The IceCube collaboration has discovered a new, cosmic component of high-energy neutrinos. Although neutrino oscillations suggest that the cosmic neutrino spectrum is almost the same for every neutrino flavor, the attempts to reconstruct it, based on different analyses, lead to different energy spectra below 100 TeV. In this work, we propose a phenomenological model that, assuming collisions between cosmic rays and hadrons as the production mechanism of high-energy neutrinos, yields quantitative expectations for each neutrino flavor. We discuss the detectability of the prompt component of the atmospheric neutrino spectrum, pointing out the most relevant dataset, which has to be muon-neutrino depleted and to cover the energy region 10 - 100 TeV. We argue that the prompt component can cause the spectral difference between the High-Energy-Starting-Event (HESE) and the through-going muon datasets. Finally, we point out the need for adopting a consistent model for the interpretation of the data, stressing that a separate treatment of the different datasets is, by converse, a suboptimal procedure.