  The implementation of tensor sources in Chiral Lagrangians allows the
computation of Green functions and form factors involving tensor currents, that
is, quark bilinears of the form \bar{q}_i\sigma^{\mu\nu}q_j. Whereas only four
new terms show up at O(p^4), we find around a hundred of them at O(p^6). So it
becomes essential to ensure that this set o operators is indeed minimal and
non-redundant (i.e., it is a basis). We discuss two phenomenological
applications in the context of vector meson resonances and the radiative pion
decay.
