  Results are presented concerning the following question: If M is a
finitely-generated module with finite local cohomologies over a Noetherian
local ring (A, m), does there exist an integer n such that every parameter
ideal for M contained in m^n has the same index of reducibility? We show that
the answer is yes if M has dimension 1 or if M has dimension 2 and positive
depth. This research is closely related to work of Goto-Suzuki and
Goto-Sakurai; Goto-Sakurai have supplied an answer of yes in case M is
Buchsbaum.
