Simple separable UCT C*-algebras can now be classified by simple invariants in the unital case, provided that the nuclear dimension is finite. Toms and Winter raise the question whether this might also be true assuming only Jiang-Su stability (a consequence of finite nuclear dimension). (This is known if there is a unique trace, or if the trace simplex is Bauer.) The subclass of Jiang-Su stable algebras with finite nuclear dimension exhausts the invariant, as can be seen from models, and so classifiability of the Jiang-Su stable class would settle the question, at least for algebras satisfying the UCT (which may be redundant).