  We look for 3-dimensional Poisson-Lie dualizable sigma models that satisfy
the vanishing beta-function equations with constant dilaton field. Using the
Poisson-Lie T-plurality we then construct 3-dimensional sigma models that
correspond to various decompositions of Drinfeld double. Models with nontrivial
dilaton field may appear. It turns out that for ``traceless'' dual algebras
they satisfy the vanishing beta-function equations as well.
  In certain cases the dilaton cannot be defined in some of the dual models. We
provide an explanation why this happens and give criteria predicting when it
happens.
