in search of the cubic phase of the Li+ ion-conducting perovskite La2/3-xLi3xTiO3 (LLTO), several samples, quenched and heated at different temperatures, are examined by powder X-ray diffraction (XRD). The best structural model (for 0.06 < x < 0.14)-probably representing an average situation-is discussed in comparison with various other structural studies. It presents a tetragonal unit cell (space group P4/mmm; a approximate to a(p,) c = 2a(p)) in which La3+ ions and vacancies are always unequally distributed in the two different A sites, centers of the perovskite dodecahedral cages. The quenching experiments bring the evidence of a very fast disordering/ordering of La3+ ions between their two unequivalent positions, and the in situ thermodiffractometry experiments show that the La3+ ion thermal diffusion becomes noticeable above 800 degreesC and depends on the solid solution composition x. Although the thermal diffusion of the La3+ ions occurs above 800 degreesC, the disordering of these ions remains limited for low x values (with c/2a values slightly greater than 1) even at 1200 degreesC, while a nearly complete disordering is reached at 1200 degreesC for x=0.11 (with c/2a very close to 1). As reported by earlier authors, the kinetics of the fast La3+ ions disordering/ordering in the temperature range 900-1200 C has to be fully considered during the preparation of the samples, and the thermal history can noticeably change the La3+ ion partition and hence the electrical conductivity of the prepared phase. The equilibrated samples can be obtained by using proper heating time and temperature.