situ XRD studies performed across the 3.3 < - > 3.95 V redox step indicate that these additional states are probably associated to structural features.