We present a novel method that aims at providing a more stable selection of feature subsets when variations in the training process occur. This is accomplished by using an instance-weighting process -assigning different importances to instances as a preprocessing step to a feature weighting method that is independent of the learner, and then making good use of both sets of computed weigths in a standard Nearest-Neighbours classifier. We report extensive experimentation in well-known benchmarking datasets as well as some challenging microarray gene expression problems. Our results show increases in stability for most subset sizes and most problems, without compromising prediction accuracy.