Reversible electrochemical intercalation of Li into the Li1-xTiyV1-yS2 dichalcogenides, which was frustrated in the 1970s by the use of 1 M LiClO4 in propylene carbonate as the electrolyte, is reinvestigated with 1 M LiPF6 in ethylene carbonate:diethyl carbonate (1:1). The choice of the electrolyte allows full electrochemical cycling between MS2 and LiMS2 (M=V or Ti0.3V0.7). The as-prepared LizMS2 (z approximate to 0.9) samples were fully lithiated after the first discharge, and from a subsequent charge of LiVS2 to VS2, the room-temperature solubility limits of the parent 3S phase, the Li-rich hexagonal phase, the intermediate alpha and beta phases, and the hexagonal Li-poor hexagonal phase have been determined. Introduction of Ti in LiTi0.3V0.7S2 remarkably improves the capacity at high cycling rates and increases the voltage by about 0.2 V.