TeX3[Al(ORF)4] (X=Cl, Br, I; RF=C(CF3)3) were synthesized by the reaction of Ag[Al(ORF)4] and TeX4 or the reaction of AuX, Ag[Al(ORF)4], and elemental tellurium in liquid SO2. The compounds were characterized by 125Te NMR in solution and by X-ray diffraction, Raman, and IR spectroscopy in the solid state. The vibrational spectra and the crystal structure show very weak secondary interactions, indicating “pseudo gas phase conditions” in the condensed phase. The observed trend of the 125Te NMR chemical shifts along the [TeX3]+ series follows neither the monotonous decrease known as “normal halogen dependence” nor the increase known as “inverse halogen dependence”. By relativistic two-component calculations based on the ZORA approach, we find that this “abnormal halogen dependence” results from an interplay of relativistic and solvent effects, where non-negligible scalar relativistic effects and intermediate-sized spin-orbit effects compensate to some extent. The reasons for these trends are evaluated in the context of the Te s-orbital character of the TeX bonds and compared with the halogen dependence(s) within the isoelectronic [SeX3]+ and PX3 series and related trihalomethyl [CX3]+ cations.