  We compute the asymptotics of the determinants of certain $n\times n$
Toeplitz + Hankel matrices $T_n(a)+H_n(b)$ as $n\to\infty$ with symbols of
Fisher-Hartwig type. More specifically we consider the case where $a$ has zeros
and poles and where $b$ is related to $a$ in specific ways. Previous results of
Deift, Its and Krasovsky dealt with the case where $a$ is even. We are
generalizing this in a mild way to certain non-even symbols.
