  Suppose that a finite solvable group $G$ acts faithfully, irreducibly and
quasi-primitively on a finite vector space $V$. Then $G$ has a uniquely
determined normal subgroup $E$ which is a direct product of extraspecial
$p$-groups for various $p$ and we denote $e=\sqrt{|E/\bZ(E)|}$. We prove that
when $e=2,3,4,8,9,16$, $G$ will have regular orbits on $V$ when the
corresponding vector space is not too small.
