2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125750We 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.Approximately 18 pages, AMSTeX. One non-essential figureCombinatoricsGroup Theory20F55text