  In the setting of the integers, Granville, Harper and Soundararajan showed
that the upper bound in Hal\'{a}sz's Theorem can be improved for smoothly
supported functions. We derive the analogous result for Hal\'{a}sz's Theorem in
$\mathbb{F}_q[t]$, and then consider the converse question of when the general
upper bound in this version of Hal\'{a}sz's Theorem is actually attained.
