We report on the absence of the so-called fishtail or peak effect in the magnetisation curves of properly oxygenated high purity (5N) single crystals of YBa2Cu3O7−δ. As we recently reported [1] high pressure oxygenation procedures are suitable to produce a monotonous dependence of the critical current density with the magnetic field. In this article we report furthermore how to reversibly produce or remove this effect on the same crystal by proper oxygenation methods. Along with the high purity of the samples, — due to crystal growth in non reactive BaZrO3 crucibles —, this proves that at least in pure samples the fishtail effect is due to different oxygenation states and/or oxygen distributions. In less pure samples, however, other sources for this anomaly like metallic impurities can act as an additional source for the fishtail anomaly.