  We consider general theories of a massive spin-2 particle $h_{\mu\nu}$ on a
Minkowski background. A decomposition of $h_{\mu\nu}$ in terms of helicity
eigenstates allows us to directly test whether any given theory possesses a
consistent description as a massive spin-2 representation of the Poincar\'e
group. We demonstrate (i) that any nonlinear theory with an Einsteinian
derivative structure either contains ghosts or does not describe a weakly
coupled spin-2 and (ii) that there exists a two-parameter family of
non-Einsteinian cubic self-interactions which constitute a ghost-free massive
spin-2 theory.
