It was shown by Bessis that the Hurwitz action is transitive on minimum-length reflection factorizations of a Coxeter element in a finite Coxeter group. In this talk, I'll explain how to extend Bessis's result to longer factorizations, showing that two factorizations of a Coxeter element into an arbitrary number of reflections lie in the same orbit under the Hurwitz action if and only if they use the same multiset of conjugacy classes. The proof makes use of a surprising lemma about the acuteness structure of minimal dependent sets in root systems. This work is joint with Vic Reiner.