In so-called ‘Bracketing Paradoxes’, it seems to be necessary to assign two incompatible constituent structures to a single expression. The paper outlines empirical and conceptual difficulties with three main current approaches and discusses in detail the problem of ‘paradoxical’ expressions relating to people, such as transformational grammarian, theoretical linguist, serial composer, and Southern Dane. It is shown that such expressions can be formed productively by means of a process of analogical back-formation defined strictly over existing entries in the permanent lexicon, a novel type of productive word formation process.