A fast backward elimination algorithm is introduced based on a QR decomposition and Givens transformations to prune radial-basis-function networks. Nodes are sequentially removed using an increment of error variance criterion. The procedure is terminated by using a prediction risk criterion so as to obtain a model structure with good generalisation properties. The algorithm can be used to postprocess radial basis centres selected using a k-means routine and, in this mode, it provides a hybrid supervised centre selection approach.