  Let B be a unital C*-algebra, let A be a unital subalgebra, and let E be a
conditional expectation from B to A with index-finite type and a quasi-basis of
n elements. Then the topological stable rank satisfies \tsr (B) \leq \tsr (A) +
n - 1. As an application, we show that if a unital inclusion A \subset B of
C*-algebras has index-finite type and finite depth, and A is simple with stable
rank one and Property (SP), then B has cancellation. In particular, if A is a
simple unital C*-algebra with stable rank one and Property (SP), and a finite
group G acts on A, then the crossed product has cancellation. Separately, if
the group is the integers, we obtain cancellation under the additional
hypotheses that the group action is outer and is trivial on K_0 (A).
