  We complete the study of the Poisson-Sigma model over Poisson-Lie groups.
Firstly, we solve the models with targets $G$ and $G^*$ (the dual group of the
Poisson-Lie group $G$) corresponding to a triangular $r$-matrix and show that
the model over $G^*$ is always equivalent to BF-theory. Then, given an
arbitrary $r$-matrix, we address the problem of finding D-branes preserving the
duality between the models. We identify a broad class of dual branes which are
subgroups of $G$ and $G^*$, but not necessarily Poisson-Lie subgroups. In
particular, they are not coisotropic submanifolds in the general case and what
is more, we show that by means of duality transformations one can go from
coisotropic to non-coisotropic branes. This fact makes clear that
non-coisotropic branes are natural boundary conditions for the Poisson-Sigma
model.
