While the nucleon excitation spectrum below 2 GeV is fairly well explored experimentally, little is known about the resonances above this mass. Since the number of relevant partial waves grows with energy, additional theoretical constraints are necessary to constrain the amplitudes. Dispersive approaches allow one to use high-energy data to constrain the low-energy models that aim at mapping the baryon spectrum. I illustrate how the dispersive approach of Finite-Energy Sum Rules can be used to do the inverse: predicting the scattering amplitudes at high energies based on low-energy models.