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High-entropy (HE) ceramics, by analogy with HE metallic alloys, are an emerging class of solid solutions composed of a large number of species. These materials offer the benefit of large compositional flexibility and can be used in a wide variety of applications, including thermoelectrics, catalysts, superionic conductors and battery electrodes. We show here that the HE concept can lead to very substantial improvements in performance in battery cathodes. Among lithium-ion cathodes, cation-disordered rocksalt (DRX)-type materials are an ideal platform within which to design HE materials because of their demonstrated chemical flexibility. By comparing a group of DRX cathodes containing two, four or six transition metal (TM) species, we show that short-range order systematically decreases, whereas energy density and rate capability systematically increase, as more TM cation species are mixed together, despite the total metal content remaining fixed. A DRX cathode with six TM species achieves 307 mAh g-1 (955 Wh kg-1) at a low rate (20 mA g-1), and retains more than 170 mAh g-1 when cycling at a high rate of 2,000 mA g-1. To facilitate further design in this HE DRX space, we also present a compatibility analysis of 23 different TM ions, and successfully synthesize a phase-pure HE DRX compound containing 12 TM species as a proof of concept.