Hard carbons from various precursors heat-treated at 1000-2000 degrees C follow a common rule with regard to their structure-capacity correlation for lithium intercalation. A nanostructure containing a large fraction of highly strained carbon layers with large interlayer spacings and small crystallite sizes is a prerequisite to achieve reversible capacities in the range 300-450 mAh/g. P-doping of carbon derived from a polymer precursor causes a softening of the hard carbon structure by decreasing the strain on carbon layers, reducing interlayer spacing and increasing the crystallite sizes. It also induces a reduction of the number of nanopores which become larger in size. The amount of space reduction by the softening effect, however, is more than compensated by the dopant so that capacities of 550 mAh/g and first cycle efficiencies improved up to 83% are achieved.