  In this communication I analyze the problem of complete exceptionality of
wave propagation in a class of spin 2 field theories. I show that, under the
imposition of the good weak-field limit, only two Lagrangians are completely
exceptional. These are the linear Fierz Lagrangian, and a Born-Infeld-like
Lagrangian. As a byproduct, I reobtain the result that in a nonlinear theory,
spin 2 particles follow an effective metric that depends on the nonlinearities
of the Lagrangian.
