Thick electrodes with sodium and even anions intercalation organic compounds integrated in a neutral-pH aqueous battery offer unique advantages in terms of round trip efficiency, environmental impact, and scalability for off or in-grid renewable energy storage. Herein we report on the first anion-rocking chair / dual-ion organic battery. The latter reaches 35 Wh/kgmaterials at C/8 rate. It shows remarkable cyclability and Coulombic efficiency in a cheap and neutral NaClO4 electrolyte pouch cell with highly loaded millimeter thick electrodes (5 mAh/cm²). This achievement is based on a thorough study of a commercial benzene TEMPO compound (4-hydroxy TEMPO benzoate) and its naphthalene derivative (4-carboxy TEMPO naphthalate) as cathode materials, and a bipyridinium-naphthalene oligomer as the anode. Combined UV-vis spec-troelectrochemistry and operando XRD account for the much improved cyclability of the hydrophobic 4-carboxy TEMPO naphthalate at the expense of a lower specific capacity. This trend is reversed in the case of the 4-hydroxy TEMPO benzoate derivative. Results show kinetic limitations of the 4-hydroxy TEMPO benzoate are associated with the surrounding composite electrode, while inner-grain ionic and/or electronic transports play a decisive role for the 4-carboxy TEMPO naph-thalate.