Rank-sets of indecomposable modules over one-dimensional rings

Let RR be a one-dimensional, reduced Noetherian ring with finite normalization, and suppose there exists a positive integer NRNR such that, for every indecomposable finitely generated torsion-free RR-module MM and every minimal prime ideal PP of RR, the dimension of MPMP, as a vector space over the localization RPRP (a field), is less than or equal to NRNR. For a finitely generated torsion-free RR-module MM, we call the set of all such vector-space dimensions the rank-set   of MM. What subsets of the integers arise as rank-sets of indecomposable finitely generated torsion-free RR-modules? In this article, we give more information on rank-sets of indecomposable modules, to supplement previous work concerning this question. In particular we provide examples having as rank-sets those intervals of consecutive integers that are not ruled out by an earlier article of Arnavut, Luckas and Wiegand. We also show that certain non-consecutive rank-sets never arise.