The notion of rigid designation has become a widely accepted, if not unproblematic one in connection with the function of proper names. In this paper, some less ‘rigid’ uses of proper names will be looked at. Proprial lemmas – that is to say, words that function prototypically as proper names – may sometimes function as common nouns rather than as proper names, for instance in "There are two Johns in my class". On the other hand, proprial lemmas may also receive some amount of modification without acquiring the ‘categorizing’ function of common nouns, but rather retaining the rigid, unique designation associated with proper names, as in "An angry Blair left the meeting yesterday". The aim of the present paper is twofold: (i) to offer a workable terminological and conceptual framework to deal with these different constructional schemata involving proprial lemmas, and (ii) to propose a tentative classification of both ‘restrictive’ and ‘non-restrictive’ modification of proprial lemmas into distinct subtypes. In the end, it is hoped, these endeavours may shed a new light on the nature and potential of proper names and proprial lemmas.