Inflation persistence has been put forward as one of the potential reasons of divergence among euro area members. It has also been proposed that the new EU Member States (NMS) may struggle with even higher persistence due to convergence factors. We argue that persistence may not be as different between the two country groups as one might expect. However, this empirical result can only be obtained if the adequate estimation methods, reflecting the scope of the convergence process the NMS went through, are applied. We emphasize that a time-varying mean models suggest similar or lower inflation persistence for the NMS compared to euro area countries while more traditional parametric statistical measures assuming a constant mean deliver substantially higher persistence estimates for the NMS than for the euro area countries. This difference is due to frequent breaks in inflation time series in the NMS. Structural persistence measures show that backward-looking behavior may be a more important component in explaining inflation dynamics in the NMS than in the euro area countries.