Photon counts statistics have been shown to provide a sensitive tool for characterizing gamma-ray source populations and the composition of the gamma-ray sky. In this contribution, we extend the use of the standard 1-point probability distribution function (1pPDF) to decompose the high-latitude gamma-ray flux observed with Fermi-LAT into emission from point sources, Galactic foreground, and diffuse isotropic background. To that aim, we perform an energy-binned analysis of the gamma-ray data between 1 and 171 GeV. We measure the source-count distribution $\mathrm{d}N/\mathrm{d}S$ in several energy bins, and we demonstrate that our results extend current measurements driven by point-source catalogs to so far undetected source contributions. The source-count distribution as a function of flux is found to be compatible with a broken power law. Upper limits on further possible breaks as well as the angular power of unresolved sources are derived. We discuss the composition of the gamma-ray sky and future prospects and capabilities of the 1pPDF method.