  In this note we give applications of recent results coming mostly from the
third paper of this series. It is shown that the number of irreducible
characters in a $p$-block of a finite group with abelian defect group $D$ is
bounded by $|D|$ (Brauer's $k(B)$-Conjecture) provided $D$ has no large
elementary abelian direct summands. Moreover, we verify Brauer's
$k(B)$-Conjecture for all blocks with minimal non-abelian defect groups. This
extends previous results by various authors.
