Rechargeable cells can be made using two different intercalation compounds, in which the chemical potential of the intercalant differs by several eV, for the electrodes. In this paper, the authors discuss the factors that play a role in the selection of appropriate lithium intercalation compounds for such cells. For ease of cell assembly the cathode should be stable in air when it is fully intercalated, like LiNiO{sub 2}. For the anode, the chemical potential of the intercalated Li should be close to that of Li metal, like it is in Li{sub x}C{sub 6}. The authors discuss the intercalation of Li in LiNiO{sub 2} and then in petroleum coke. Then, the authors show that LiNiO{sub 2}/coke cells have high energy density, long cycle life, excellent high-temperature performance, low self-discharge rates, can be repeatedly discharged to zero volts without damage, and are easily fabricated. In the authors' opinion this type of cell shows far more promise for widespread applications than traditional secondary Li cells using metallic Li anodes.