There is a considerable sub-literature, stretching back over 35 years, addressed to the question: Precisely which general terms ought to be classified as rigid designators? More fundamentally: What should we take the criterion for rigidity to be, for general terms? The aim of this paper is to give new grounds for the old view that if a general term designates the same kind in all possible worlds, then it should be classified as a rigid designator. The new grounds in question (...) have to do with excavating the connection between rigid designation and semantic structure. Other original contributions of the present work consist in developing responses to some objections to this approach to rigid designation. (shrink)