  There is mounting evidence that the IceCube findings cannot be described
simply invoking a single power-law spectrum for cosmic neutrinos. We discuss
which are the minimal modifications of the spectrum that are required by the
existing observations and we obtain a universal cosmic neutrino spectrum, i.e.
valid for all neutrino flavors. Our approach to such task can be outlined in
three points: 1) we rely on the throughgoing muon analysis above 200 TeV and on
the high-energy starting events (HESE) analysis below this energy, requiring
the continuity of the spectrum; 2) we assume that cosmic neutrinos are subject
to three-flavor neutrino oscillations in vacuum; 3) we make no assumption on
the astrophysical mechanism of production, except for no tau neutrino component
at the source. We test our model using the information provided by HESE
shower-like events and by the lack of double pulses and resonant events. We
find that a two power-law spectrum is compatible with all observations. The
model agrees with the standard picture of pion decay as a source of neutrinos,
and indicates a slight preference for a pgamma mechanism of production. We
discuss the tension between the HESE and the throughgoing muons datasets around
few tens TeV, focussing on the angular distributions of the spectra. The
expected number of smoking-gun signatures of nu-tau induced events (referred to
as double pulses) is quantified: in the baseline model we predict 0.65 double
pulse events in 5.7 years. Uncertainties in the predictions are quantified.
