An attempt to use the Gabriel and Relative Neighbourhood graphs for editing the Nearest Neighbour rule is presented, along with some extensions to apply editing and condensing in a combined way. Experiments on synthetic as well as real databases have been carried out in order to investigate the classification accuracy of the edited and edited-condensed sets using the approaches presented and other traditional methods. Results show that the schemes proposed outperform the classical editing algorithms, and are comparable to Hart's condensing.