  We develop the effective theory for perturbations around black holes with
scalar hair, in two directions. First, we show that the scalar-Gauss--Bonnet
theory, often used as an example exhibiting scalar black hole hair, can be
deformed by galileon operators leading to order unity changes to its
predictions. The effective theory for perturbations thus provides an efficient
framework for describing and constraining broad classes of scalar-tensor
theories, of which the addition of galileon operators is an example. Second, we
extend the effective theory to perturbations around an axisymmetric, slowly
rotating black hole, at linear order in the black hole spin. We also discuss
the inclusion of parity-breaking operators in the effective theory.
