  Let $G$ be a $t$-tough graph on $n\ge 3$ vertices for some $t>0$. It was
shown by Bauer et al. in 1995 that if the minimum degree of $G$ is greater than
$\frac{n}{t+1}-1$, then $G$ is hamiltonian. In terms of Ore-type hamiltonicity
conditions, the problem was only studied when $t$ is between 1 and 2, and
recently the author proved a general result. The result states that if the
degree sum of any two nonadjacent vertices of $G$ is greater than
$\frac{2n}{t+1}+t-2$, then $G$ is hamiltonian. It was conjectured in the same
paper that the ``$+t$" in the bound $\frac{2n}{t+1}+t-2$ can be removed. Here
we confirm the conjecture. The result generalizes the result by Bauer,
Broersma, van den Heuvel, and Veldman. Furthermore, we characterize all
$t$-tough graphs $G$ on $n\ge 3$ vertices for which $\sigma_2(G) =
\frac{2n}{t+1}-2$ but $G$ is non-hamiltonian.
