In most experimental works, different values of the chemical diffusion coefficient of guest ions in ion-insertion electrodes (IIEs) are evaluated by different techniques, e.g. PITT, GITT and EIS. In fact, the main problem comes from the lack of relevant models to fit accurately the responses of IIEs in the time domain. The aims of this article are the following: first to propose different models for analysis of PITT experimental data (e.g. models derived from equivalent circuit analogs, or using the concept of anomalous diffusion, or assuming that the diffusion length is fluctuating in a Gaussian fashion around a mean value), next to give a general procedure for calculation of potentiostatic current transients from the above models by numerical inversion of Laplace transforms, and finally to discriminate between the candidate models by comparison with experimental data through a non-linear fit procedure. The whole procedure is applied in this article to the analysis of PITT experimental data (issued from the specialized literature) relative to lithium-ion insertion into Li x CoO2 thin-films electrodes.