Data of energy economy of battery electric vehicles without a range extender internal combustion engines (BEV) and with a range extender internal combustion engine (BEVx) are reviewed and integrated with simulations by models. A BEV with an on-board, high efficiency, electricity generator based on a positive ignition (PI) internal combustion engine (ICE) is then proposed as a way to improve the uptake of the BEV improving their range and performance as well as their economic and environmental impact. The small ICE, that is working continuously, stationary, fixed load and speed, and the generator similarly optimized for a single point operation, permit an efficiency fuel chemical-to-electric approaching 50%. This is much better than producing electricity centralized from combustion fuels (average efficiency with included distribution and recharging losses at about 30%), and it does not require any electric recharging infrastructure. Simple but reliable extrapolations from the production BEV and BEVx of different battery capacity on the same vehicle platform, plus the simulations, demonstrate that this BEVy may deliver miles-per-gallon (MPG) working gasoline 13% better than any present plug-in-hybrid-electric-vehicle (PHEV) currently available, and MPGe (MPG-equivalent) working electric 12% better than the existing BEV on the same platform with a larger battery pack and no range extender, or 27% better than the BEVx on the same platform with a larger battery pack and range extender. Finally, this BEVy may permit a range over 600 miles with 10 gallons of gasoline onboard, in line with the best PHEV currently available.