New high-voltage cathode materials for lithium and Li-ion batteries, with the general formula LiMgdeltaNi0.5-deltaMn1.5O4 (delta=0.00, 0.05 and 0.10), have been synthesized and characterized. The crystal structure of these cubic spinel materials has been refined with space group P4(3)32 with the following site occupation: Li+ on 8c, Mg2- on 4b, Ni2- on 4b/12d, Mn4+ on 12d/4b and O2- on 24e and 8c. Refinement with space group Fd3m was not possible. As a function of the Mg content, it was found that: (1) the cubic lattice constant increases from 8.1685 Angstrom (delta=0.00) and 8.1703 Angstrom (delta=0.05) to 8.1733 Angstrom (delta=0.10); (II) the flat potential profile at 4.7 V vs. Li/Li+ (delta=0.00) changes to a slightly sloping profile with an increased average potential of 4.75 V (delta=0.10); (III) the cyclability and the conductivity of the materials improve. It is concluded that LiMgdeltaNi0.50-deltaMn1.5O4 (delta<0.10) are promising cathode materials that, when combined with a low-voltage anode material like LiCrTiO4, can result in similar to 3.25 V rechargeable Li-ion battery with spinel electrodes.