  We systematically explore ultraviolet complete models where flavour
hierarchies emerge, via approximate accidental symmetries, from an underlying
flavour non-universal gauge structure. In order to avoid large quantum
corrections to the Higgs mass, the first layer of non-universality, separating
the third generation from the light ones, should appear at the TeV scale. A
handful of models survive the combined criteria of naturalness in the Higgs
sector, having a semi-simple embedding in the UV, and compatibility with
experiments. They all feature quark-lepton unification in the third family and
a non-universal electroweak sector. We study in more detail the interesting
option of having colour and hypercharge non-universal at the TeV scale, while
$\mathrm{SU}(2)_L$ remains universal up to high scales: this gauge structure
turns to be very efficient in secluding the Higgs from large quantum
corrections and predicting flavour mixing consistent with data. In all cases,
these models imply a rich TeV-scale phenomenology within the reach of
near-future direct and indirect experimental searches.
