A lithium-ion rechargeable cell is described which contains an electrolyte comprising a pyrazolium cation, an imidazolium cation, or a combination thereof, as well as lithium ion, and at least one non-Lewis acid derived counter-ion and which has a ratio of cathode capacity to anode capacity of 1 or less, 1 or greater, and preferably about 1.3 or greater. Electrochemical cells containing an anode, a cathode, and the ionic liquid electrolytes preferably have effective charge/discharge capacity and charging efficiency at low temperatures and at high temperatures.