The annual cycle of temperature and precipitation changes as projected by climate models is of fundamental interest in climate impact studies. Its estimation, however, is impaired by natural variability. Using a simple form of the delta change method, we show that on regional scales relevant for hydrological impact models, the projected changes in the annual cycle are prone to sampling artefacts. For precipitation at station locations, these artefacts may have amplitudes that are comparable to the climate change signal itself. Therefore, the annual cycle of the climate change signal should be filtered when generating climate change scenarios. We test a spectral smoothing method to remove the artificial fluctuations. Comparison against moving monthly averages shows that sampling artefacts in the climate change signal can successfully be removed by spectral smoothing. The method is tested at Swiss climate stations and applied to regional climate model output of the ENSEMBLES project. The spectral method performs well, except in cases with a strong annual cycle and large relative precipitation changes.