  It is shown that perturbations around backgrounds with one non-homogeneous
dimension, namely of co-homogeneity 1, can be canonically simplified, a
property that is shown to hold to any order in perturbation theory. Recalling
that the problem naturally reduces to 1d, a procedure is described whereby for
each gauge function in 1d two 1d fields are eliminated from the action - one is
gauge and can be eliminated without a constraint and the other is auxiliary.
These results generalize the results of hep-th/0609001 from linear to
non-linear perturbations and they unify two cases of physical interest:
cosmological perturbations and perturbations to static spherically symmetric
backgrounds. An application to black strings is discussed in some detail.
