  We study the holomorphic extendibility of $\text{Op}(p)u$, when $p$ is an
analytic symbol, and explicit information is available on the domains of
holomorphic extendibility of both $p$ and $u$. By a contour deformation
argument, we obtain a precise local estimate of the domain of holomorphy of
$\text{Op}(p)u$ in terms of the information on $p$ and $u$.
