  In this article we consider a certain distinguished set $U(\Omega,m)
\subseteq \{1,2,\ldots,2g+1,\infty\}$ that can be attached to a marked
hyperelliptic curve of genus $g$ equipped with a small period matrix $\Omega$
for its polarized Jacobian. We show that as $\Omega$ and the marking $m$ vary,
this set ranges over all possibilities prescribed by an argument of Poor.
