Graphites as active materials for negative electrode in lithium batteries are particularly attractive because of their large capacity of lithium intercalation and their low average voltage. In some conditions, they are known to suffer from low reversibility of the initial intercalation process. This phenomenon is shown to be unambiguously related to an exfoliation of graphene layers, that can occur even in EC based electrolytes. Occurrence of a clear correlation between the extent of irreversible behaviour and rhombohedral phase content of graphites is discussed. Milling or thermal treatment of pristine graphites are also shown to influence electrochemical properties.