 The paradigm example of non-rigid designators, since the work of of Kripke, has been definite descriptions like ‘the brightest non-lunar object in the evening sky’. However, some definite descriptions, such as ‘the successor of 2’, are rigid designators; their rigidity seems to arise in virtue of facts about metaphysical reality, in this case, the necessity of mathematical facts, rather than facts about the semantic properties of expressions. Such definite descriptions are therefore “de facto” rigid designators. The Russellian view that definite descriptions are quantified expressions is also widely held. Since it is natural to think of rigidity but not, in view of Russell, to think of definite descriptions in connection with singularity, the question dawns of how to think about rigidity with categories of expressions other than singular terms. This broad topic, which surfaces in other connections too, has received much discussion in recent years. 