For a connected graph $G$, the Wiener index $W$ and the Harary index $H$ are defined as $W=\sum _{u,v}d(u,v)$ and $H=\sum _{u,v}1/d(u,v)$, respectively. Recently, in MATCH 91 (2024) 287, the extremal value of the product $W\cdot H$ was studied and shown that $W\cdot H\ge (\genfrac{}{}{0ex}{}{n}{2})$, with equality for the complete graph. We now extend this result to all graphs of order $n$ and size $m$, and characterize the respective species with minimum $W\cdot H$-value.