We study uniform perturbations of crossed product C * -algebras by amenable groups. Given a unital inclusion of C * -algebras C ⊆ D and sufficiently close separable intermediate C * -subalgebras A, B for this inclusion with a conditional expectation from D onto B, if A = C ⋊ G with G discrete amenable, then A and B are isomorphic. Furthermore, if C ⊆ D is irreducible, then A = B.