NOVELTY - Operating a lithium-ion cell comprises: electrochemically forming the cell from an open circuit voltage (OCV) to either a first lower voltage limit (LVL) different from the OCV or a first upper voltage limit (UVL) higher than the OCV after the cell is made, where the first LVL is 0.1-4.6 volts; and cycling the cell by discharging the cell to a voltage no lower than a second LVL and charging the cell to a voltage no higher than a second UVL.    USE - The method is useful for operating a lithium-ion cell.    ADVANTAGE - The method operates a high energy density lithium-ion cell using a high-capacity cathode active material (with a specific capacity significantly greater than 250 g to 3540 mAh/g) that: can be readily prepared without going through an energy-intensive sintering process; is amenable to being lithium intercalation-free or fast lithium intercalation, leading to a significantly improved power density; electrically and thermally conductive, enabling high-rate capability and effective heat dissipation; and contains little or no oxygen, reducing or eliminating the potential fire hazard or explosion.    DETAILED DESCRIPTION - Operating a lithium-ion cell comprises: electrochemically forming the cell from an open circuit voltage (OCV) to either a first lower voltage limit (LVL) different from the OCV or a first upper voltage limit (UVL) higher than the OCV after the cell is made, where the first LVL is 0.1-4.6 volts; and cycling the cell by discharging the cell to a voltage no lower than a second LVL and charging the cell to a voltage no higher than a second UVL. The lithium-ion cell comprises: (a) a positive electrode (cathode) comprising a carbon or graphitic material as a cathode active material having a surface area to capture and store lithium on it, where the cathode forms a mesoporous structure having a pore size of 2-50 nm and a specific surface area of greater than 50 m2/g; (b) a negative electrode (anode) comprising an anode active material; (c) a porous separator disposed between the anode and the cathode; (d) a lithium-containing electrolyte in ionic contact with the anode and the cathode; and (e) a lithium source disposed in at least one of the two electrodes to obtain an open circuit voltage (OCV) of 0.5-2.8 volts when the cell is made. An INDEPENDENT CLAIM is also included for the lithium-ion cell comprising the positive electrode (cathode), the negative electrode (anode) comprising a prelithiated anode active material or a combination of a lithium source and an anode active material, a porous separator disposed between the anode and the cathode and a lithium-containing electrolyte in ionic contact with the anode and the cathode.