  In this paper we deal with polarizations on a nodal curve $C$ with smooth
components. Our aim is to study and characterize a class of polarizations,
which we call "good", for which depth one sheaves on $C$ reflect some
properties that hold for vector bundles on smooth curves. We will concentrate,
in particular, on the relation between the $\underline{w}$-stability of
$\mathcal{O}_C$ and the goodness of $\underline{w}$. We prove that these two
concepts agree when $C$ is of compact type and we conjecture that the same
should hold for all nodal curves.
