  Lorentz-invariant massive gravity is usually associated with a strong
coupling scale $\Lambda_3$. By including non-trivial effects from the
Stueckelberg modes, we show that about these vacua, one can push the strong
coupling scale to higher values and evade the linear vDVZ-discontinuity. For
generic parameters of the theory and generic vacua for the Stueckelberg fields,
the $\Lambda_2$-decoupling limit of the theory is well-behaved and free of any
ghost or gradient-like instabilities. We also discuss the implications for
nonlinear sigma models with Lorentzian target spaces.
