This paper analyses the relation between the use of similarity in Memory-Based Learning and the notion of backed-off smoothing in statistical language modeling. We show that the two approaches are closely related, and we argue that feature weighting methods in the Memory-Based paradigm can offer the advantage of automatically specifying a suitable domain-specific hierarchy between most specific and most general conditioning information without the need for a large number of parameters. We report two applications of this approach: PP-attachment and POS-tagging. Our method achieves state-of-the-art performance in both domains, and allows the easy integration of diverse information sources, such as rich lexical representations.