Rechargeable battery systems and rechargeable battery system operational methods are described. According to one aspect, a rechargeable battery system includes a plurality of rechargeable battery modules coupled between a plurality of terminals, wherein the rechargeable battery modules individually comprise a plurality of rechargeable battery cells and charge balancing circuitry configured to implement, for individual ones of the rechargeable battery modules, first charge balancing operations to increase the balancing of states of charge of the rechargeable battery cells of individual ones of the rechargeable battery modules, and to implement second charge balancing operations to increase the balancing of states of charge of the rechargeable battery modules with respect to one another.