  We continue our study of ends of non-compact manifolds, with a focus on the
inward tameness condition. For manifolds with compact boundary, inward
tameness, has significant implications. For example, such manifolds have stable
homology at infinity in all dimensions. We show that these manifolds have
'almost perfectly semistable' fundamental group at each end. That observation
leads to further analysis of group theoretic conditions at infinity, and to the
notion of a 'near pseudo-collar' structure. We obtain a complete
characterization of n-manifolds (n>5) admitting such a structure, thereby
generalizing earlier work. We also construct examples illustrating the
necessity and usefulness of new conditions introduced here. Variations on the
notion of a perfect group, with corresponding versions of the Quillen Plus
Construction, form an underlying theme.
