We prove that soft theorems uniquely fix tree-level scattering amplitudes in a wide range of massless theories, including Yang-Mills, gravity, the nonlinear sigma model, Dirac-Born-Infeld, dilaton effective theories, extended theories like the NLSM⊕ϕ^{3} (nonlinear sigma model ϕ^{3}), as well as some higher derivative corrections to these theories. We conjecture the same is true even when imposing more general soft behavior, simply by assuming the existence of soft operators, or by imposing gauge invariance or the Adler zero only up to a finite order in soft expansions. Besides reproducing known amplitudes, this analysis reveals a new higher order correction to the NLSM and two interesting facts: the subleading theorem for the dilaton, and the subsubleading theorem for DBI follow automatically from the more leading theorems. These results provide motivation that asymptotic symmetries contain enough information to fully fix a holographic S matrix.