  The global contribution of unresolved gamma-ray point sources to the
extragalactic gamma-ray background has been recently measured down to gamma-ray
fluxes lower than those reached with standard source detection techniques, and
by employing the statistical properties of the observed gamma-ray counts. We
investigate and exploit the complementarity of the information brought by the
one-point statistics of photon counts (using more than 10 years of Fermi-LAT
data) and by the recent measurement of the angular power spectrum of the
unresolved gamma-ray background (based on 8 years of Fermi-LAT data). We
determine, under the assumption that the source-count distribution of the
brightest unresolved objects is dominated by blazars, their gamma-ray
luminosity function and spectral energy distribution down to fluxes almost two
orders of magnitude smaller than the threshold for detecting resolved sources.
The different approaches provide consistent predictions for the gamma-ray
luminosity function of blazars, and they show a significant complementarity.
