High-statistics differential cross sections for the reactions gamma p -> p eta and gamma p -> p eta-prime have been measured using the CLAS at Jefferson Lab for center-of-mass energies from near threshold up to 2.84 GeV. The eta-prime results are the most precise to date and provide the largest energy and angular coverage. The eta measurements extend the energy range of the worlds large-angle results by approximately 300 MeV. These new data, in particular the eta-prime measurements, are likely to help constrain the analyses being performed to search for new baryon resonance states.