 Rigidity’s work is compatible with descriptivism. Although some philosophers seem to have the impression that the important work that rigidity performs is to refute descriptivism, this seems to be a mistake. A related impression is that the important work that Kripke performs is to refute descriptivism: the rigidity of terms and more just falls out of anti-descriptivism, so anti-descriptivism is what really matters at bottom (see below,  §4.2).  But there are strong reasons to resist this assessment of rigidity’s importance or lack thereof, too.