Ghost-free massive gravity models generically have a strong coupling scale of Λ3 = (MPlm2)1/3. However, for one of these models—minimal massive gravity—it is not clear what this scale is in the subset of solutions with vanishing vector modes, since there are then no interactions at the scale Λ3. We show that there are always scalar-tensor interactions at a scale arbitrarily close to Λ3 around the Minkowski vacuum solution. This explicitly confirms and completes previous research establishing that Λ3 effectively is the maximal strong coupling scale for all ghost-free (de Rham, Gabadadze, Tolley) massive gravity models (on Minkowski). In the process, we also revisit and clarify the construction of generic Lorentz-invariant massive gravity models, explicitly constructing an improved nonredundant expansion for these models.