We describe the preparation of hard carbon samples from epoxy resins. These materials are shown by wide angle X-ray diffraction to be constructed of graphene sheets of small lateral extent (about 25 Å in diameter). By controlling the synthesis conditions, it is possible to prepare materials wherein the fraction of graphene sheets present as single layers can be adjusted. Using small angle X-ray scattering, we show that these materials incorporate small nanopores between the single layers, which are about 15 Å in diameter. This suggests that the single layers are arranged more or less like a “house of cards”. Lithium can be inserted reversibly into these materials and the amount of lithium that can be inserted increases as the fraction of single layers in the sample increases. This suggests that the mechanism of lithium insertion in these materials is surface adsorption of lithium on the internal surfaces of the single-layer graphene sheets. We compare the insertion of lithium in these carbons to that which occurs in soft carbons with insignificant numbers of single layers and no measurable nanoporosity.