This paper addresses some issues concerning the definition and measurement of inflation persistence in the context of the univariate approach. First, it is stressed that any estimate of persistence should be seen as conditional on the given assumption for the long run level of inflation and that such long run level should be allowed to vary through time. Second, a non-parametric measure of persistence is suggested which explores the relation between persistence and mean reversion. Third, inflation persistence in the U.S. and the Euro Area is re-evaluated allowing for a time varying mean and it is found that estimates of persistence crucially depend on the function used to proxy the mean of inflation. In particular, the widespread belief that inflation has been more persistent in the sixties and seventies than in the last twenty years is shown to obtain only for the U.S. and for the special case of a constant mean.