I will discuss two properties for C*-algebras which are both considered (particularly to those working on the classification programme) to be measures of regularity or ”good behaviour”: finite decomposition rank (a noncommutative version of finite topological dimension) and Z-stability (tensorial absorption of a strongly self absorbing C*-algebra). What is known and conjectured about classification of C*-algebras suggests that these properties should be equivalent, for the class of simple, separable, finite, nonelementary, nuclear C*-algebras; in fact, this constitutes a part of the somewhat grander Toms-Winter conjecture. I will discuss this conjecture, including evidence that it is true, without even requiring the hypothesis of simplicity.