Trivial centralizers for codimension-one attractors

We show that if Lambda is a codimension-one hyperbolic attractor for a C(r) diffeomorphism f, where 2 <= r <= infinity, and f is not Anosov, then there is a neighborhood of f in Diff(r)(M) and an open and dense set of such that any g is an element of has a trivial centralizer on the basin of attraction for Lambda.