  We extend the Brauer-Siegel theorem to new families of number fields, both in
the classical setting of asymptotically bad families and in the more general
framework due to Tsfasman and Vl\u{a}du\c{t} of asymptotically exact families.
We introduce a notion of Galois complexity for extensions of number fields, and
show that the generalized Brauer-Siegel theorem, as conjectured by Tsfasman and
Vl\u{a}du\c{t}, holds for families in which the complexity does not grow too
fast. This allows to unify and extend all previously known results. The crucial
step in our work is the proof of a new version -- stated in terms of our Galois
complexity -- of a fundamental principle due to Stark descending exceptional
zeroes of zeta functions down to quadratic number fields. Among the hitherto
unknown cases we are able to treat are the families of number fields contained
in the solvable Galois closure of a given number field.
