Many learning algorithms make an implicit assumption that all the attributes present in the data are relevant to a learning task. However, several studies have demonstrated that this assumption rarely holds; for many supervised learning algorithms, the inclusion of irrelevant or redundant attributes can result in a degradation in classification accuracy. While a variety of different methods for dimensionality reduction exist, many of these are only appropriate for datasets which contain a small number of attributes (e.g. < 20). This paper presents an alternative approach to dimensionality reduction, and demonstrates how it can be combined with a Nearest Neighbour learning algorithm. We present an empirical evaluation of this approach, and contrast its performance with two related techniques; a Monte-Carlo wrapper and an Information Gain-based filter approach.