Lithium batteries have the highest energy density of all rechargeable batteries and are favoured in applications where low weight or small volume are desired - for example, laptop computers, cellular telephones and electric vehicles(1). One of the limitations of present commercial lithium batteries is the high cost of the LiCoO2 cathode material. Searches for a replacement material that, Like LiCoO2, intercalates lithium ions reversibly have covered most of the known lithium/transition-metal oxides, but the number of possible mixtures of these(2-5) is almost limitless, making an empirical search labourious and expensive. Here we show that first-principles calculations can instead direct the search for possible cathode materials. Through such calculations we identify a large class of new candidate materials in which non-transition metals are substituted for transition metals. The replacement with non-transition metals is driven by the realization that oxygen, rather than transition-metal ions, function as the electron acceptor upon insertion of Li. For one such material, Li(Co,Al)O-2, we predict and verify experimentally that aluminium substitution raises the cell voltage while decreasing both the density of the material and its cost.