  We show that separable, simple, unital C*-algebras with finite decomposition
rank absorb the Jiang-Su algebra Z tensorially. This has a number of
consequences for Elliott's program to classify nuclear C*-algebras by their
K-theory data. In particular, it completes the classification of C*-algebras
associated to uniquely ergodic, smooth, minimal dynamical systems by their
ordered K-groups.
