Two criteria for rigid designation are distinguished; one according to which 'e' is rigid if 'e might not have been e' is false and the other according to which 'e' is rigid if it designates the same thing in all possible worlds in which it designates anything at all. Such criteria are not equivalent since 'x could not but be f' is not entailed by 'nothing other than x could be f'. I illustrate the latter lack of entailment.