Rhombohedral NASICON compounds with general formula Li1+xTi2-xScx(PO4)(3) (0 <= x <= 0.5) have been prepared using a conventional solid-state reaction and characterized by X-ray diffraction (XRD), nuclear magnetic resonance (NMR), and impedance spectroscopy. The partial substitution of Ti4+ by Sc3+ and Li+ in pristine LiTi2(PO4)(3) increases unit-cell dimensions and the number of charge carriers. In Sc-rich samples, the analysis of XRD data and Li-6/Li-7, P-31, and Sc-45 MAS NMR spectra confirms the presence of secondary LiScO2 and LiScP2O7 phases that reduce the amount of lithium incorporated in the NASICON phase. In samples with x < 0.3, electrostatic repulsions between Li ions located at M1 and M3 sites increase Li mobility. For x >= 0.3, ionic conductivity decreases because of secondary nonconducting phases formed at grain boundaries of the NASICON particles (core-shell structures). For x = 0.2, high bulk conductivity (2.5 x 10(-3) S.cm(-1)) and low activation energy (E-a = 0.25 eV) measured at room temperature make Li1.2Ti1.8Sc0.2(PO4)(3) one of the best lithium ionic conductors reported in the literature. In this material, the vacancy arrangement enhances Li conductivity.