A room-temperature all-solid-state rechargeable battery cell containing a tandem electrolyte consisting of a Li+-glass electrolyte in contact with a lithium anode and a plasticizer in contact with a conventional, low cost oxide host cathode was charged to 5 V versus lithium with a charge/discharge cycle life of over 23,000 cycles at a rate of 153 mA·g-1 of active material. A larger positive electrode cell with 329 cycles had a capacity of 585 mAh·g-1 at a cutoff of 2.5 V and a current of 23 mA·g-1 of the active material; the capacity rose with cycle number over the 329 cycles tested during 13 consecutive months. Another cell had a discharge voltage from 4.5 to 3.7 V over 316 cycles at a rate of 46 mA·g-1 of active material. Both the Li+-glass electrolyte and the plasticizer contain electric dipoles that respond to the internal electric fields generated during charge by a redistribution of mobile cations in the glass and by extraction of Li+ from the active cathode host particles. The electric dipoles remain oriented during discharge to retain an internal electric field after a discharge. The plasticizer accommodates to the volume changes in the active cathode particles during charge/discharge cycling and retains during charge the Li+ extracted from the cathode particles at the plasticizer/cathode-particle interface; return of these Li+ to the active cathode particles during discharge only involves a displacement back across the plasticizer/cathode interface and transport within the cathode particle. A slow motion at room temperature of the electric dipoles in the Li+-glass electrolyte increases with time the electric field across the EDLC of the anode/Li+-glass interface to where Li+ from the glass electrolyte is plated on the anode without being replenished from the cathode, which charges the Li+-glass electrolyte negative and consequently the glass side of the Li+-glass/plasticizer EDLC. Stripping back the Li+ to the Li+-glass during discharge is enhanced by the negative charge in the Li+-glass. Since the Li+-glass is not reduced on contact with metallic lithium, no passivating interface layer contributes to a capacity fade; instead, the discharge capacity increases with cycle number as a result of dipole polarization in the Li+-glass electrolyte leading to a capacity increase of the Li+-glass/plasticizer EDLC. The storage of electric power by both faradaic electrochemical extraction/insertion of Li+ in the cathode and electrostatic stored energy in the EDLCs provides a safe and fast charge and discharge with a long cycle life and a greater capacity than can be provided by the cathode host extraction/insertion reaction. The cell can be charged to a high voltage versus a lithium anode because of the added charge of the EDLCs.