Carbons made by pyrolyzing epoxy novolak resins at 1000 degrees C are made up predominantly of single graphene sheets, having a lateral dimension of about 25 Angstrom, which are arranged somewhat like a ''house of cards.'' This structure implies significant micro- or nanoporosity. Such carbons can reversibly react with large amounts of lithium in a mechanism thought to involve the adsorption of lithium on the internal surfaces of nanopores. We have studied the effect of controlled oxidation of these samples, which changes the pore structure, on the subsequent electrochemical insertion of lithium in these materials. Using Brunauer, Emmett, and Teller surface area measurements, methylene blue adsorption tests, powder x-ray diffraction, and small angle x-ray scattering (SAX), we are able to correlate the changes in pore structure to the electrochemical behavior of these samples. Initially, the pores are small (of the order of 15 Angstrom), as are their openings, and the electrolyte cannot penetrate the pores, so excellent behavior is observed. Reversible specific capacities for Li as large as 570 mAh/g have been observed, with little irreversible capacity. As the samples are oxidized, the pores do not grow significantly in volume, as measured by SAX, but the size of their openings apparently does, to the point where the electrolyte can penetrate the pores, leading to irreversible electrolyte decomposition reactions during the first electrochemical reaction of lithium with the carbon, and hence large irreversible capacity. Burnoffs as small as 5% are enough to transform the samples from excellent to poor. In addition, chemisorbed oxygen (from the oxidation treatment) appears to react with lithium, leading to increases in both irreversible and reversible capacities. However, the reversible capacity due to the chemisorbed oxygen shows large hysteresis. A pictorial model is proposed that is consistent with the results.