  The minimal type-I seesaw framework with texture-zero Yukawa and mass
matrices inspired by Occam's razor is incompatible with normally-ordered
neutrino masses (currently preferred by data) when lepton mixing originates
solely from the neutrino sector. Moreover, the lightest right-handed neutrino
mass required to generate the observed baryon asymmetry of the Universe via
leptogenesis ($M_1 \sim 10^{14}$ GeV) is in conflict with vanilla scenarios for
Peccei-Quinn) axion dark matter where the reheating temperature of the Universe
is typically below $10^{12}$ GeV. In this work, we present a new Occam's razor
setup which overcomes these problems by including charged-lepton mixing
parametrized by a single angle, which is predicted to be very close to the
quark Cabibbo angle. Furthermore, the atmospheric mixing angle lies in the
second octant and the leptogenesis scale is lowered to $\sim 5.5\times 10^{10}$
GeV, lifting the tension with the axion dark-matter hypothesis.
