  Representations of small quantum groups $u_q({\mathfrak{g}})$ at a root of
unity and their extensions provide interesting tensor categories, that appear
in different areas of algebra and mathematical physics. There is an ansatz by
Lusztig to endow these categories with the structure of a braided tensor
category. In this article we determine all solutions to this ansatz that lead
to a non-degenerate braiding. Particularly interesting are cases where the
order of $q$ has common divisors with root lengths. In this way we produce
familiar and unfamiliar series of (non-semisimple) modular tensor categories.
In the degenerate cases we determine the group of so-called transparent objects
for further use.
