  The account of the Poisson-Lie T-duality is presented for the case when the
action of the duality group on a target is not free. At the same time a
generalization of the picture is given when the duality group does not even act
on $\si$-model targets but only on their phase spaces. The outcome is a huge
class of dualizable targets generically having no local isometries or
Poisson-Lie symmetries whatsoever.
