  We determine the \emph{exact} minimum $\ell$-degree threshold for perfect
matchings in $k$-uniform hypergraphs when the corresponding threshold for
perfect fractional matchings is significantly less than $\frac{1}{2}
\binom{n}{k- \ell}$. This extends our previous results that determine the
minimum $\ell$-degree thresholds for perfect matchings in $k$-uniform
hypergraphs for all $\ell\ge k/2$ and provides two new (exact) thresholds:
$(k,\ell)=(5,2)$ and $(7,3)$.
