Electrochemical double-layer capacitors exhibit high power and long cycle life but have low specific energy compared with batteries, limiting applications. Redox-enhanced capacitors increase specific energy by using redox-active electrolytes that are oxidized at the positive electrode and reduced at the negative electrode during charging. Here we report characteristics of several redox electrolytes to illustrate operational/self-discharge mechanisms and the design rules for high performance. We discover a methyl viologen (MV)/bromide electrolyte that delivers a high specific energy of ∼14 Wh kg(-1) based on the mass of electrodes and electrolyte, without the use of an ion-selective membrane separator. Substituting heptyl viologen for MV increases stability, with no degradation over 20,000 cycles. Self-discharge is low, due to adsorption of the redox couples in the charged state to the activated carbon, and comparable to cells with inert electrolyte. An electrochemical model reproduces experiments and predicts that 30-50 Wh kg(-1) is possible with optimization.