We used a two-step fluorination of natural or synthetic graphites, the one at the ambient temperature in the presence of F2+ IF5+ HF and the second in the temperature range of 100 – 350°C in F2atmosphere. This led to graphite fluorides characterized by the planarity of the carbon hexagons (sp2hybridization), by the iono-covalent character of the C-F bondings and by the high F/C ratio, close to unity. These graphite fluorides were compared to conventional, highly covalent CFx(sp3hybridization) in their electrochemical performances in lithium batteries, especially regarding the high rate discharge capability. We found a large advantage with the iono-covalent CFxthat is they sustain a 5 C rate discharge where the covalent ones failed to discharge under 4 C. The difference is tentatively related to the internal structure and to the higher electrical conductivity of iono-covalent CFx.