Using well-cycled, thin composite graphite electrodes we analyze carefully the limitations of potentiostatic and galvanostatic intermittent titration techniques (PITT and GITT, respectively) for determination of the differential (incremental) intercalation capacitance, C dif, and the chemical diffusion coefficient, D, of Li ions in these ion-insertion electrodes (IIEs). We demonstrate the superiority of the GITT over PITT to determine these quantities as the former technique allows for a more accurate determination of C dif and hence D which closely approach to the spinodal domain related to the first-order phase transition during ion-insertion. We show that GITT is also more effective in eliminating the parasitic contributions of background currents to the total measured response. A pronounced difference in the initial, intrinsic kinetics of formation of a new phase in the bulk of the old one has been observed depending on the direction of titration (phases less saturated with Li are formed faster during deintercalation than the Li-rich phases in the course of intercalation).