Lorentz-invariant massive gravity is usually associated with a strong coupling
scale Λ3. By including non-trivial effects from the St¨uckelberg 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
St¨uckelberg fields, the Λ2-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.