  We provide a complete list of two- and three-component Poisson structures of
hydrodynamic type with degenerate metric, and study their homogeneous
deformations. In the non-degenerate case any such deformation is trivial, that
is, can be obtained via Miura transformation. We demonstrate that in the
degenerate case this class of deformations is non-trivial, and depends on a
certain number of arbitrary functions. This shows that the second
Poisson-Lichnerowicz cohomology group does not vanish.
