  Let $\mathbb{C}_v$ be a characteristic zero algebraically closed field which
is complete with respect to a non-Archimedean absolute value. We provide a
necessary and sufficient condition for two tame polynomials in
$\mathbb{C}_v[z]$ of degree $d \ge 2$ to be analytically conjugate on their
basin of infinity. In the space of monic centered polynomials, tame polynomials
with all their critical points in the basin of infinity form the tame shift
locus. We show that a tame map $f\in\mathbb{C}_v[z]$ is in the closure of the
tame shift locus if and only if the Fatou set of $f$ coincides with the basin
of infinity.
