Na-ion batteries provide one of the most promising alternatives for Li-ion batteries due to the high abundance and low cost of Na. The strongly electropositive character of Na enables almost comparable cell potentials. Here we show that by lowering the cutoff voltage from 0.3 to 0 V vs Na/Na+ the capacity of the Na2Ti6O13 negative electrode material can be enhanced from 49.5 mAh/g (Na2+1Ti6O13) to a promising 196 mAh/g (Na2+4Ti6O13) for at least 10 cycles, after which it gradually reduces. To understand the structural changes in situ X-ray diffraction is performed and compared with density functional theory calculations. A consistent picture of the evolution in lattice parameters and Na-ion positions is presented. The results show that Na-ion intercalation in the Na2+xTi6O13 host structure is limited to Na2+2Ti6O13 and proceeds through a solid solution reaction. Only small changes in lattice parameters promote that the insertion reaction is highly reversible. Further increasing the Na composition below 0.3 V appears to lead to loss in crystallinity, which in combination with solid electrolyte interface formation is suggested to be the origin of the gradually reducing reversible capacity.