Though it is often claimed that some general terms are rigid designators, it has turned out to be difficult to give a satisfying definition that (1) avoids making all general terms rigid (the overgeneralization problem), and (2) even if a non-rigid reading is available, makes that non-rigid reading matter (the trivialization problem). Several authors have attempted to develop examples that meet the trivialization challenge, with Martí and Martínez-Fernández providing what is, perhaps, the most convincing strategy. I show that the type of example Martí and Martínez-Fernández offer nevertheless fails to meet the trivialization challenge and, accordingly, that we should still have serious doubts about whether continuing the search for a non-trivial definition of general term rigidity would be fruitful.