Different series of LiMn2O4-based spinels were studied, all presenting two reduction steps at 4.5 and 3.3 V in addition to the "normal" spinel plateaus around 4 V. A correlation was found between the capacity recovered on these additional steps, the manganese oxidation degree, and the cell parameter of a given spinel. By means of in situ synchrotron diffraction we were able to detect the appearance of a new set of diffraction peaks upon oxidation of the 3.3 V step at 3.95 V, that disappeared on subsequent reduction at 3.3 V. Electron diffraction and high resolution electron microscopy studies on partially delithiated samples revealed the formation of double hexagonal layers upon oxidation, consistent with the additional peaks observed in the in situ experiments. Finally, a model to explain the existence of the redox steps at 4.5 and 3.95/3.3 V based on the creation of these double hexagonal layers is proposed.