  We test a data-driven approach based on QCD factorization for charmless
three-body $B$-decays by confronting it to measurements of CP violation in $B^-
\to \pi^- \pi^+ \pi^-$. While some of the needed non-perturbative objects can
be directly extracted from data, some others can, so far, only be modelled.
Although this approach is currently model dependent, we comment on the
perspectives to reduce this model dependence. While our model naturally
accommodates the gross features of the Dalitz distribution, it cannot
quantitatively explain the details seen in the current experimental data on
local CP asymmetries. We comment on possible refinements of our simple model
and conclude by briefly discussing a possible extension of the model to large
invariant masses, where large local CP asymmetries have been measured.
