A 40Wh/kg Li-ion battery using a Li4Ti5O12 nanostructured anode and a composite activated carbon LiCoO2 cathode was built using plastic Li-ion processing based on PVDF-HFP binder and soft laminate packaging. The specific power of the device is similar to that of an electrochemical double-layer supercapacitor (4000W/kg). The high power is enabled by a combination of a nanostructured negative electrode, an acetonitrile based electrolyte and an activated carbon/LiCoO2 composite positive electrode. This enables very fast charging (full recharge in 3min). The effect of electrode formulation and matching ratio on energy, power and cycle-life are described. Optimization of these parameters led to a cycle-life of 20% capacity loss after 9000 cycles at full depth of discharge (DOD).