This paper identifies a class of homology
n-spheres that are codimension-
(n+1) shape m
simpl-fibrators but are not shape m
simpl-fibrators (a concept introduced by the author). Actually, the main result (Theorem 4.4) provides more general description of
n-manifolds that are codimension-
(k+1) shape m
simpl-fibrators for
2
k
n. It establishes that any closed orientable PL
n-manifold homotopically determined by
π1, with Hopfian fundamental group and
Hi(N)=0 for
0<i<k
n, where
k
2, is a codimension-
(k+1) shape m
simpl-fibrator.