I will present a new method to characterize unresolved point sources (PSs), generalizing traditional template fits to account for non-Poissonian photon statistics. I will apply this method to Fermi gamma-ray data to characterize PS populations in the Inner Galaxy. I will show that in the energy range ~1.9 to ~11.9 GeV and within 10 degrees of the Galactic Center with |b| > 2 degrees, ~5-10% of the flux can be accounted for by a population of unresolved PSs, distributed consistently with the observed ~GeV gamma-ray excess in this region. The excess is fully absorbed by such a population, in preference to dark-matter annihilation. The inferred source population is dominated by near-threshold sources, which may be detectable in future searches. I will comment on ongoing work to identify members of this new source population using gamma ray data along with input from other wavelengths.