The structures of Li3V6O13 and Li(3+delta)V6O13, delta approximately 0.3, have been determined by single-crystal X-ray diffraction. Both compounds have the space group C2/m, with very similar cell parameters. In Li3V6O13, the Li atoms are found in the Wyckoff positions 4(i) and 2(b) with multiplicities of four and two, respectively. Since Li3V6O13 exhibits no superstructure reflections, it is concluded that Li3V6O13 contains one disordered lithium ion in an otherwise ordered centrosymmetric structure. On inserting more lithium into the structure, the Li(3+delta)V6O13 phase is formed with the homogeneity range 0 < delta < 1. It is concluded that the site for the extra inserted lithium ion is closely coupled to the position of the disordered lithium ion in Li3V6O13. A mechanism for this behaviour and for the further formation of the Li6V6O13 end-phase in the LixV6O13 system is proposed.