  We establish multiplicity results for geometrically distinct contractible
closed Reeb orbits of non-degenerate contact forms on a broad class of
prequantization bundles. The results hold under certain index requirements on
the contact form and are sharp for unit cotangent bundles of CROSS's. In
particular, we generalize and put in the symplectic-topological context a
theorem of Duan, Liu, Long, and Wang for the standard contact sphere. We also
prove similar results for non-hyperbolic contractible closed orbits and briefly
touch upon the multiplicity problem for degenerate forms. On the combinatorial
side of the question, we revisit and reprove the enhanced common jump theorem
of Duan, Long and Wang, and interpret it as an index recurrence result.
