We report progress on the \NL vs \UL problem. [-] We show unconditionally
that the complexity class $\ReachFewL\subseteq\UL$. This improves on the
earlier known upper bound $\ReachFewL \subseteq \FewL$. [-] We investigate the
complexity of min-uniqueness - a central notion in studying the \NL vs \UL
problem. We show that min-uniqueness is necessary and sufficient for showing
$\NL =\UL$. We revisit the class $\OptL[\log n]$ and show that {\sc
ShortestPathLength} - computing the length of the shortest path in a DAG, is
complete for $\OptL[\log n]$.