Statistical methods for modelling extremes of stationary sequences have received much attention. The most common method is to model the rate and size of exceedances of some high constant threshold; the size of exceedances is modelled by using a generalized Pareto distribution. Frequently, data sets display non-stationarity; this is especially common in environmental applications. The ozone data set that is presented here is an example of such a data set. Surface level ozone levels display complex seasonal patterns and trends due to the mechanisms that are involved in ozone formation. The standard methods of modelling the extremes of a non-stationary process focus on retaining a constant threshold but using covariate models in the rate and generalized Pareto distribution parameters. We suggest an alternative approach that uses preprocessing methods to model the non-stationarity in the body of the process and then uses standard methods to model the extremes of the preprocessed data. We illustrate both the standard and the preprocessing methods by using a simulation study and a study of the ozone data. We suggest that the preprocessing method gives a model that better incorporates the underlying mechanisms that generate the process, produces a simpler and more efficient fit and allows easier computation.