  We compare our upper bounds on the exponential growth constant
$\phi(\Lambda)$ characterizing the asymptotic behavior of spanning forests on
Archimedean lattices $\Lambda$ with recently derived upper bounds. Our upper
bounds on $\phi(\Lambda)$, which are very close to the respective values of
$\phi(\Lambda)$ that we have calculated, are shown to be significantly better
for these lattices than the new upper bounds.
