  This article is the second installment in a series on the Berkovich
ramification locus for nonconstant rational functions f: P^1 -> P^1. Here we
show the ramification locus of f is contained in a strong tubular neighborhood
of finite radius around the connected hull of the critical points if and only
if f is tamely ramified at all of its critical points. When the ground field
has characteristic zero, this bound may be chosen to depend only on the residue
characteristic. We give two applications to classical non-Archimedean analysis,
including a new version of Rolle's theorem for rational functions.
