  We investigate the importance of choosing good tetrads for the study of the
field equations of $f(T)$ gravity. It is well known that this theory is not
invariant under local Lorentz transformations, and therefore the choice of
tetrad plays a crucial role in such models. Different tetrads will lead to
different field equations which in turn have different solutions. We suggest to
speak of a good tetrad if it imposes no restrictions on the form of $f(T)$.
Employing local rotations, we construct good tetrads in the context of
homogeneity and isotropy, and spherical symmetry, where we show how to find
Schwarzschild-de Sitter solutions in vacuum. Our principal approach should be
applicable to other symmetries as well.
