  We develop a method for proving sup-norm and H\"older estimates for
$\overline{\partial}$ on wide class of finite type pseudoconvex domains in
$\mathbb{C}^n$. A fundamental obstruction to proving sup-norm estimates is the
possibility of singular complex curves with exceptionally high order of contact
with the boundary. Our method handles this problem, and in $\mathbb{C}^3$, we
prove sup-norm and H\"older estimates for all bounded, pseudoconvex domains
with real-analytic boundary.
