The reaction $\gamma N \rightarrow \eta N$ is studied in the high-energy regime (with photon lab energies $E^{lab}_7 \gamma \gt 4 $   GeV ) using information from the resonance region through the use of finite-energy sum rules. We illustrate how analyticity allows one to map the $t$ dependence of the unknown Regge residue functions. We provide predictions for the energy dependence of the beam asymmetry at high energies.