We show that every nuclear, O_\infty-stable *-homomorphism with a separable, exact domain has nuclear dimension at most 1. In particular, separable, nuclear, O_\infty-stable C*-algebras have nuclear dimension 1. We also characterise when O_\infty-stable C*-algebras have finite decomposition rank in terms of quasidiagonality and primitive-ideal structure. This is joint work with Joan Bosa, Aidan Sims, and Stuart White.