In order to be able to treat mobile tumours with active, scanned proton therapy, adequate motion mitigation techniques have to be applied. Re-scanning is such an approach, where the interplay effect between tumour motion and treatment delivery is statistically smeared out. Different re-scanning methods have been used for the irradiation of a spherical target volume and motion amplitudes of up to 10 mm. The resulting dose distributions have been captured in two dimensions by imaging a scintillating screen at the iso-centre for different motion starting phases. Dose inhomogeneity increased approximately linearly with motion amplitude, while the influence of motion period and direction was small. Re-scanning the whole target volume reduced the interplay effect more than re-scanning only the iso-energy layers. Even for 10 mm motion amplitude, no hot or cold spots were seen for 10 re-scans of the whole volume. A fast energy change and fast beam scanning is vital for this kind of re-scanning, as available on Gantry 2 at the Paul Scherrer Institute. For larger motion amplitudes, re-scanning should be combined with gating, breath-hold or tracking to reduce the internal target volume.