  We study generalized disformal transformations, including derivatives of the
metric, in the context of the Effective Field Theory of Inflation. All these
transformations do not change the late-time cosmological observables but change
the coefficients of the operators in the action: some couplings are effectively
redundant. At leading order in derivatives and up to cubic order in
perturbations, one has 6 free functions that can be used to set to zero 6 of
the 17 operators at this order. This is used to show that the tensor
three-point function cannot be modified at leading order in derivatives, while
the scalar-tensor-tensor correlator can only be modified by changing the scalar
dynamics. At higher order in derivatives there are transformations that do not
affect the Einstein-Hilbert action: one can find 6 additional transformations
that can be used to simplify the inflaton action, at least when the dynamics is
dominated by the lowest derivative terms. We also identify the leading
higher-derivative corrections to the tensor power spectrum and bispectrum.
