Nonparametric estimation of abrupt changes in a regression function involves choosing smoothing (bandwidth) parameters. The performance of estimation procedures depends heavily on this choice. So far, little attention has been paid to the crucial issue of choosing appropriate bandwidth parameters in practice. In this article we propose a bootstrap procedure for selecting the bandwidth parameters in a nonparametric two-step estimation method. This method results in a fully data-driven procedure for estimating a finite (but possibly unknown) number of changepoints in a regression function. We evaluate the performance of the data-driven procedure via a simulation study, which reveals that the fully automatic procedure performs quite well. As an illustration, we apply the procedure to some real data.