A significant limitation of rechargeable lithium-ion batteries arises because most of the ionic current is carried by the anion, the ion that does not participate in energy-producing reactions. Single-ion-conducting block copolymer electrolytes, wherein all of the current is carried by the lithium cations, have the potential to dramatically improve battery performance. The relationship between ionic conductivity and morphology of single-ion-conducting poly(ethylene oxide)-b-polystyrenesulfonyllithium(trifluoromethylsulfonyl)imide (PEO-PSLiTFSI) diblock copolymers was studied by small-angle X-ray scattering and ac impedance spectroscopy. At low temperatures, an ordered lamellar phase is obtained, and the "mobile" lithium ions are trapped in the form of ionic clusters in the glassy polystyrene-rich microphase. An increase in temperature results in a thermodynamic transition to a disordered phase. Above this transition temperature, the lithium ions are released from the clusters, and ionic conductivity increases by several orders of magnitude. This morphology-conductivity relationship is very different from all previously published data on published electrolytes. The ability to design electrolytes wherein most of the current is carried by the lithium ions, to sequester them in nonconducting domains and release them when necessary, has the potential to enable new strategies for controlling the charge-discharge characteristics of rechargeable lithium batteries.