We tackle two different problems of text categorization (TC), namely feature selection and classifier induction. Feature selection (FS) refers to the activity of selecting, from the set of r distinct features (i.e. words) occurring in the collection, the subset of r′ ≪ r features that are most useful for compactly representing the meaning of the documents. We propose a novel FS technique, based on a simplified variant of the X ² statistics. Classifier induction refers instead to the problem of auto- matically building a text classifier by learning from a set of documents pre-classified under the categories of interest. We propose a novel variant, based on the exploitation of negative evidence, of the well-known k-NN method. We report the results of systematic experimentation of these two methods performed on the standard Reuters-21578 benchmark.