Lithium thiophosphate glasses and glass ceramics are a promising class of electrolytes for all-solid-state lithium-ion batteries. Heat treatment of completely amorphous glasses often leads to a conductivity enhancement, which can be attributed either to the formation of highly conducting crystallites or to fast Li+ ion transport at the interface between amorphous phases and crystallites. Here, we demonstrate a novel conductivity enhancement mechanism in amorphous 0.33 LiI+0.67 Li3PS4 glasses during a single annealing step at 180°C. The combination of electrochemical impedance, 7Li NMR, and positron-annihilation lifetime spectroscopy gives indication for an annealing-induced formation of monovacancies in the bulk amorphous phase, which act as stepping stones for fast Li+ ion transport. The maximum conductivity achieved after annealing was 6.5 mS.cm-1, the highest value observed so far for amorphous thiophosphate-based electrolytes.