The structure of the fully ordered alpha-Na3Ti2(PO4)(3) NASICON compound was elucidated using high-quality single-crystal data. The cation/vacancy distribution forms a homogeneous 3D arrangement and could represent the absolute cationic ordering available in the full Na3M2(PO4)(3) series, as verified for M = Fe. For M = Ti, the reversible alpha ->gamma transition was observed at 85 degrees C, leading to the standard disordered R (3) over barc gamma model. Through JPDF analysis, the most probable Na+ zigzag M(2)-M(1) diffusion scheme was directly deduced using our accurate crystallographic data.