  We continue the study of the maximally clustered elements for simply laced
Coxeter groups which were recently introduced by Losonczy. Such elements
include as a special case the freely braided elements of Losonczy and the
author, which in turn constitute a superset of the $iji$-avoiding elements of
Fan. Our main result is to classify the MC-finite Coxeter groups, namely those
Coxeter groups having finitely many maximally clustered elements. Remarkably,
any simply laced Coxeter group having finitely many $iji$-avoiding elements
also turns out to be MC-finite.
