  We completely characterize the spectrum of a weighted composition operator
$W_{\psi, \varphi}$ on $H^{2}(\mathbb{D})$ when $\varphi$ has Denjoy-Wolff
point $a$ with $0<|\varphi '(a)|< 1$, the iterates, $\varphi_{n}$, converge
uniformly to $a$, and $\psi$ is in $H^{\infty}(\mathbb{D})$ and continuous at
$a$. We also give bounds and some computations when $|a|=1$ and $\varphi
'(a)=1$ and, in addition, show that these symbols include all linear fractional
$\varphi$ that are hyperbolic and parabolic non-automorphisms. Finally, we use
these results to eliminate possible weights $\psi$ so that $W_{\psi, \varphi}$
is seminormal.
