There is increasing evidence that the presence of mobile ions in perovskite solar cells can cause a current-voltage curve hysteresis. However, it is still subject of ongoing debates how exactly mobile ions influence the device operation. We use drift-diffusion simulations incorporating mobile ions to describe IV-curves of preconditioned methylammonium lead iodide perovskite solar cells and compare them with experimental results. Our simulation results show that the hysteresis depends on the extent of surface recombination and on the diffusion length of charge carriers. We provide a detailed explanation for the reduced hysteresis of perovskite solar cells with high power conversion efficiencies. We find that in high-efficiency solar cells ion migration is still present, but does not cause a hysteresis effect. In these devices charge extraction is mainly driven by diffusion of free electrons and holes.